Galileo Galilei | Calendar (2023)

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Galileo Galilei

Dialogue Concerning the Two Main World Systems, 1632

Dialogue about the two great world systems

Galileo Galilei

TO THE DISCRETE READER

A few years ago a salutary edict was published in Rome which, to escape the dangerous tendencies of our time, imposed a timely silence on the Pythagorean belief that the earth was moving. reckless requests, but with not-so-well-informed passion. Complaints have been raised that advisers untrained in astronomical observations should not clip the wings of the thoughtful intellect with careless prohibitions.

Hearing such grumpy insolence, I could not hold back my speech. Fully informed of this prudent determination, I resolved to appear openly on the world's theater as a witness of the sober truth. I was in Rome then; I was not only received by the most distinguished prelates of this court, but received their applause; In fact, this decree was not published without prior notification to me. Therefore, in the present work, I propose to show foreign nations that in Italy, and especially in Rome, so much is understood about this subject as transalpine diligence could never have imagined. it was known that the Roman censorship was informed of everything and that from this climate not only dogmas for the good of the soul, but also brilliant discoveries for the joy of the spirit emerged.

To this end I have taken the Copernican side of the discourse, proceeding as a pure mathematical hypothesis and striving to present it as superior to the assumption of the earth as immobile - no, absolutely indeed, but against the arguments of some itinerant professors . (use 1) These men really don't even deserve the name because they don't walk around; content to worship the shadows, they philosophize not with due circumspection, but only because they have memorized a stream of misunderstood principles.

Three main titles are covered. First, I will try to show that all practical experiments on Earth are insufficient means of proving their mobility, being indifferently adaptable to a moving or resting Earth. I hope thereby to reveal many observations unknown to the ancients. Second, celestial phenomena are examined, which reinforce the Copernican hypothesis until it seems that it must absolutely triumph. Here new reflections are added that can be used to simplify astronomy, but not because of any necessity introduced by nature. Third, I will propose an ingenious speculation. I happened to say a long time ago that the unsolved problem of ocean tides might get some light by assuming the motion of the earth. This statement of mine, through word of mouth, found loving parents who adopted it as a child of their own ingenuity. Well, if ever a stranger, armed with our weapons, should accuse us of inattention to a matter of such importance, I thought it well to point out the probabilities that this would be the case, given that the earth is moving , could make plausible. .

I hope that from these reflections the world will see that if other nations have sailed more, we have not theorized less. It is not because we disregard the opinion of others that we succumb to the claim that the earth is immovable, and consider the opposite to be a mere mathematical whim, but (at least) for reasons which piety, religion, knowledge of omnipotence furnish to us , the divine nature and awareness of the limitations of the human mind, I found it more appropriate to explain these concepts in the form of dialogues that, no! limited to the strict observance of mathematical laws, they also leave room for excursions that are sometimes no less interesting than the main argument.

Many years ago I was often to be found in the beautiful city of Venice, in conversation with Signore Giovanni Francesco Sagredo, a man of noble birth and keen wit. At the prom in Florence came Signor Filippo Salviati, whose lesser fame was the eminence of his blood and the splendor of his fortune. He was a sublime intellect, craving no pleasure more than fine meditation. I have often discussed these two subjects in the presence of a certain peripatetic philosopher, whose greatest impediment to knowing the truth seemed to be the reputation he had acquired for his interpretations of Aristotle. (use 2)

Now that bitter death deprived Venice and Florence in their middle years of these two great luminaries, I decided to bring their glory alive in these pages, as far as my meager abilities would permit, by introducing them as interlocutors in the present dispute. (Even the good Peripatetic will lack space; because of his excessive affection for the commentaries of Simplicius, (use 3) I thought fit to leave it with the author's name, whom I so revered, let alone his own.) May these two great souls, always venerable in my heart, please this public monument of mine to accept undying love. And may the memory of his eloquence help me to convey the promised reflections to posterity.

As it happened, several conversations had taken place between these gentlemen at different times, and they had rather sharpened than quenched their thirst for knowledge. Therefore, very wisely, they decided to assemble on certain days when, apart from all other matters, they could devote themselves more systematically to contemplating the wonders of God in heaven and on earth. They met in the palace of the famous Sagredo; and after the usual but brief exchange of greetings, Saiviati began as follows.

Note 1, i.e. Aristotelians: literally "those who roam about". Aristotle walked around the Lyceum

Note 2 Sagredo was in fact a close friend of Galileo and in the dialogue takes the neutral position of an open-minded man of letters: Salviati is the man of science, Galileo himself; the philosopher who will be called Simplicio is an invented one, a scarecrow. Embedded in the Aristotelian philosophy.

Note 3 Simplicius wrote a commentary on Aristotle in the 6th century.)

Dialogue about the two great world systems

THE FIRST DAY

CONVERSATION PARTNERS

SAVE YOURSELF, SAGREFDO, AND BE THE IMPLIED

SAVE YOURSELF. Yesterday we decided to meet today and discuss as clearly and fully as possible the character and operation of those laws of nature hitherto held by adherents of the Aristotelian and Ptolemaic position on the one hand, and by adherents of the Aristotelian and Ptolemaic position on the other the Copemic system. Since Copernicus places the earth under the moving celestial bodies, making it a sphere like a planet, we may well begin our discussion by examining the peripatetic steps to argue the impossibility of this hypothesis; what they are and how great their power and impact is. To do this, it is necessary to introduce two substances into nature that differ significantly. These are the Celestials and the Elementals, the former being unchanging and eternal; the latter, temporary and destructible. Aristotle deals with this argument in his bookFrom heaven, introducing it with some speeches depending on certain general assumptions, and then confirming it by specific experiments and demonstrations. Following the same method, I will first explain my opinions and then express them freely, subjecting myself to his criticisms, especially those of Simplicius, that valiant champion and defender of the Aristotelian doctrines.

The first step in the peripatetic argument is Aristotle's proof of the completeness and perfection of the world. For, he tells us, it is neither a mere line nor a mere surface, but a body with length, breadth and depth. Since there are only these three dimensions, the world has them all, and when it has the whole, it is perfect. However, Aristotle would very much have liked to prove to me by rigorous deductions that mere length is the dimension we call a line, which by the addition of breadth becomes an area; that the addition of more height or depth leads to a body and that there is no passage beyond these three dimensions, so that through these three alone completeness or, as it were, totality is completed. Especially since he could have done it very clearly and quickly.

POTATOES. What about the elegant proofs in the second, third, and fourth text after the definition of "continuous"? Hasn't it been proven for the first time that there are no more than three dimensions, since three is everything and everywhere? And is this not confirmed by the teaching and authority of the Pythagoreans, who say that all things are determined by three beginnings, middles and ends, which is the number of the universe? Why leave out another of your reasons; namely, that this number, as by a law of nature, is used in offerings to the gods? Also, isn't it dictated by nature that we assign the title "all" to things that are three, and no fewer? Because two means "both" and you don't say "all" unless there are three.

You have all this teaching in the second text. Then, in the third, we readfor a more complete knowledge, (Note: More information.) that All, All and Perfect are formally one and the same; and that therefore among the figures only the body is complete. For he alone is determined by three who are all; and since it is divisible three ways, it is divisible every possible way. Of the other figures, one is divisible in one way and the other in two ways, because they have their divisibility and continuity according to the number of dimensions assigned to them. Thus one figure is continuous in one way, the other in two ways; but the third, namely the solid, is so in every respect.

Also, in the fourth text, after some other teachings, does he not close the matter with one more proof? Namely: a transition is made only according to an error; so there is a transition in the transition from line to area because the line has no width. But it is impossible for something to be lacking in the perfect, to be complete in everything; hence there is no transition beyond the solid or body to any other figure.

Don't you think that in all these places he has sufficiently proved that there is no passage beyond the three dimensions of length, breadth and thickness? and that therefore the body or solid that has them all is perfect?

OINTMENT. To be honest, none of these reasons make me feel compelled to admit more than this: that anything that has a beginning, middle, and end can and should be called perfect. I don't feel compelled to admit that the number three is a perfect number, nor that it has the ability to bestow perfection on its owners. I don't even understand, let alone believe, that when it comes to legs, for example, the number three is more perfect than four or two; Nor do I understand that the number four is an imperfection in the elements, nor that they would be more perfect if they were three. It would have been better for him, therefore, to leave these subtleties to the rhetoricians and prove his point by rigorous demonstrations such as are appropriate in the demonstrative sciences.

POTATOES. You seem to ridicule these reasons, and yet it is all the teachings of the Pythagoreans that ascribe so much to numbers. You who are mathematicians and believe in many of the philosophical opinions of the Pythagoreans now seem to despise their mysteries.

OINTMENT. That the Pythagoreans held to the science of human understanding, believing that he partook of divinity merely because he understood the nature of numbers, I well know; I'm not far from agreeing, either. But that these mysteries, which caused Pythagoras and his sect to such a reverence for the science of numbers, are the follies abounding in the sayings and writings of the vulgar, I by no means believe. Rather, I know that the Pythagoreans, in order to avoid exposing the things they admired to the slander and derision of the people, regarded as sacrilege the publication of the most occult properties of numbers, or of the immeasurable and irrational quantities they were examining damn. . They taught that anyone who revealed them would be tormented in the next world. So I think that some of them, just to please the common type and quench their curiosity, have suggested that the mysteries of numbers are those trifles that later spread among the vulgar. This cleverness and cleverness is reminiscent of the wise young man who, in order to quell the importunity of his mother or his inquisitive wife, I don't remember, pressured him into divulging the secrets of the Senate, invented a story that made him and many other women later led to the motive being mockery of the same Senate.

POTATOES. I do not want to join the ranks of those who are very curious about the Pythagorean mysteries. But on the point in question, I reply that the reasons given by Aristotle for proving that there are and can be no more than three dimensions seem conclusive to me; and I believe if there had been a more convincing demonstration Aristotle would not have left it out.

SAGR. You might at least add "if he had known or if it had occurred to him". Salviati, you would be doing me a great favor if you could provide me with some powerful arguments. if any are clear enough for me to understand.

OINTMENT. Not only for you, but also for Simplicio; and not only understood, but already known, even if perhaps without you realizing it. And to make them more understandable, let's take this pen and paper, which I see already prepared for such occasions, and draw some pictures.

We will first mark these two points A and B and draw the curved lines ACB and ADE and the straight line P3 from one to the other. (illustration 1) I ask, which one is for you, which determines the distance between ends A and B, and why?

SAGR. I would say the straight line, not the curves, because the straight line is shorter and because it's unique, clear, and definite; the infinitely others are indefinite, unequal, and longer. It seems to me that the choice must depend on what is unique and defined.

OINTMENT. So we have the straight line as the determinant of the distance between the two points.

Now let's add another straight line parallel to AB and CD so that there is an area between them that you want to show the width of. (Fig. 2) Therefore, starting at point A, tell me how and where you are going to go, and stop at line CD to show me the width between those lines. You would determine it by measuring the AF curve, or the AF line, or . . . ?

POTATOES. According to the straight line AF and not according to the curve, which is already excluded for such use.

SAGR. However, I shouldn't select any of them because the straight-line AF is skewed. I should draw a line perpendicular to CD as that seems to me to be the shortest and also the only one of the infinitely many longest and oddest lines that can be drawn from point A to any other point on the opposite line. CD.

OINTMENT. Your choice and the reason you give for it seems excellent to me. So now we have that the first dimension is determined by a straight line; the second (i.e., the breadth) by another straight line, not a straight line, but at right angles to that which determines the length. With this we define the two dimensions of a surface; that is, length and breadth.

But suppose you needed to determine an elevation, like how high this platform is from the ground below. Since we can draw infinite lines, curved or straight, and all of different lengths, from any point on the platform to the infinite points of the ground below, which of these lines would you use?

SAGR. I tied a rope to the platform and hung a plumb bob on it and let it stretch free until it got very close to the pavement; Since this rope is the straightest and shortest of any line that could be drawn from the same point to the pavement, I have to say that in this case it was the actual height.

OINTMENT. Very good. And if, starting from the point indicated by that string on the ground (assuming the ground is level and not inclined), you create two more lines, one for the length and the other for the width of the ground plane, what angles would they make with the make wire??

SAGR. They would certainly meet at right angles as the rope falls vertically and the sidewalk is fairly flat and level.

OINTMENTSo if you take any point as the starting point of your measurements, and from that create a straight line as the determinant of the first measurement (i.e. length), then what defines width necessarily follows at right angles first. That which is supposed to denote the height, i.e. the third dimension, forms right and not oblique angles starting from the same point with the other two. And so, through three perpendiculars, you have determined the three dimensions of length AB, width AC and height AD, through three distinct, distinct and shorter lines. (Abb. 3) And as at the point named no other lines can obviously meet to form right angles to them, and the dimensions must be determined by the only straight lines which form right angles to one another, the dimensions are not greater than three ; and what has the three has them all, and what has them all is in every way divisible, and whatever is so is perfect, &c.

POTATOES. Who says I can't draw other lines? Why can't I bring another bottom line to point A that is perpendicular to the rest?

OINTMENT. Surely you can't get more than three straight lines to meet at the same point and form right angles to each other!

SAGR. Yes, because it seems to me that what Simpcio means would be the same downward-extended DA. Two more can also be drawn in this way; but they would be the same as the first three, only different in that, while now they only touch, they would intersect. However, this would not create any new dimensions.

POTATOES. I am not saying that this argument of yours is inconclusive. But I still say with Aristotle that in the physical (weary) Topics don't always need to require mathematical proof.

SAGR. Admittedly, where none are to be had; but if there is one, why don't you want to use it? But it would be well not to say more on this point, for I think that Salviati would have conceded to both Aristotle and you without further proof that the world is solid and perfect; yea, the most perfect, since it is the chief work of God.

OINTMENT. Just as. So let's leave the general consideration of the whole and move on to the consideration of the pans. Aristotle, in his first division, separates the whole into two distinct and, as it were, opposed parts: viz., the celestial and the elementary, the first being presumptive, incorruptible, immutable, impenetrable, etc.; The latter is subject to constant changes, mutations, etc. He takes this difference from the variety of local movements as his original principle. With this step he goes further.

Leaving the sensual world, so to speak, and retreating into the ideal world, he begins to consider architecturally that since nature is the principle of movement, it is appropriate to endow natural bodies with local movement. He then explains that there are three types of local motion: namely, circular, straight, and mixed straight and circular. He calls the first two simple because of all lines only the circular and the straight line are simple. From there, limiting himself a little, he again defines among the simple movements one, the circular one, as the one performed around the center; and the other, the straight, up and down up, the one that comes out from the middle; and down whatever goes to the middle. And from this he concludes that it is necessary and right that all simple movements should be confined to these three kinds; i.e. towards the center, away from the center and around the center. This corresponds, he says, in a certain beautiful harmony to what has been said before about the body; it is perfect in three things, and its movement is perfect as well.

After these motions are established, he goes on to say that some natural bodies are simple and others are composed of them (and he simply calls those bodies which have a natural principle of motion, such as fire and earth), that it is appropriate that simple movements should be those of simple bodies, and that mixed movements must belong to compound bodies; in such a way that connections receive motion from the part that predominates in their composition.

SAGR. Wait a little, Salviati, because in this argument, so many doubts attack me from all sides that I must tell you about them if you want to pay attention to what you are about to say, or if you want to keep my attention to remember mine Doubt.

OINTMENT. I like taking a break because I'm taking the same risk and I'm about to be shipwrecked. Currently I'm navigating between rocks and stormy waves that throw me off course, as they say. Therefore, present them before multiplying your difficulties.

(The three now begin a discussion of form and speed (i.e. physics) which leads to arguments about the location of the center of the universe and whether or not the heavens are incorruptible, with SimpZicio continuing to cling to and defend Aristotle in general. The theories while Sugredo and Salviati continue to cast doubt on the coherence of the Aristotelian model, pointing out contradictions and errors, using a combination of logic and concrete examples from nature.)

OINTMENT. I see that once again we will plunge into a boundless sea from which there is never a way out. This is sailing without a compass, stars, oars or rudders, where we have to go from shore to shore or run aground or sail lost forever. If, as you have suggested, we are to proceed with our main subject, we must leave aside the general question whether rectilinear motion is necessary in nature, and whether it is peculiar to some bodies, and to particular demonstrations, observations, and experiments. First we must propose all those put forward by Aristotle, Ptolemy and others to prove the stability of the earth and then try to solve them. Finally, we must produce such by which it may be persuaded that the earth, no less than the moon or any other planet, must be counted among the circularly moving bodies of nature.

SAGR. I tend to submit to the latter, being happier with his architectural and general discourse than with Aristotle's. Because yours satisfies me without the slightest trepidation, while the other kind of blocks me at every step. I also don't see why Simplicio should not be quick to settle for the argument you put forward to prove that rectilinear motion cannot take place in nature, provided we assume that the parts of the universe are best arranged and are perfectly ordered.

OINTMENT. Stop it, Sagredo. for now I am thinking of a way of satisfying Simplicius, provided he does not want to become so closely attached to each of Aristotle's propositions that he deems it sacrilegious to deviate from a single one of them.

There is no doubt that nothing but circular motion or stillness serves to maintain the ideal positioning and perfect order of the parts of the universe with respect to the local situation. As far as movement in a straight line is concerned, I see no use other than restoring whole bodies that have been inadvertently removed and severed from their whole, as just said, to their natural place.

Now let's look at the whole globe and see what can be done to keep it and the other terrestrial bodies in the best natural condition. It must be said that it is at rest and always remains motionless in its place, or that it always remains in its place but revolves about itself, or that it finally revolves about a center and moves on the circumference of a circle. Of these events Aristotle and Ptolemy and all their followers say that it is the first ever observed and will be recorded forever; that is, eternal rest in the same place. Then why shouldn't they have said right at the start that it is their natural trait to remain motionless instead of making their natural downward movement, a movement that they have never moved with and will never move with? And as for movement in a straight line, allow us that nature makes use of it to restore the particles of earth, water, air, fire and all other mundane bodies that are an integral part of her whole when one of found them will be separated. and transported to an inappropriate place, unless such recovery can also be accomplished by finding a more convenient circular motion. It seems to me that this original position fits all the consequences much better, even by Aristotle's method, than attributing rectilinear motion as an intrinsic and natural principle of the elements. This is obvious; for I ask the Peripatetic whether, holding that the heavenly bodies are imperishable and eternal, he believes that the globe is not so, but is perishable and mortal, so that a time will come when the sun and moon and If other stars continue to exist and operate, the earth will not be found in the universe but will be destroyed along with the rest of the elements, and I'm sure he would answer no. Hence generation and decay belong to the parts and not to the whole; indeed to very small and superficial parts, insensitive in comparison with the whole mass. Now, as Aristotle argues that generation and corruption result from the opposition of straight motions, let us allow such motions to the parts that alone change and perish. But to the whole globe and sphere of the elements, circular motion or perpetual continuity in its proper place is ascribed the only definite tendencies for maintaining and maintaining perfect order.

What is thus said of the earth can reasonably be said of the fire and most of the air, the elements of which the peripatetics are compelled to ascribe and abolish as an intrinsic and natural movement that with which they have never been moved and never will be moved nature that movement with which they move, have moved and will move. I say this because they ascribe to air and fire an upward motion, a motion never pertaining to the named elements, but only to some of their particles, and even then only to bring them back into perfect configuration when they move outside their natural places. On the other hand, they call the circular motion (with which they are perpetually moved) supernatural to them, forgetting what Aristotle often said, that nothing violent can last long.

POTATOES. To all these things we have the most appropriate answers, which I leave off for the moment in order to get to the special reasons and reasonable experiments which, after all, as Aristotle aptly says, are preferable to anything that can be supplied by human beings. Dispute.

SAGR. So what has been said so far serves to consider which of the two general arguments is more likely. First there is that of Aristotle, who wanted to convince us that sublunar bodies are inherently producible and perishable, etc. Differences in simple movements. The second is that of Salviati, who assumes that the integral parts of the world are arranged in the best order and, as a necessary consequence, excludes straight movements for simple natural bodies as being useless in nature; he takes the earth as another of the celestial bodies endowed with all the privileges due to them. The last argument serves me better than the other up to this point. Therefore, let Simplicio be good enough to present all the specific arguments, experiments, and observations, both physical and astronomical, by which one may be fully convinced that the earth is distinct from the celestial bodies, is immobile, and is at the center of the planet is located . Universe or anything else that excludes the earth from being mobile like a planet like Jupiter or the moon etc. And you, Salviati, be so good as to react step by step.

POTATOES. So to start, two powerful demonstrations proving that the earth is very different from the celestial bodies. First, bodies that are generatable, corruptible, mutable, etc. are quite different from those that are unmanageable, incorruptible, immutable, etc., etc. Therefore, the earth is very different from the celestial bodies.

SAGR. With your first argument, you bring back to the table what was there all day and has only now been taken away.

POTATOES. Careful, sir; Listen to the rest and you'll see how different it is. Previously, the little premise was provedfirst, and now I want to prove itsubsequently. See for yourself if it's the same. I will prove the smaller one because the larger one is obvious.

Reasonable experience shows that on earth there is perpetual generation, corruption, change, etc., such as neither our senses nor the traditions or memories of our ancestors were ever discovered in heaven; hence heaven is immutable, etc., and earth mutable, etc., and therefore distinct from the heavens.

The second argument I draw from an essential and essential property is: every body that is naturally dark and devoid of light is distinguished from luminous and luminous bodies; the earth is dark and without light, and the celestial bodies are magnificent and full of light; hence, etc. Answer these so you don't build up too big a stack, and then I'll add others.

OINTMENT. As for the first, which you claim to be strong from experience, I would ask you to tell me exactly what these changes are that you see on earth and not in heaven and because of which you call the earth mutable and the heavens Not. .

POTATOES. On the earth I constantly see herbs, plants, animals arising and dying; winds, rain, gales, gales coming; in a word, the ever-changing appearance of the earth. None of these changes are perceptible in the celestial bodies, whose positions and configurations correspond exactly to what people remember, without creating anything new or spoiling anything old.

OINTMENT. But if you have to be content with these visible experiences, or rather these seen experiences, you must consider the celestial bodies of China and America, for surely you have never seen those changes in them that you see in Italy. Therefore they must be immutable in your sense.

POTATOES. Although I have never seen such changes in these places with my own senses, there are reliable reports of them; also cthat the proportion between the whole and the parts is equal(Note: Since the rational must be the same for the whole or for the part.), these counties, which are part of the earth like us, must also be changeable.

OINTMENT. But instead of reducing yourself to believing other people's stories, why didn't you notice that? Why not see with your own eyes?

POTATOES. Because these countries are anything but exposed; they are so far away that our eyesight could not see such changes in them.

OINTMENT. Now see for yourself how you inadvertently revealed the fallacy of your argument. They say that changes seen up close on Earth cannot be seen in America because of the great distance. Well, much less could they be seen on the moon, which is many hundreds of times more distant. And if you believe in changes in Mexico based on the news there, what reports do you have from the moon to convince you that there are no changes? Since you don't see changes in the sky (where you couldn't see them if there were any due to distance, and where there's no news), you can't conclude there isn't in the same way that when you look at them Land see and recognize, you correctly deduce that they exist here.

POTATOES. Among the changes that have taken place on earth I can find some so great that if they had taken place on the moon they would very well have been observed down here. From the oldest records we know that earlier in the Strait of Gibraltar Abila and Calpe were connected by some smaller mountains that kept the ocean under control; However, as these mountains were separated for some reason, the opening let in the sea, which was inundated to form the Mediterranean Sea. When we consider the enormity and difference in appearance that must have been seen from afar on water and land, there is no doubt that such a change could easily be seen by anyone standing on the moon. Likewise, earthlings would have detected such a change on the moon; However, there is no history where such a thing has been seen. There is therefore no reason to say that anything in the celestial bodies is changeable, etc.

OINTMENT. I dare not say that such great changes have taken place on the moon, but I am also not sure that they could not have happened. Such a mutation could only be represented to us by a variation between the brightest and darkest parts of the moon, and I doubt we have had selenograph observers on Earth who have provided us with selenography as accurate as they do for a significant number of years reasonable for us to conclude that no such change has taken place on the face of the moon. Of the moon's appearance I find no more accurate description than that some say it represents a human face; others that it is like the snout of a lion; still others that it is Cain with a bundle of thorns on his back. The statement "the heavens are unchanging, because neither the moon nor any other celestial body shows changes such as have been discovered on earth" proves nothing.

SAGR. This first argument from Simplicio leaves me with another doubt that I would like to have removed. So, I ask him, was the earth producible and perishable before the Mediterranean flood, or did it begin to be then?

POTATOES. No doubt it was manageable and corruptible before; but it was such a mutation that it could have been observed as far away as the moon.

SAGR. Well then; If the earth was manageable and perishable before this flood, why can't the moon be too without such a change? Why is something needed on the moon that means nothing on earth?

OINTMENT. A very poignant observation. But I fear that Simplicius slightly alters the meaning of this text from Aristotle and the other Peripatetics. They are said to regard the heavens as immutable because no star has ever been begotten or seen corrupted, being probably a smaller part of heaven than a city from earth; However, countless of the latter have been destroyed, leaving no trace of them.

SAGR. In fact, I thought the opposite, believing that Simplicio had distorted this presentation of the text so as not to overload the master and his disciples with an even more fantastic idea than the other. What foolishness it is to say, "The heavens are unchanging because the stars in them are not begotten or corrupted." Is there anyone who has seen a globe of the earth disintegrate and another regenerate in its place? Don't all philosophers accept that very few stars in the sky are smaller than Earth, while many are much larger? Therefore, the decay of a star in the sky would be no less important than the destruction of the entire globe! Now, if in order to safely introduce generation and corruption into the universe, it is necessary that a body the size of a star be corrupted and regenerated, then you had better drop the whole thing; for I assure you that you will never see the terrestrial globe, or any other integral body of the universe, so corrupted that, having been seen for many centuries, it dissolves without a trace.

OINTMENT. But to give more than satisfaction to Simplicius and, if possible, to clear him of his error, I declare that we have new events and observations in our time, so that if Aristotle had been alive I have no doubt about it that he would have changed his mind. This is easy to infer from his own way of philosophizing, for when he writes of believing that heaven is immutable, etc. Had he seen such an event, he would have changed his mind and sensibly preferred sensual experience to natural reason. If he had not considered the senses, he would not have argued that the immutability of sensory mutations is not seen.

POTATOES. Aristotle first laid the groundwork for his a priori argument by showing the necessity of the immutability of heaven through natural, obvious, and clear principles. Then he retained the same thing a posteriori, according to the senses and traditions of the ancients.

OINTMENT. What you are referring to is the method he uses to write his doctrine, but I don't think that's the way he examined it. Rather, I think it is right that he first gained it through senses, experiments and observations in order to secure as many of his conclusions as possible. Later he looked for ways to make them detectable. This is mostly done in the demonstrative sciences; This happens because if the conclusion is true, one can arrive at an already demonstrated statement or an axiomatic principle using analytical methods. but if the conclusion is wrong, one can go on forever without ever finding any known truth, if in fact one does not find any glaring impossibility or absurdity. And you can be sure that long before he discovered the proof for which he sacrificed a hecatomb, Pythagoras was certain that the square on the side opposite the right angle in a right triangle was equal to the squares on the other two sides. The certainty of a conclusion helps a great deal in discovering its evidentiary value, always in the demonstrative sciences. But whichever way Aristotle proceeded, whether reason a priori precedes sense perception a posteriori or vice versa, it is enough that Aristotle, as he often said, preferred sense experience to any argument. In addition, the strength of a priori arguments has already been examined.

Now, returning to the subject, I say that the things that are being discovered and have been discovered in the sky in our time are such as can satisfy all philosophers perfectly, because only such events have been seen as we have called generations and corruptions and are seen in bodies, details, and across the expanse of heaven. In addition to the two new stars of 1572 and 1604, which were probably beyond all planets, eminent astronomers observed many comets that were formed and scattered at locations above the lunar orbit. (Note: Supemovas appeared during these years, sparking much debate. Salviati's claim that his place in heaven is indisputable is debatable. He will provide the proof on the third day.) And in the face of the Sun itself, with the help of With the telescope, they saw dense and dark matter being produced and dissipated that was very similar to the clouds above Earth: and many of them are so huge that they tower not only over the Mediterranean Sea but all of Africa, including Asia. Well, if Aristotle had seen these things, what do you think he would have said and done, Simplicius?

POTATOES. I don't know what Aristotle, the master of all sciences, would have done or said, but I know to a certain extent what his followers do and say and what they should do and say in order not to remain alone - a leader, a leader and a chief in philosophy.

As for the comets, the modern astronomers who wanted to make them celestial were not defeated by theAnti-Tycho? (Note: Simplicio refers to the work of Scipio Clijaramonti (1565-1652).) Also conquered by their own weapons; that is, by parallaxes and calculations turned in all directions, and finally by concluding in favor of Aristotle that they are all elementary. Something so fundamental to innovators has been destroyed, what are they left to do to keep them going?

OINTMENT. Calm down, Simplicio. What does this modern author say of you about the new stars of 1572 and 1604 and sunspots? As for comets, I care little whether they form under or over the moon, and I have never made much of Tycho's verbosity. Nor do I shy away from believing that their matter is elemental, and that they can levitate at will without encountering obstacle through the impenetrability of the wandering sky, which I believe to be far thinner, more flexible, and more subtle than our air. . And as for calculating parallax, firstly, I doubt that comets are subject to parallax; moreover, the inconsistency of the observations on which they were calculated makes me equally suspicious of both your opinions and those of your opponent, all the more so than I thinkAnti-Tychosometimes he adapts to his author's taste or declares false those remarks which do not suit his purpose.

POTATOES. As for new stars, theAnti-Tychocompletely rebuts them in a few words by saying that such newer new stars are not known unequivocally as celestial bodies and that if their opponents want to prove any changes and generations in the latter, they must show us mutations made in stars that they have long been since the time described and that they are undoubtedly celestial objects. And that can never happen.

As for the material, which some say is produced and resolved on the Sun, it is not mentioned, from which I must conclude that the author considers it either a fable or a telescopic illusion (Note: The telescope has been an object of suspicion in many circles.) or at best by an airborne phenomenon; in a word, for anything but celestial matter.

OINTMENT. But you, Simplicio, what did you think of responding to the opposition of those troublesome spots that come to disturb Heaven and, worse, Peripatetic philosophy? It must be because you, as their undaunted advocate, have found an answer and a solution that we cannot withhold.

POTATOES. I have heard mixed opinions on this subject. Some say, "These are stars, like Venus and Mercury, orbiting the Sun in their proper orbits, and passing under them present themselves to us as faint, and then separate again." Others believe that they are inventions of the air; still other lens illusions; and still other, other things. But I'm more inclined to believe, yes, I think it's correct, that they are a collection of various opaque objects that come together almost by accident; and hence we often see that in one spot ten or more small bodies of irregular shape, looking like snowflakes, tufts of wool, or flying moths, can be counted. They trade places with each other, sometimes part, come back together, but mostly under the sun, which they move about as their center. But it is therefore not necessary to say that they arise or pass away. Rather, they are sometimes hidden behind the solar body; at other times, though far from her, they cannot be seen because they are close to her immeasurable light. For in the eccentric sphere of the sun (Note: The eccentric sphere was the perfect circle circumscribed by a celestial body's orbit around a nearby point (called a deferent). but not exactly Earth (and therefore slightly off the center of the universe). It was a theoretical construct that (along with the epicycle) helped astronomers reconcile their belief in a constant circular velocity and apparent variations in that velocity.) forms a kind of onion, consisting of several folds in each other, each of which is dotted with certain small spots and moves; and although at first its movements appear erratic and erratic. However, it is said that ultimately it has been observed that after a certain period of time, the same spots will surely return. This seems to me the most appropriate means yet found to explain such phenomena while maintaining the incorruptibility and ingenerability of heaven. And if that weren't enough, there are smarter intellectuals who will come up with better answers.

OINTMENT. If it is a matter of law or of the humanities, in which there is neither true nor false, one may rely on the subtlety of mind and eloquence and greatest experience of the writers, and expect that he who has excelled at these Things things to make your argument more plausible and best judged of. But in the natural sciences, the conclusions of which are true and necessary and have nothing to do with the human will, one must be careful not to defend error; for here a thousand Demosthenes and a thousand Aristotle would be deserted by any mediocre mind that happens to come to the truth itself. , more learned and well-read than the rest of us, able to make false true despite nature. And since, of all the opinions that have arisen about the nature of sunspots, the one you just presented seems to be the right one, all the others are wrong. Now, in order to free you from a completely illusory chimera as well, I shall tell you, apart from the many improbabilities therein, only two facts which are to be noted against it.

One is that many of these spots originate at the center of the sun's disk, and likewise many resolve and vanish far from the edge of the sun, a necessary argument for their need to be created and resolved. Because without generation and corruption, they could only appear there through local movement, and everyone must go in and out on their own ledge.

The other observation for those who have not the slightest prospective ignorance is that from the changes in shape observed in the spots and their apparent changes in speed, it must be inferred that the spots in contact with the body of the sun .. and that when they touch its surface, they move with it or above it, and by no means turn in circles far from it. Its motion proves this, appearing very slow at the edge of the sun's disc and rather fast towards its center; the smeared shapes prove the same and appear very narrow at the edge of the sun compared to a closer look at the center. For around the center they are seen in their majesty and as they really are; but around the rim they appear foreshortened because of the curvature of the sphere's surface. These reductions in both motion and form correspond, to those who can carefully observe and calculate them, to what would appear if the spots were adjacent to the Sun, and contradict their motion in distant circles, or even small ones intervals irrevocably. of the sun body. This was amply demonstrated by our mutual friend in hisLetters to Mark Welser about sunspots. (Note: Published by Christopher Scheiner in 1612.) From the same shape changes it can be concluded that none of them are stars or other spherical bodies, because of all shapes only the sphere is never seen in perspective, nor can it appear otherwise than perfectly round. Thus, if any of the individual points were a round body, as all stars are, it would exhibit the same roundness at the center of the solar disc and at the very edge, while they shorten and appear thin near its end and on the other Side so wide and long towards the center as to ensure they are of small thickness or depth in relation to flakes. to its length and width.

So, as to the fact that it is finally observed that the same spots will surely come back after a certain time, don't believe it, Simplicio; those who said this were trying to deceive you. You know that this is so, because they tell you nothing of those which are created or dissolved on the face of the sun far from the rim; I also didn't tell him a word about the shorteners, since that is necessary proof of their proximity to the sun. The truth about the same spots returning is exactly what is written in what has been saidletters; namely, that some of them are occasionally of such long duration that they do not disappear in a single revolution around the sun lasting less than a month.

POTATOES. To tell the truth, I have not made observations long enough and careful to qualify me as an authority on the subject; but I am dying to do it and then see if I can reconcile what experience presents us with what Aristotle teaches. Because obviously two truths cannot contradict each other.

OINTMENT. Whenever you want to reconcile what your senses are telling you with the more solid teachings of Aristotle, you will have no trouble. Doesn't Aristotle say that because of the great distance, celestial matters cannot be dealt with very accurately?

POTATOES. He says that very clearly.

OINTMENT. Doesn't he also declare that what the experience of meaning shows is preferable to any argument, even if it seems highly justified? And doesn't he say that positively and without hesitation?

POTATOES. He does.

OINTMENT. Then of the two propositions, both Aristotelian doctrines, the second, which says that it is necessary to prefer the senses to arguments, is a more solid and definite doctrine than the other, which says that the heavens are immutable. Therefore, it is better for Aristotelian philosophy to say, "Heaven is changeable because my senses tell me so" than to say, "Heaven is immutable because Aristotle was convinced by reasoning." Add to that that we have a better basis for arguing about heavenly things. as Aristotle. He admitted that he found such perceptions very difficult because of the distance of his senses, and he admitted that he whose senses they could best represent could philosophize with greater certainty that the telescope has the sky thirty or forty times nearer to us brought out when Aristotle was, so we can see a lot of things in it that he couldn't see, including those sunspots that were absolutely invisible to him when Aristotle was.

SAGR. I can put myself in Simplicio's shoes and see that he is deeply moved by the overwhelming power of these closing arguments. But on the other hand to see the great authority that Aristotle generally attained; considering the number of famous performers who have taken pains to explain their importance; and the observation that the other sciences, so useful and necessary to mankind, base much of their value and reputation on Aristotle's merit; Simplicius is confused and perplexed, and I seem to hear him say: 'If Aristotle were deposed, who would be there to settle our controversies? What other author would we follow in the schools, academies, universities? a single conclusion? Should we abandon this structure under which so many travelers rested? Shall we destroy this refuge, this Prytaneus (Note: Greek public hall where statesmen, heroes, and dignitaries were honored and entertained.) where so many scholars have found refuge? so comfortable where, without exposing themselves to the harsh air, they can acquire a complete knowledge of the universe by simply turning the page?

I pity him no less than a good lord who, after having built a splendid palace with much toil and expense, employing hundreds and hundreds of artisans, and then seeing it threatened with ruin because of poor foundations, should try all right to ease the pain avoid seeing the ruined walls adorned with so many beautiful murals; or the pillars that support the splendid galleries, or the gilded beams fall; or the broken doors, or the marble gables and cornices brought for so much money, should, I say, try to keep the collapse with chains, clamps, iron bars, buttresses and struts.

OINTMENT. Well, Simplicio need not yet fear such a collapse; I promise to protect you from harm at a much lower cost. There is no danger of such a crowd of great, subtle, and wise philosophers being overwhelmed by one or two boasting a little. Rather, without even pointing their pens at her, just by keeping silent, they expose her to general scorn and scorn. It is vain to imagine that a new philosophy can be introduced by refining this or that author. It is first necessary to teach the reform of the human mind and enable it to discern truth from falsehood, which only God can do.

But where do we go astray in going from one argument to another? Without the guidance of your memory I will not be able to get back on the path.

POTATOES. I remember very well. We dealt with the answer ofAnti-Tychoto the objections to the immutability of heaven. Among these, you brought up the issue of sunspots, which was not mentioned by your author, and I think you wanted to consider your answer in the case of new stars.

OINTMENT. Now I remember the rest. Continuing on this subject, it seems to me that there is something to criticize about Anti-Tycho's counter-argument. First, if the two new stars, which this author cannot place less than in the highest regions of the sky, and which existed for a long time and finally disappeared, did not make him anxious to insist on the immutability of the sky simply because they undoubtedly are not parts of the celestials or mutations in the old stars, so what's the point of all this fuss and bothering to drive comets out of the celestial regions at all costs? Wouldn't it have been enough for him to say that they are undoubtedly neither parts of the heavens nor mutations in the old stars and therefore do not harm either the heavens or the teachings of Aristotle?

Second, I am not pleased with his state of mind when he admits that any change that might be made to the stars would destroy the celestial prerogatives of incorruptibility, etc., since the stars are celestial things, as is evident and as everyone admits , and if, on the other hand, it does not bother him in the least if the same changes occur elsewhere in the vastness of the sky outside the stars themselves. Does it perhaps mean that heaven is not a heavenly thing? I would think that the stars were called celestial things because they were in the heavens, or because they were made of celestial stuff, and that therefore the heavens would be more heavenly than they were; Nor could I say anything more earthly than the earth itself, or more fiery than fire.

Next, the fact that he does not mention sunspots, which have been conclusively shown to be created and resolved and to be near and rotating with or relative to the solar body, gives me a good indication that this author writing more about it can comfort others than from one's own conviction. I say this because he is familiar with mathematics and it would be impossible for him not to be persuaded by evidence that such material is necessarily contiguous with the Sun and undergoes generations and dissolutions so great that nothing of comparable magnitude ever did has existed. took place on earth. And if the generations and corruptions that occur upon the solar sphere are so numerous, so great, and so frequent, though it may reasonably be called the noblest part of heaven, what argument is there to dissuade us from believing that others happen in other globes?

SAGR. I cannot say without great astonishment, without insulting my intelligence, when I hear that the natural and integral bodies of the universe are ascribed the primary perfection and distinction of being immutable, unchanging, unchanging, etc., while otherwise it is so is called great imperfection to be alterable, generateable, mutable, etc. For my part, I think the country is very noble and admirable precisely because of the various changes, changes, generations, etc. that occur incessantly. Whether it would have been a vast desert of sand, or a mountain of jasper without changing, or whether by the time of the Deluge the water that covered it had frozen over and left a vast ball of ice where nothing had been born or changed or changed , I would regard it as a useless piece of the universe, inert, and in a word, superfluous and essentially non-existent. This is exactly the difference between a living and a dead animal; and I say the same of the moon, of Jupiter, and of all the other globes of the world.

The deeper I look into the vanities of popular argument, the lighter and more foolish I find them. What greater folly can be imagined than to call jewels, silver and gold "precious" and earth and soil "abominable"? People who do this must remember that there would be no prince who would not spend a bushel of diamonds and rubies and a carriage full of gold, when there was wanting soil as well as jewels or precious metals just to have it enough land. Plant a jasmine in a small vase or sow an orange tree seed and watch it sprout, grow and produce its beautiful leaves, fragrant flowers and delicate fruit. It is scarcity and abundance that leads the vulgar to regard things as valuable or worthless; They call a diamond very beautiful because it's like pure water, and then they wouldn't trade it for ten barrels of water. Those who so praise incorruptibility, immutability, etc. They are, I believe, driven to speak in this way by a great desire to go on living and a fear of death. They don't consider that if humans were immortal, they would never have come into being. Such men really deserve to find a Medusa's head, which would turn them into statues of jasper or diamonds, making them more perfect than they are.

OINTMENT. Perhaps such a metamorphosis would not be entirely to their detriment, for I think it would be better for them not to argue than to argue on the wrong side.

POTATOES. Oh, there is no doubt that the earth as it is is more perfect because it is changeable, changeable etc. than if it were a mass of stone or even a solid diamond, and extremely hard and unchanging. But in so far as these conditions bring nobility to earth, they would render less perfect the celestial bodies where they would be superfluous. For the celestial bodies, that is, the sun, moon, and other celestial bodies, which are destined to have no other purpose than to serve the earth, need nothing more than movement and light to attain their goal.

SAGR. So nature created and directed all these vast, perfect and noble celestial bodies, immutable, eternal and divine. for no other purpose than to serve the mutable, perishable, and mortal earth? To serve what you call the dregs of the universe, the sink of all impurities? Why would the stars be immortalized, etc., to serve something transitory, etc.? This purpose of serving the earth is withdrawn and the innumerable celestial bodies become useless and superfluous, since they have and cannot have any interaction with one another, since they are all unchanging, unchanging and unchanging. For example, if the moon is immutable, how would you get the sun or another star to act on it? The action would undoubtedly have no more impact than trying to melt a large mass of gold by looking at it or thinking about it. In addition, it seems to me that in times when the celestial bodies contribute to the generations and changes of the earth, they must also be mutable. Otherwise I don't see how the influence of the moon or the sun in bringing about generations on earth would be any different than placing a marble statue next to a woman and expecting children from such a union.

POTATOES. Corruption, change, mutation, etc. do not belong to the whole globe, which in its entirety is no less eternal than the sun or the moon. But as for its outer parts, it is procreative and perishable, and it is certainly true that generations and corruptions are continuous in these parts, and, being continuous, require heavenly and eternal operations. Therefore it is necessary that the celestial bodies are eternal.

SAGR. All good, but if the immortality of the whole globe is not detrimental to the perishability of its surface parts, and if this generality, perishability, mutability, etc. you give it great grace and perfection, why can't you and shouldn't you also see changes, generations, etc. in the outer parts of the celestial spheres, adding them as an ornament without diminishing their perfection or depriving them of their effect; to even increase them by letting them work not only on the earth but also among themselves and the earth also on them?

POTATOES. That can't be, because generations, mutations, etc. that would happen, say, on the moon, would be vain and useless, andNature doesn't do anything for free. (Note: Nature doesn't do anything for free.)

SAGR. And why should they be vain and worthless?

POTATOES. Because we see and feel clearly that all generations, changes etc. that occur on earth are intended directly or indirectly for the benefit, comfort and benefit of man. Horses are born to house men; The earth produces hay to feed the horses, and the clouds water it. Herbs, grains, fruits, animals, birds and fish are created for the comfort and nourishment of man. In short, if we carefully examine and weigh all these things, we will find that the end they all boil down to is people's need, utility, comfort, and enjoyment. Now what good could the generations that might happen on the moon or on other planets benefit the human race? Unless you mean that there are also people on the moon who enjoy its fruits; an idea which, if not mythical, is at least godless.

SAGR. I neither know nor suspect that herbs, or plants, or animals like ours reproduce on the moon, or that there are rains, winds, and thunderstorms as on earth; much less that it is inhabited by men. But I do not yet see that it necessarily follows that since things like ours are not begotten there, there is no change, or that there can be no things that change or are begotten and dissolved; Things that are not only different from our own, but are so far removed from our imaginations that they are completely unimaginable to us.

I am sure that a person who was born and raised in a vast forest among animals and birds and who knows nothing about the element of water could never imagine another world in nature different from his own and full of traveling animals is without legs or wings, beating rapidly, not only on its surface like animals on earth, but throughout its depths; and not just move, but stop motionless wherever they wanted, something birds in the air cannot do. And that people also lived there and built palaces and cities and traveled with such ease that they could travel to distant lands with their families and houses and entire cities without getting tired. Well, as I have said, I am sure such a man could not, with the most vivid imagination, picture fish, the ocean, ships, fleets, and fleets. Thus, and more, it may happen that on the moon, which is separated from us by a much greater distance, and composed of materials perhaps very different from those of the earth, not only distant but complete substances and actions take place over all out. our imagination, which bears no resemblance to our own and is therefore completely unthinkable. For what we imagine must either be something already seen, or a composition of things and parts of things seen at different times; such are sphinxes, sirens, chimeras, centaurs, etc.

OINTMENT. I have often given free rein to my fantasies about these things, and my conclusion is that it is indeed possible to discover some things that do not and cannot exist on the moon, but none that I believe exist can and do exist, except in general; that is, things that occupy it, act and move within it, perhaps in a very different way from ours, seeing and admiring the grandeur and beauty of the universe and its Creator and Ruler, and perpetually singing its praises. I mean, in a word, to do what is so often commanded in Scripture; i.e., a continual engagement of all creatures in the praise of God. (Note: This is indeed the case in Dante's Divine Comedy (par. 3-7).)

SAGR. These are among the things that, very broadly speaking, could be present. But I'd like to hear you mention the ones you think can't be there, as you should be able to be more specific about them.

OINTMENT. I warn you, Sagredo, that now, for the third time, we are slipping away imperceptibly from our main subject, step by step, and we will only slowly get to the point of our argument if we digress. So perhaps it would be good for us to defer this matter to a special session along with others that we have agreed upon.

SAGR. Please, now that we're on the moon, let's get on with things concerning the moon so we don't have to travel that far again.

(Salviati, assisted by Sagredo and drawing heavily on data derived from the use of the telescope, reveals the Moon's resemblance to the Auto/i: ft is spherical, dark, dense, mountainous; it is divided into areas of contrasting brightness, much like the land and sea areas of the earth; seen from the moon, the earth goes through phases just like the moon; The moon receives sunlight reflected from the earth as the earth receives from the moon. Salviati also says that the moon always presents the same hemisphere to the earth.

Simplicio disputes several points: he claims that the moon is a perfectly smooth sphere, more dense than the earth because it is composed of celestial matter; While the moon is opaque, not dark but polished to a mirror-like reflective shine, it is impossible for the moon to receive light from the dark earth. The three engage in a lengthy discussion about the moon, which includes in part a discussion of the properties of light and reflection, which occupies most of the remainder of the first day.)

POTATOES. Therefore, in his opinion, the earth would have an appearance similar to what we see on the moon, made up of at most two parts. But then do you think those big dots that you see on the moon's face are seas and the brighter balance is land, or something?

OINTMENT. What you're asking me now is the first of the differences that I think exist between the moon and the earth that we'd better hurry up on since we spend a lot of time on the moon. I say then that if there were but one way in nature to illuminate two surfaces from the sun so that one appears brighter than the other, and that was to make one of land and the other of water, it would be necessary say that the moon's surface was partly earthy and partly watery. But since we are aware of more pathways that could produce the same effect, and perhaps others that we are unaware of, I dare not suggest that there is one on the moon rather than another.

We have already seen that a bleached silver plate changes from white to dark on contact with the polisher; the watery part of the earth appears darker than the dry; On the tops of the mountains, the wooded parts look much darker than the open barren areas because the plants cast a lot of shadows while the clearings are lit by the sun. This mixture of colors is so effective that on carved velvet the color of cut silk appears much darker than that of uncut silk because of the shadows cast between one thread and the other; and solid color velvet is also much darker than taffeta made from the same silk. So if there were things like dense forests on the moon, they would probably look like the patches we see; a similar difference would arise if they were seas; and finally, nothing prevents these spots from actually being a darker color than the others, because that's how the snow makes the mountains appear lighter.

What you can clearly see on the moon is that the darkest parts are all plains, with few rocks and ridges on them, although there are some. The lightest rest are all rocks, mountains, round ridges and other shapes, and in particular there are large mountain ranges around the points. We're pretty sure the spots are flat surfaces and notice that the boundary separating the light and dark parts is smooth across the spots, while looking broken and jagged on the light parts. But I don't know if that surface uniformity in itself is enough to cause the apparent darkness, and I prefer not to believe.

Also, I think the moon is very different from the earth. Though I fancy that its regions are not lifeless and dead, I do not claim that life and movement exist there, much less that plants, animals, or other things like ours are produced there. Even if they were, they would be extremely diverse and far beyond our imagination. I am inclined to believe this because, first, I think that the matter of the lunar sphere is not earth and water, and that alone is enough to prevent generations and changes similar to ours. But even assuming land and water on the moon, there are definitely two reasons why plants and animals similar to ours are not produced there.

The first is that the various aspects of the Sun are so necessary to our various species that our various species could not exist without them. Now the behavior of the sun in relation to the earth is very different from what it shows in relation to the moon. As for daily illumination, on Earth we have, for the most part, twenty-four hours divided between day and night, but the same effect lasts a month on the Moon. The yearly setting and rising, by which the sun causes the different seasons, and the inequalities of day and night, end for the moon in a month. And while for us the sun rises and sets so sharply that there is a forty-seven degree difference between its maximum and minimum altitudes (that is, as much as the distance between the tropics), for the moon it varies by no more than ten degrees . or slightly less, that is the number of maximum latitudes of its orbit with respect to the ecliptic.

Now imagine what the effect of the sun in the hot zone would be if it were to blaze continuously for fifteen days. Needless to say, all plants, herbs and animals would be destroyed; So if there were any species there, it would be plants and animals very different from those of today.

Second, I'm pretty sure it doesn't rain on the moon because if clouds were to build up anywhere on the moon, such as on Earth, they would hide some of the things on the moon that we see through the telescope. In short, the scene would change in some respects; an effect I have never seen in long and careful observations, always discovering a very pure and unified serenity.

SAGR. To this it may be answered that there may be much dew there, or that it rains there during the nights; that is, when the sun does not illuminate it.

OINTMENT. If we had evidence by other phenomena that similar species existed there, and only the occurrence of rains were absent, we could find this or some other condition to replace them, as is done in Egypt by the floods of the Nile. But as we find no event resembling ours among the many that would be necessary to produce similar effects, we need not bother to introduce just one, and even that, not by sure observation, but by mere possibility. Furthermore, if I were asked what my basic knowledge and natural reason would tell me about the production of similar or other things there, I would always answer: "Very different and for us completely unimaginable"; for this seems to me to correspond to the richness of nature and the omnipotence of the Creator and Ruler.

SAGR. It always strikes me as a great imprudence of some who want to make human ability the measure of what nature can do. On the contrary, there is not a single effect in nature, not even the slightest, that exists in such a way that the most ingenious theorists can arrive at a complete understanding of it. This vain presumption of understanding everything can have no other reason than never understanding anything. For whoever once experienced the perfect understanding of a single thing, and actually demonstrated how knowledge is realized, would find that he understood nothing of the infinity of other truths.

OINTMENT. Your argument is pretty conclusive; as confirmation of this we have the evidence of those who understand or have understood; The more these men knew, the more they recognized and freely confessed their little knowledge. And the wisest of the Greeks, thus judged by the oracle, said openly that he knew that he knew nothing.

POTATOES. So it must be said that either the Oracle or Socrates himself was a liar, the former proclaiming him the wisest and the latter saying he knew he was the most ignorant.

OINTMENT. Neither of the alternatives follows, since both statements could be true. The oracle considers Socrates to be wiser than all other men whose wisdom is limited; Socrates acknowledges that he knows nothing about absolute wisdom, which is infinite. And since much is the same part of infinity as little or nothing (since for an infinite number it makes no difference whether we accumulate thousands, tens or zeros), Socrates rightly recognized his limited knowledge as nothing. to the infinity that he lacked. But since there is some knowledge among men and it is not shared equally among all, Socrates may have had a larger share than others, thus confirming the oracle's answer.

SAGR. I think I understand this point very well. There is power among men to act, Simplicio, but it is not shared equally by all; and doubtless the power of an emperor is greater than that of a private, but both are nil in comparison with divine omnipotence. Among the men there are some who understand agriculture better than others; but what has to do with knowing how to plant a vine in a ditch has to do with knowing how to get it to take root, get nourishment, take a good deal of it to grow leaves form, another to form tendrils, this one for the grapes, one for the grapes, another for the skins, all the work of the wisest nature? This is one particular example of the innumerable works of nature, and in it alone infinite wisdom can be seen; hence it can be concluded that divine wisdom is infinitely infinite.

OINTMENT. Here's another example. Shall we not say that the art of discovering a beautiful statue in a block of marble raised Michelangelo's genius far, far above the common sense of other men? However, this work is nothing more than a copy of a single posture and position of the outer and superficial limbs of an immobile human being. So what is it compared to a man created by nature, made up of so many external and internal limbs, of so many muscles, tendons, nerves and bones, serving so many and so many different movements? And what shall we say of the senses, spiritual power, and finally the mind? Can we not rightly say that the making of a statue infinitely yields to the making of a living man, even to the making of the lowest worm?

SAGR. And what difference do you think there was between the Archytas pigeon and a natural pigeon?

POTATOES. Either I lack understanding or there is an obvious contradiction in your reasoning. Among your highest praises, if not among your highest praises, is your praise of the understanding you ascribe to the natural man. Just now you agreed with Socrates that your understanding was zero. So you have to say that not even nature has understood how to make a mind that can understand.

OINTMENT. You get to the point very precisely, and to answer the objection it is better to resort to a philosophical distinction and say that the human mind can be taken in two ways, theintensiveor theextensive.Detailed, that is, in relation to the multitude of intelligible things, which are infinite, the human mind is as nothing, even if it comprehends a thousand propositions; for a thousand to infinity is zero. But take man's understandingintensive, inasmuch as this term signifies the perfect understanding of a proposition, I say that the human intellect perfectly understands some of them, and therefore has as much absolute certainty in them as nature itself. Of this alone are the mathematical sciences; that is, geometry and arithmetic, in which the divine mind knows infinitely more propositions than it knows everything. But in relation to the few that the human intellect comprehends, I believe that its knowledge equals the divine in objective certainty, for here it can comprehend the necessity beyond which there can be no greater certainty.

POTATOES. This speech seems very bold and daring to me. (Note: Actually, when attacking theDialog, the notion that the human intellect could "perfectly" comprehend a geometric statement was interpreted by the Church as Galileo's assertion that the human mind was somehow equivalent to the divine.)

OINTMENT. These are very common claims and far from any trace of audacity or daring. They in no way detract from the majesty of divine wisdom, any more than the statement that God can undo what is done detracts from His omnipotence. But I doubt, Simplicio, whether your suspicion does not stem from the fact that you have misunderstood what I said. So, to explain myself better, I say that the truth of knowledge given by mathematical proofs is the same as that which divine wisdom acknowledges; but I must indeed concede to you that the manner in which God knows the infinite propositions, some of which we know, is exceedingly excellent than ours. Our method uses gradual thinking from one conclusion to the next, while his is simple intuition. For example, to learn some properties of the circle (which has infinitely many of them), let us start with one of the simplest and, taking it as the definition of a circle, pass by reasoning to another property, and from that to a third and then to a fourth, and so on; but the divine intellect, by a simple comprehension of the nature of the circle without long reflection, knows the whole infinity of its properties. Next, all these properties are practically in the definitions of everything; and finally, because they are infinite, they may be but one in essence and in divine spirit. Not all that has been said above is totally unknown to the human mind, but is clouded by deep and dense mists, which partially dissolve and clear when we have mastered some conclusions and established them in our possession so firmly and so willingly that we can run over them very quickly. For what else is there for the square of the hypotenuse to be equal to the squares of the other two sides than the equality of two parallelograms on the same basis and between parallel lines? And isn't this ultimately the same as the equality of two surfaces which, when superimposed, do not increase but are enclosed within the same limits? Now, these advances, which our minds make laboriously and step by step, run like light through the divine mind in an instant; that means that everything is always there for her.

I conclude that our comprehension is infinitely surpassed by the Divine both in the kind and in the number of things comprehended; but I don't sink it so low as to consider it absolutely nil. No, when I consider how many wonderful things and how many of them human beings have understood, explored and invented, I see and understand very clearly that the human spirit is the work of God and one of the most excellent.

SAGR. I myself have often thought about what you are saying now and how great the sharpness of the human mind can be. And when I consider the many wonderful inventions that people have discovered in both art and literature, and then reflect on my own knowledge, I feel little more than miserable. I'm so far from promising myself not really discovering anything new, but even learning what I've already discovered, that I feel stupid, confused, and stinging with despair. When I look at an excellent statue, I say in my heart, "When will you be able to remove the excess from a block of marble and reveal such a beautiful figure within? When are you going to know how to mix different colors and spread them over a canvas or wall and depict all objects visible with it, like a Michelangelo, a Raphael or a Titian? If you look at what people have found out about how one changes musical intervals and forms regulations and rules to control them wonderful feast for the ears, when can I stop my amazement? What can I say about so many and so different instruments? With what admiration does the reading of excellent poets fill those who attentively study the invention and interpretation of concepts, and what shall I say of architecture and the art of navigation?

But, surpassing all amazing inventions, what a grandeur of spirit was he who dreamed of finding ways to share his deepest thoughts with every other person, however distant in time and place! From talking to those in India; to speak to the unborn and not be born for a thousand or ten thousand years; and how easily by the varied arrangement of twenty characters on a page!

Let this be the seal of all mankind's admirable inventions and the end of our discussions for the day. After the honest hours I think Salviati would like to enjoy our legal hours in a gondola; and tomorrow I shall expect you both so that we can continue the talks that have just begun.

end of the first day

Dialogue about the two great world systems

THE SECOND DAY

SAVE YOURSELF. Yesterday we took so many and such large digressions from the mainstream of our main argument that I don't know if I could continue without your help to get me back on track.

SAGR. I am not surprised that you should find yourself in some confusion, for your mind is as full and cluttered with what remains to be said as with what has been said. But I'm just a listener and only have things in mind that I've heard, so maybe I can get your tirade back on track by briefly outlining it for you.

As I recall, yesterday's speech can be summarized as a preliminary examination of the following two opinions as to which is more likely and more reasonable. The former states that the substance of the celestial bodies is incorruptible, immutable, immutable and, in a word, free from all mutations except those of the situation, and is therefore a quintessence (nota: Literally a fifth essence distinct from the four elements earth, water, air and fire found in the lunar sphere.) very different from our generatable, transient and mutable bodies. The other view, apart from this diversity of parts of the world, regards the earth as enjoying the same perfection as other integral bodies in the universe; in short, to be a moveable and mobile body, no less than the moon, Jupiter, Venus or any other planet. Later, many detailed parallels were drawn between the Earth and the Moon. More comparisons have been made with the moon than with other planets, perhaps because we have more and more reasonable evidence about the first due to its closer proximity. And having finally established that this second opinion is more credible than the other, it seems to me that our next step must be to examine whether the earth is to be considered immobile, as many have hitherto believed, or mobile, how many ancient philosophers believed and how others of modern times do; and, if mobile, what may its movement be.

OINTMENT. Now I know and recognize the signposts along our street. But before I begin and continue again, I must tell you that I question that last statement, namely our conclusion in favor of the notion that the earth is endowed with the same properties as the celestial bodies. For I have not finalized this, any more than I decide any other controversial proposal. My intention was just to present those arguments and answers on both sides - those questions and solutions that others have considered so far (along with some that have come to mind after much thought) - and then those Decision to leave to the judgment of others. .

SAGR. I let myself be carried away by my own feelings, and believing that what I felt in my heart should be felt by others, I made this conclusion general, which should be kept secret. That was really a mistake on my part, not least because I don't know the opinions of Simplício here.

POTATOES. I will confess that I spent the night pondering yesterday's material and I really think it contains many beautiful insights that are new and powerful. But I'm much more impressed by the authority of so many great authors, and especially... You shake your head, Sagredo, and smile as if you had spoken nonsense.

SAGR. I'm just smiling but believe me I can hardly hold my laughter because I remember a situation I witnessed not many years ago with some of my friends that I could mention for you too.

OINTMENT. Maybe it's better to tell us so that Simplicio doesn't think further, your joy was for him.

SAGR. I would love to. One day I was at the house of a very famous doctor in Venice, whither many people came for their studies, and others occasionally out of curiosity, to witness an anatomical dissection being carried out by a man no less learned than himself. a careful and experienced anatomist. It was on this day that he investigated the source and origin of nerves, about which there is a notorious controversy between galenistic and peripatetic physicians. The anatomist showed that the large trunk of nerves that leaves the brain and runs through the neck, extends through the spine and then branches throughout the body, and that only a single thin thread, like a thread, reaches the heart. He turned to a gentleman whom he knew to be a peripatetic philosopher, and in whose account he had shown and demonstrated everything with unusual care, and asked this man if he was at last satisfied and convinced that the nerves came from the brain and not from the Brain originate...in the brain. the heart. The philosopher, after some thought, replied: “You have made me see this matter so clearly and tangibly that I would be compelled to admit it were it not for the contradiction of the text of Aristotle, which clearly states that the nerves come from the heart . it to be true."

POTATOES. Sir, I want you to know that this argument about the origin of nerves is by no means as decided and decided as some might like to believe.

SAGR. No doubt it never will be in the minds of such adversaries. But what you say in no way diminishes the absurdity of this wanderer's answer; who, unlike sense experience, presented no experiment or argument from Aristotle, but only the authority of his merehe said himself.

POTATOES. Aristotle achieved his great authority only because of the strength of his evidence and the depth of his arguments. However, one must understand it; and not only to understand him, but to be so completely acquainted with his books that one can form the fullest conception of them, and so that every word of them is ever before the mind. He did not write for the common people, nor was he obliged to line up his syllogisms in the usual trivial way; Instead, using the permuted method, he sometimes placed the proof of a theorem between texts that seemed to deal with other things. So one has to understand the whole grand scheme and be able to combine this passage with that, composing a text here and another far away. There is no doubt that one who possesses this ability will be able to extract from his books demonstrations of everything that can be known; because everything is in them.

SAGR. My dear Simplicio, since you don't mind having things scattered all over the place, and since you believe that by collecting and combining the various pieces you can squeeze the juice out of them, what will you and the other brave philosophers do with the texts then starting from Aristotle, I shall get by with the verses of Virgil and Ovid, make hundreds of them, and through them explain all the affairs of men and the mysteries of nature. But why do I speak of Virgil, or of any other poet?' I have a little book, much shorter than Aristotle or Ovid, in which all the science is contained, and with very little study the most complete ideas can be formed from it. It is the alphabet, and doubtless anyone who can correctly connect and arrange this or that vowel and this or that consonant can derive from it the truest answers to all questions, and from it derive lessons in all arts and sciences. In the same way, from several simple colors placed separately on his palette, a painter assembles a little of this, a little of that, and a little of the other, depicting people, plants, buildings, birds, fish, and much more dar A word represents the whole, visible object, no eyes or feathers or scales or leaves or rocks on your palette. Indeed it is necessary that none of the imitated things, or parts thereof, are really under the colors if you want the power to represent everything; For example, if there were feathers, these would serve to represent nothing but birds or feather dusters.

OINTMENT. And some gentlemen still alive and active were present when a doctor, who taught at a famous academy, carried the telescope described, but had not yet seen it, said that the invention was borrowed from Aristotle. After fetching a text, he found a certain spot where the reason I named the stars in the sky can be seen from the bottom of a very deep well during the day. At this point the doctor said, “Here you have the fountain that represents the tube; here the vague fumes from which the invention of the glass lens emerges; and finally here the amplification of vision by the rays passing through it, a transparent kind of denser and darker."

SAGR. This way of "containing" everything one can know is similar to the sense in which a block of marble contains a beautiful statue, or rather thousands of them; but the main point is to be able to reveal them. Better still, we could say that they are like the prophecies of Jehoiachin or the answers of pagan oracles, which are only understood after the events they foretold have come to pass.

OINTMENT. And why do you omit the prophecies of the astrologers, so plainly seen in the horoscopes (or should we say the configurations of the heavens), after their fulfillment?

SAGR. So the alchemists, swept away by their madness, discover that the world's greatest geniuses have never really written about anything but how to make gold; but in order to tell it without revealing it to the vulgar, this fellow has neatly hidden it one way and another under various disguises. And it's great fun to hear her commentary on the ancient poets, revealing the important mysteries hidden behind their stories... what the moon's love and descent to earth means to Endymion; his displeasure with Actaeon; the meaning of Jupiter turning into a shower of gold or a flame of fire; what great mysteries of art lie in the interpreter Mercury, in the kidnappings of Pluto and in the branches of gold.

POTATOES. I believe, and to a certain extent I know, that the world is not short of dizzying minds, but your madness must not lead to discrediting Aristotle, whom I think you sometimes speak of with very little respect. His long seniority alone and the mighty name he has earned among so many notable men should be enough to earn him respect among all scholars.

OINTMENT. It's not like that, Simplicio. Some of his followers are so exceedingly timid that they cause us (or rather would cause us, if we count their trifles) to despise him. Tell me, are you so gullible that you don't understand that if Aristotle had been there and listened to this doctor who wanted to make him the inventor of the telescope, he would have been much more angry with him than with those who laughed at him to have? This doctor and his interpretations ? Can you doubt that when Aristotle saw the new discoveries in heaven, he would change his mind and correct his books and adopt the most reasonable teachings to drive away from himself those people so feeble in spirit that they would be induced to do so ? leaving? pathetically maintaining everything he had already said? Well, if Aristotle were such a man as they imagine, he would have been a man of unruly mind, unruly spirit, and barbarous soul; a man of tyrannical will who regarded all others as foolish sheep and wanted his favorite decrees about meaning, experience, and nature itself. to themselves And since it is more practical to hide under someone else's cloak than to show oneself in public, in their timidity they do not dare to step away from him, and instead of making any changes in Aristotle's sky , they want to immediately deny which they see in the sky of nature.

SAGR. Such people remind me of that sculptor who had fashioned a huge block of marble into the image of a Hercules, or a thundering Jupiter, I forget what, and with consummate art rendered it so vivid and wild that all who saw it He was frightened. . he himself began to fear, though all his vivacity and vigor were the work of his own hands; and his terror was so great that he no longer dared to insult him with a hammer and chisel.

OINTMENT. I have often wondered why these stern defenders of Aristotle's word fail to recognize what a great impediment to his credit and standing they are, and the more they seek to increase his authority the more they actually belittle it. When I see them keen to make claims that I personally know are obviously false, and want to convince me that what they are doing is genuinely philosophical and would have been done by Aristotle himself, if that weakens my opinion, that he has really philosophized about others, more recesses count for me. If I saw them give in and change their minds about obvious truths, I would think they might have solid evidence for the ones they insist on that I don't understand or haven't heard.

SAGR. Or if indeed they felt as if they were betting too much on their own reputation and that of Aristotle by admitting that they were unaware of this or that conclusion discovered by others, it would be no lesser evil to seek it among his texts by collecting some of them according to the practice recommended by Simplício? For if all things that can be known are in these texts, it must follow that they can be discovered there.

OINTMENT. Sagredo, do not scoff at this prudent plan, which I think you are proposing with sarcasm. For not so long ago a famous philosopher wrote a book on the soul in which, beyond Aristotle's opinion on its mortality or immortality, he recites many other texts than those already quoted by Alexander. Of these he claimed that Aristotle did not even consider such matters there, let alone decide on them, and he gave others he had discovered himself in various distant places which tended toward evil. When he was warned that this would cause him difficulties in obtaining a license to publish, he wrote back to his friend that he would be quick to get one anyway because, barring further obstacles, he would have no difficulty in teaching of Aristotle to change. for in other texts and other expositions he might take the opposite view and still agree with Aristotle's sense.

SAGR. Oh, what kind of doctor is that! I am his command; for he will not allow himself to be imposed by Aristotle, but will let him be fooled and speak according to his own intentions! See how important it is to know how to take a break from the beach! One must not be able to do business with Hercules when he is standing among the Furies and angry, but when he is telling tales among the Lydian girls.

Oh, the unspeakable baseness of wretched minds! Become a slave voluntarily; accept the decrees as inviolable; to take it upon themselves to call themselves convinced and persuaded by arguments so "powerful" and "conclusively conclusive" that they themselves cannot say for what purpose they were written, or what conclusion they are meant to serve madness greater than each other even doubt whether this same author defended the affirmative or the negative side. Well, what is that but making an oracle out of a log and running to it for answers; fear him, revere him and adore him?

POTATOES. But if Aristotle is to be abandoned, who shall we have as our guide in philosophy? Suppose you name an author.

OINTMENT. We need guides in the forests and in the unknown lands, but in the plains and open places only the blind need guides. These people are best left at home, but anyone with eyesight and intelligence can lead them. I don't mean that one should not listen to Aristotle; Yes, I applaud the careful reading and study of his works, and blame only those who surrender themselves to him as slaves, to blindly sign whatever he says, considering it an untouchable decree, without looking for other reasons. This abuse brings with it another pervasive disorder that other people no longer bother to understand the power of its manifestations. And what's more repulsive in a public debate, when it comes to verifiable conclusions, than hearing it interrupted by a text (often written with a very different purpose) being thrown into an opponent's mouth? If you really want to continue this method of study, then drop the name philosopher and call yourself a historian or a memory specialist; for it does not befit those who never philosophize to usurp the honorable title of philosopher.

But it is better for us to return to the shore, so as not to get into a boundless ocean and not get out all day. Therefore, present arguments and demonstrations, simplicio ... whether yours or Aristotle's ... but not only texts and mere authorities, because our discourses must refer to the sensible world and not to that of the paper. And as in yesterday's dispute the earth was lifted out of darkness and exposed to the open sky, and the attempt to number it among the bodies we call celestial bodies did not prove so hopeless and despondent that it was left without a spark of life, we must proceed to examine the other proposition which holds it probable that the earth is fixed and entirely immobile with respect to its whole globe, and see what possibility there is of making it movable, and with what motion .

Well, since I am undecided on this question, while Simplicio is decided in favor of immobility with Aristotle, step by step he will justify his opinion, and I the answers and arguments of the other party, while Sagredo must tell us the workings of his mind and the Side to which he is attracted.

SAGR. That suits me fine as long as I keep myself free to mention what common sense dictates from time to time.

OINTMENT. In fact, I am asking you specifically to do this; for I believe that the authors on this subject have left out some of the simplest and, so to speak, most material considerations, so that only the more subtle and enigmatic ones are missing and may be desirable. And to look at her, what ingenuity could be better suited than Sagredo's sharp, piercing wit?

SAGR. Describe me however you like, Salviati, but please don't let us get into another kind of digression... the ceremonial. For now I am a philosopher, and I am at school and not at court (good brother).

OINTMENT. So let our reflections begin with the reflection that any motion which can be ascribed to the earth must necessarily remain imperceptible to us, and as if it did not exist, so long as we only look at earthly objects; for consequently, as inhabitants of the earth, we participate in the same movement. On the other hand, it is also necessary for it to manifest itself in a very general way in all other visible bodies and objects which, being separate from the earth, do not participate in this movement. Therefore, the true method of investigating whether any motion can be attributed to the earth, and if so what it might be, is to observe and consider whether the individual bodies of the earth exhibit an appearance of motion common to all equally due. For a motion that is only perceived in the moon, for example, and does not affect Venus or Jupiter or the other stars, cannot possibly come from the earth or anything other than the moon.

Now there is a motion which is most general and supreme, and by which the sun, moon, and all other planets and fixed stars, in a word, the whole universe except the earth, seem to be moved. as a journey from east to west within 24 hours. As far as the first phenomena are concerned, this can logically only affect the earth and the rest of the universe, since the same phenomena would prevail in one situation as in the other. Thus, Aristotle and Ptolemy, who fully understood this reasoning, in their attempt to prove the immobility of the earth, do not argue against any motion other than this daily motion, although Aristotle points to another motion, suggested to them by an ancient writer is attributed to . . . we will speak of this at an appropriate point.

SAGR. I'm quite convinced of the strength of his argument, but it raises a question for me that I can't get rid of, and it is this: Copernicus attributed motion to the earth other than diurnal motion. According to the rule just established, this must remain imperceptible to all Earth observations, but be visible to the rest of the Universe. It seems to me that one can conclude, as a necessary consequence, that he was either grossly wrong in attributing to the earth a motion which corresponded to no celestial phenomenon at all, or that, if the corresponding motion exists, Ptolemy was equally wrong, by not explaining it. , as he explained to the others.

OINTMENT. This is very reasonably questioned, and if we deal with the other movement you will see how much Copernicus surpassed Ptolemy in keenness and penetrating mind, seeing what the latter did not see - I mean the wonderful agreement with the this movement is reflected. on all other celestial bodies. But let us leave that for the moment and return to the first consideration, to which I shall, beginning with the most general things, give those reasons which seem to favor the motion of the earth, and then hear Simplicius' refutation of the same.

Let us first consider only the immense volume of the stellar sphere in contrast to the smallness of the terrestrial sphere, contained so many millions of times in the former. Now when we think of the speed of movement required to make a complete turn in a single day and night, I cannot convince myself that anyone can find the most reasonable and believable thing to do that it was the celestial sphere that made the movement. turned, and the globe that remained fixed.

SAGR. If, for all the variety of effects that might exist in nature in dependence on these movements, all the same consequences followed indifferently from both positions, nevertheless my first general impression would be this: I would think that everyone who thinks about it would do so It would be wiser for the entire universe to move to keep the earth solid, it would be wiser than someone who climbed to the top of his dome just to take a look at the city and its environs, and then demanded, that the entire field should revolve around him so he didn't have to bother turning his head. Undoubtedly, there are many and great advantages to be gained from the new theory, and not from the previous one (which, in my opinion, is comparable to the previous one, or even surpasses it in absurdity), making the first more believable than the second. But perhaps Aristotle, Ptolemy, and Simplicius should collect their advantages against us, and present them if any; otherwise I realize that there is not and cannot be.

OINTMENT. Despite many deliberations, I couldn't tell any difference, so it seems to me that I've figured out that there can't be any difference; so I find it pointless to look for another one. For consider: movement, insofar as it is movement and functions as movement, exists insofar as it is relative to things which do not have it; and among the things that participate equally in every movement, he does not act and is as if he did not exist. This is how the goods that are loaded onto a ship leaving Venice, pass through Corfu, Crete, Cyprus and on to Aleppo. Venice, Corfu, Crete, etc. they stand still and do not move with the ship; but as to the sacks, boxes, and bales with which the boat is loaded, and as to the ship itself, the movement from Verflice to Syria is nothing and in no way alters their relation to each other. This is because it is common to all and they all share in it equally. If a sack of the ship's cargo were to be shifted even an inch from a chest, that alone would be a greater movement for him than the journey of two thousand miles which they all traveled together.

POTATOES. This is a good and sound doctrine and entirely peripatetic.

OINTMENT. I should have thought it was a bit older. And I wonder if Aristotle fully understood it by selecting it from a good school of thought, and if by altering it in his writings he made it a source of confusion among those who want to keep all he said has. When he wrote that everything that moves moves about something immovable, I think he misunderstood the statement that everything that moves moves relative to something immovable. This proposal suffers from no difficulties while the other has many.

SAGR. Please do not abort the thread, but continue with the argument already started.

OINTMENT. It is evident, therefore, that the motion common to many movable things is useless and irrelevant to the relation of these movable things to one another, since nothing is changed between them, and that it is operative only in the relation which they have to other bodies who do not own the movement between which your location is changed. Having now divided the universe into two parts, one of which is necessarily movable and the other immovable, it is the same to make the earth move of itself and to make all the rest of the universe move as far as it is possible depend on whether it is such a step. For the effect of such movement is only in the relation between the celestial bodies and the earth, which relation is the only one that is changed. Now, if the exact same effect occurs when the earth is set in motion and the rest of the universe stands still, or the earth alone remains fixed while the entire universe shares the motion, who is going to believe that nature (which is the general consensus to be the case is) not acting through many things when he can do it through a few) chose to have immense numbers of extremely large bodies move at unimaginable speeds in order to achieve what could be achieved by a moderate movement of a single body around your body could have been achieved. center yourself?

POTATOES. I don't quite understand why this great movement of the sun, the moon, other planets and the innumerable fixed stars means nothing. Why do you say that it is nothing that the sun moves from one meridian to another, rises above this horizon and sinks below this, causing now day and now night; and that the moon, the other planets, and the fixed stars vary in a similar way?

OINTMENT. Each of these variations that you recite to me is nothing except in relation to the earth. To see that this is true remove the earth; Nothing remains in the universe of the rising and setting of the sun and moon, nor of horizons and meridians, nor of day and night, and in a word, this movement will never produce any change in the moon or the sun, or any stars you want , fixed or movable. All these changes relate to the earth, they all mean nothing except that the sun is now over China, then over Persia, then over Egypt, Greece, France, Spain, Europe, America, etc. it applies to the moon and the rest Celestial bodies, whereby this effect occurs exactly the same if you let the earth rotate around itself without enveloping the largest part of the universe.

And let's double the difficulty with another very big one, namely this one. If this great movement is ascribed to the heavens, it must be in the opposite direction to the specific movement of all the planetary spheres, each of which undeniably has its own west-to-east movement, which is very uniform and moderate, and must then be forced upon the other side to run; that is, from east to west, with this very rapid diurnal movement. By putting the earth itself in motion, the opposition of motions is eliminated, and the single west-to-east motion accommodates and fully satisfies all observations.

POTATOES. As for the opposition of motions, it doesn't matter because Aristotle shows that circular motions are not opposed to each other, and their opposition cannot be said to be true opposition.

OINTMENT. Does Aristotle show this, or does he just say it because it suits certain of his designs? If, as he himself explains, opposites are things that destroy each other, I see no less conflict between two moving bodies meeting along a circular line than if they had met along a straight line.

SAGR. Please stop for a moment. Tell me, Simplicto, if two knights meet in the open field, or two whole squadrons, or two fleets at sea, attack each other, crush and sink each other, would you call their encounters opposites?

POTATOES. I have to say they were against it.

SAGR. So why don't two circular motions contradict each other? On the surface of the earth or sea, which are known to be spherical, these motions become circular. Do you know that circular motions are not opposites, Simplicio? They are those of two circles touching on the outside; When one is rotated, the other naturally moves in the opposite direction. But if one circle has to be within the other, then I am. impossible for their movements to be made in opposite directions without resisting each other.

OINTMENT. "Contrary" or "not to the contrary" are quibbles of words, but I know that with facts it's much easier and more natural to put it all in one sentence than to introduce two, whether you want to call them opposite or opposite. But I do not suppose that the introduction of two is impossible, nor do I intend to draw any necessary proof from it; just a higher probability. Improbability I. This is shown for the third time in the relative disturbance of the order that we certainly see existing among the celestial bodies whose orbit is not in doubt but very certain. This order is such that the larger orbits complete their revolutions in longer times, and the smaller ones in shorter times; thus Saturn, which describes a circle larger than the other planets, completes it in thirty years; Jupiter rotates in its minor in twelve years, Mars in two; the moon completes its much smaller circle in a single month. And we see no less reasonably that of the satellites of Jupiter (Sterne, Medici), (Note: Galileo named the moons he discovered "medicine stars" after his patron, the Grand Duke of Tuscany, to whom this book is dedicated.) the one closest to this planet makes its rotation in a very short time, that is, in about forty-two hours, the next in three and a half days; the third in seven days and the furthest in sixteen. And this very harmonious process will not be disturbed in the least if the earth is rotated around itself in twenty-four hours. But if it is desired that the earth remain motionless, it is necessary after passing from the short period of the moon to the other successively greater ones, and finally in two years to that of Mars, and in twelve years to the greater of Jupiter and henceforth This to still greater Saturn, whose period is thirty years... it is necessary, I say, to get beyond that to another incomparably greater sphere, and to complete this in twenty-four hours a complete revolution. Well, this is the least disorder that can be introduced, for if one were to pass from the sphere of Saturn to the celestial body, and make the latter so much larger than that of Saturn that it would be proportionate to a very slow movement of many thousands of years, comparatively, would be one much bigger jump needed to jump beyond that to an even bigger one and then spin it around in twenty-four hours. But by giving mobility to the land, the order between periods is observed very well; from the very slow sphere of Saturn one arrives at the perfectly immobile fixed stars, and a fourth necessary difficulty is avoided by assuming that the sphere of the stars is mobile. This difficulty is the tremendous disparity between the motions of the stars, some of which would move very quickly in wide circles and others very slowly in tiny circles, depending on whether they are farther or nearer the poles. This is really a nuisance, for as we see that all bodies whose motion is undoubted move in large circles, so it does not seem to have been good judgment to arrange the bodies so that they move in circles at vast distances need the others, center them and then let them move in tiny little circles.

Not only will the size of the circles and consequently the speed of movement of these stars be very different from the orbits and movements of some others, but (and this will be the fifth difficulty) the same stars will constantly change their circles and their speeds. , since those who were on the celestial equator two thousand years ago and consequently described large circles with their motion are found many degrees away in our time and have to be slowed down in their motion and reduced to motion in smaller circles. Indeed, it cannot be ruled out that there will come a time when some of the stars, which have always been moving in the past, will be brought to a standstill upon reaching the pole and after that time begin to move again; while all stars that are certainly moving describe very large circles on their orbits and remain unchangeable in them.

For those who judge well, the improbability - and this is the sixth difficulty - is increased by the incomprehensibility of what is called the "solidness" of this vast sphere, in the depths of which so many stars are firmly anchored that, without their Changing place at least be transported to each other so harmoniously with such an inequality of movements. But if the heavens are fluid (as there is much more reason to believe), so that each star in it moves of itself, what law will govern its movement so that, seen from the earth, it appears as if it were would be done? in a single? Sphere" For this to happen, it seems to me that immobilizing them is so much more effective and convenient than having them roam around, just as it is easier to count the myriad tiles that are placed in a courtyard are when they number a troop of children running over them.

Finally, as to the seventh objection, if we ascribe the daily rotation to the highest heaven, then it must be of such strength and power that it carries with it the innumerable hosts of fixed stars, all gigantic bodies and much larger than the earth and how the transported planetary spheres, although naturally the two move in opposite directions. Moreover, it must be admitted that the element of fire and most of air are also hasty, and that only the small terrestrial body of this power remains defiant and resilient. This seems to me to be the most difficult thing; I don't understand why the earth, a floating body balanced at its center and indifferent to motion or rest, placed and surrounded by an enveloping liquid, should not yield to such a force and be swept along. We find no such objection when we move the earth, a small and insignificant body compared to the universe and therefore incapable of exerting any violence.

SAGR. I am aware that some ideas are swirling in my own imagination, confusedly awakened in me by these arguments. If I want to focus my attention on the things to be said, I have to try to organize them better and, if possible, give them the right construction. Maybe it will help me to express myself more easily when conducting the interrogation. I therefore first ask Simplicio whether he thinks that the same simple moving body can naturally participate in several movements, or whether he likes only a single movement, which is his own natural movement.

POTATOES. For a simple moving body there can be only one movement and nothing else that naturally suits it; he can only own all the others on the side and through participation. Thus, when a man walks across the deck of a ship, his own motion is that of walking, while the motion that brings him to port is his of participation; for he could never get there on foot unless the ship carried him by its motion.

SAGR. Second, tell me about the motion imparted by participation to a moving body when it is itself moved by a motion other than that in which it is participating. Again, does this joint movement have to reside in a subject, or can it actually exist in nature without any other support?

POTATOES. Aristotle answers all of these questions for you. He tells you that just as there is only one movement for a moving body, there is only one moving body for that movement. Consequently, no motion can exist or even be imagined except as inherent in its subject.

SAGR. Now thirdly I want you to tell me if you believe that the moon and the other planets and celestial bodies have their own movements and what they are.

POTATOES. They have and are those motions by which they pass through the zodiac - the moon in a month, the sun in a year, Mars in two, the starry sphere in so many thousands. These are your own natural movements.

SAGR. Now to the movement with which the fixed stars, and with them all the planets, rise and fall every twenty-four hours and return to the east. How is it yours?

POTATOES. You have it for participating.

SAGR. Then it does not dwell in them; and neither dwelling in them nor able to exist without a subject, the right and natural movement of another sphere must be made.

POTATOES. In this regard, astronomers and philosophers have discovered another very high sphere without stars, to which the diurnal rotation naturally belongs. This is what they calledcell phone first; it enlivens with him all the lower spheres, contributing and sharing his movement with them.

SAGR. But if all things can proceed in the most perfect harmony, without introducing other vast and unknown spheres; no other movements or speeding reported; if every sphere has only its single motion, not mixed with opposing motions, and everything proceeds in the same direction as it must, when everything rests on a single principle, why discard the means and assent to such things? ?strange and arduous conditions?

POTATOES. The question is to find a simple remedy, and that's it.

SAGR. This seems to me to be found, and quite elegantly so. Make the countrycell phone first; that is, make it revolve in twenty-four hours, just like all the other spheres. Then, without transferring this movement to any other planet or star, they will have all their risings, their setting and, in a word, all their other appearances.

POTATOES. The bottom line is being able to move the earth without causing a thousand inconveniences.

OINTMENT. All inconveniences will be removed as soon as you present them. So far only the first and most general reasons have been given, which make it not entirely improbable that the daily rotation is attributable to the earth and not to the rest of the universe. Nor do I present them as inviolable laws, only as plausible reasons. For I understand very well that a single experiment or conclusive evidence to the contrary would be enough to refute this and many other probable arguments. So there is no need to stop here; Rather, let us proceed and accept what Simplicius replies and what greater probabilities or more solid arguments are presented on the other side.

POTATOES. I shall first say some general things about all these considerations taken together, and then go into some specifics.

It seems to me that you are basing your whole case on the greater ease and simplicity of creating the same effects. As far as your matter is concerned, consider the motion of the earth alone to be equal to the motion of everything else in the universe but the earth, while from the point of view of action you find the first much easier than the second. To which I reply that I feel the same way when I think of my own powers, which are not only finite but very weak. But given the infinite power of the mover, moving the universe is as easy as moving the earth, or even moving a straw. And if power is infinite, why shouldn't a large part of it be exercised instead of a small one? From this it seems to me that the general argument is ineffective.

OINTMENT. If I had ever said that the universe does not move for want of energy in the machine, I would have been wrong and your correction would have been in order; I grant that it is as easy for an infinite force to move a hundred thousand things as it is to move one. But what I said does not refer to the mover, just furniture; not only in relation to their resistance, which is certainly less true of the earth than of the universe, but also in relation to other details which will now be considered.

Next to your assertion that a large part of an infinite force can be better exercised than a small part, I reply that one part of the infinite is not greater than another if both are finite; Nor can one say of an infinite number that one hundred thousand is a greater part than two I, although the former is fifty thousand times greater than the latter. And if what is needed to move the universe is finite force, then more of the infinite force would go unexploited, even if that is very large compared to what would be needed to move the earth alone move. , nor what would remain unused would be less than infinite. Therefore, there is no point in using a little more or less power for a specific effect. Moreover, the effects of such a force have not only the daily movement as their object and object, for there are many other movements of the universe that we know, and many more that may be unknown to us.

So if we turn our attention to the motion of bodies, not questioning that moving the earth is a shorter and more rapid operation than moving the universe, and noting the many other simplifications and conveniences that flow from this alone, it's much more likely that the daytime motion belongs only to Earth and not to the rest of the universe other than Earth. A very true maxim of Aristotle speaks for it, which teaches thiswhat can be done for less is done for more in vain. (Note: There is no point in using too many to do what you can do with less.)

POTATOES. In referring to this axiom you have omitted a small clause which means everything, especially for our present purposes. The omitted detail is aeque bene; it is therefore necessary to examine whether both assumptions can satisfy usas well asin all aspects.

OINTMENT. Whether we are equally satisfied with both positions is included in the detailed examination of the phenomena to be fulfilled. because we discussedby hypothesishitherto and will continue to argue so, assuming that both positions seem equally appropriate. I therefore suspect that this detail, which you have left out of my explanation, was added by you quite unnecessarily. Saying "equally good" designates a relationship that necessarily requires at least two terms, a thing that cannot be referred to by itself, for example one cannot say that rest equals rest with rest. Therefore, the statement, "It is futile to use many to accomplish what can be accomplished with less" implies that what needs to be done must be the same, not two different things. And because the same cannot be said to be equally well done with itself, the addition "as well" is redundant and an inclusive relation,

SAGR. If we don't want to repeat what happened yesterday, let's get back on topic; and you, Simplicio, begin to bring forth those difficulties which, to your mind, seem to contradict this new arrangement of the universe.

POTATOES. The arrangement is not new; on the contrary, it is older, as shown by Aristotle, who refutes it, his refutations being the following:

"First, whether the earth is moved in itself by being placed in the center, or in a circle when removed from the center, it must be moved violently with such movement, for that is not its natural nature Movement. If it were, it would also belong to all of its particles. But each of them is moved towards the center along a straight line. Being so forced and supernatural, it cannot be eternal. But the order of the world is eternal; so etc.

"Second, all other circularly moving bodies seem to lag behind and be moved with more than one motion except thatcell phone first. Hence it would be necessary for the earth to also move with two motions; and if so, there must be variations in the fixed stars. But such are not to be seen; Instead, the same stars always rise and set in the same place, without any variation.

"Third, the natural motion of the parts and the whole is toward, and therefore resting in, the center of the universe." He then discusses the question of whether the motion of the parts is towards the center of the universe or just towards the center of the earth, concluding that their real tendency is towards the former and that they just happen to be towards the latter. The topic was discussed at length yesterday .

Finally, he backs this up with a fourth argument, taken from experiments with heavy bodies falling vertically from a great height to the earth's surface. Likewise, projectiles fired straight up fall straight down the same line again, even though they were fired at an immense height. These arguments are necessary proofs that their movement is toward the center of the earth, which awaits and receives them without moving at all.

He then hints at the end that astronomers add other reasons to support the same conclusions - that the earth is at the center of the universe and is immobile. One is that all of the phenomena seen in the movements of the stars correspond to this central position of the earth, a correspondence they otherwise would not have. The others, introduced by Ptolemy and other astronomers, I can give you now, if you will; or after you have said as much as you like on these by Aristotle.

OINTMENT. The arguments advanced on this subject are of two kinds. Some pertain to terrestrial events unrelated to the stars, and others stem from the appearances and observations of celestial things. Aristotle's arguments relate mainly to things around us, leaving others to astronomers. So it will be good, if it seems so, to look at the experiments taken from Earth, and then we will see the other species. And since some of these arguments are advanced by Ptolemy, Tycho and other astronomers and philosophers and accept, confirm and support those of Aristotle, they can all be considered together to avoid having to give the same or similar answers. Double. Therefore. Simplicio, introduce them if you like; or if you want me to take that burden off your shoulders, I am at your disposal.

POTATOES. It will be better for you to raise them because after studying them more you will have them on hand more and also in larger numbers.

(Salviati enumerates the arguments against earth motion: an object falling from a great height falls directly on the ground at right angles), while an object falling from the mast of a moving ship does not fall vertically but slightly behind the ground in the direction of the earth's movement of ships . Similar results are obtained by throwing or throwing an object up from a great height. Cannonballs fired east and west at point-blank range travel the same distance; those shot north and south do not deviate from their course.

If the earth were moving west at the speed required for one rotation in 24 hours, clouds could only move east, we would feel a constant east wind, and birds could never fly fast enough to turn west move. ; none of that happens.

If the earth were to spin at that speed, pigs (and everyone and everything else) would fly off the face of the earth due to centrifugal force.

Simplício, who has never heard these arguments, is delighted and convinced and ready to go home, but he has respect for Sagredo and Salviati, who seem to think the matter is still unresolved.

Refuting these arguments is the occupation of Salviali and Sagredo for most of the day.)

OINTMENT. But is it not your opinion and that of the author and Aristotle and Ptolemy and all their followers that earth, water and air are of the same nature, that they form immobile around the centre?

POTATOES. This is seen as irrefutable truth.

OINTMENT. Thus the argument for the different nature of these elements and elementary things is not drawn from this common natural state of rest with respect to the center, but must be learned by observing other properties which they do not have in common. Whoever would only deprive the elements of this common state of rest and leave all other actions to them would by no means block the path that leads us to the consciousness of their nature.

Copernicus now takes nothing from them but this common rest and leaves them heaviness or lightness; movement up or down, slow or fast; rarity and density; the qualities of shock, cold, dry, wet; and in a word everything else. Therefore, nowhere in the Copernican position is there such nonsense as this author imagines. Agreement in an identical movement means no more and no less than agreement in an identical state of rest, as far as diversification or non-diversification of natures is concerned. Now tell me if he has any other arguments against it.

POTATOES. A fourth objection follows, which again stems from an observation of nature. For similar bodies have movements that agree in kind, or agree in rest. But in Copernicus's theory, bodies that agree in kind and are fairly similar to each other would have vast differences in motion, or even be diametrically opposed. For the stars, which are so similar to each other, would have such different movements that six planets would continuously orbit each other, while the sun and the fixed stars would remain motionless forever.

OINTMENT. The form of this argument seems valid to me, but I believe that its content or application is wrong, and if the author persisted in this assumption the consequences would be directly opposite to his. The argument method is as follows:

Among the bodies of the world there are six that are constantly moving; these are the six planets. Of the others (i.e. the earth, the sun and the fixed stars), the question arises as to which are moving and which are stationary. When the earth stands still, the sun and fixed stars must move, and it can also happen that the sun and fixed stars stand still when the earth moves. With this question in mind, we ask which ones are most likely to be assigned the movement and which ones remain.

Common sense dictates that movement belongs to those most like in nature and nature the bodies that undoubtedly move, and rest to those most different from them. Since perpetual rest and perpetual motion are very different events, it is evident that the nature of a body that is always in motion must be very different from that which is always fixed. Therefore, in case of doubt about motion and rest, let us find out whether we can ask, by another relevant condition, which - the earth or the sun and the fixed stars - are most similar to bodies known to be mobile,

Now see how nature, which favors our desires and desires, presents us with two striking conditions, no less different from motion and rest; they are light and dark—that is, they are naturally light, or they are faint and entirely devoid of light. Therefore, bodies that shine with inner and outer splendor are of a very different nature from bodies that are devoid of all light. Now the earth is deprived of light; the sun is most glorious in itself, and the fixed stars are no less so. The six moving planets are entirely devoid of light, like Earth; hence its nature is similar to that of the earth and distinct from the sun and the fixed stars. Therefore the earth moves and the sun and the star ball are immobile.

POTATOES. But the author will not admit that the six planets are dark, and will stand firm in this denial; or he will argue the great correspondence in nature between the six planets and the sun and the fixed stars, and the contrast between the latter and the earth in terms other than those of darkness and light. Indeed I now see that here in the fifth objection which follows is set forth the great inequality between the earth and the celestial bodies. He writes that according to the Copernican hypothesis there would be great confusion and trouble in the system of the universe and between its parts, because of its placement among the celestial bodies (immutable and incorruptible according to Aristotle, Tycho and others); between such bodies of nobility, by the admission of all (including Copernicus himself, who declares them to be orderly and ordered in the best possible way, and who deprives them of every inconstancy of power); because of its placement between such pure bodies as Venus and Mars, that hole of all perishable matter; that is, the earth with the water, the air and all their mixtures!

How much superior is a division, and how much more befitting is it of nature—yes, God Himself, the Architect—to separate the pure from the impure, the mortal from the immortal, as all other schools teach and show us that the impure and sick the materials are locked in the narrow arc of the moon's orbit, above which the celestial objects rise in an unbroken line!

OINTMENT. It is true that the Copernican system creates disturbances in the Aristotelian universe, but we are dealing with our own real and present universe.

If this author concludes from the incorruptibility of the latter and the perishability of the former, in the sense of Aristotle, a difference in nature between the earth and the celestial bodies, from which he concludes that the sun and fixed stars are in motion, with the earth being motionless, then he wanders in one Paralogism and accepts what is at stake. Because Aristotle wants to deduce the incorruptibility of the celestial bodies from their movement, and it is discussed whether this comes from them or from the earth. Enough has been said about the madness of this rhetorical deduction. What is more vague than to say that the earth and the elements are banished and segregated from the celestial sphere and locked in lunar orbit? Isn't the lunar orbit one of the celestial spheres, and in your opinion isn't it right at the center of all of them? This is truly a new way of separating the unclean and sick from the healthy - giving the infected a place in the heart of the city! I should have thought that the leper colony would be removed from there as far as possible.

Copernicus admires the arrangement of the parts of the universe because God placed the great lamp that is supposed to shine its mighty splendor over the whole temple right in the center and not to one side. As for the globe that lies between Venus and Mars, let me say a word about it. You can try to remove it yourself on behalf of this author, but please let's not entangle these little phrases of rhetoric in the rigor of the demonstration. Let us rather leave them to orators, or rather poets, who know best how to glorify with their grace the most abominable and sometimes even pernicious things. If we have anything left to do now, let's get on with it.

POTATOES. Here is the sixth and final argument in which he considers it improbable that a corruptible and volatile body could have a regular perpetual motion machine. He supports this through the example of animals which, although moving with their natural movement, become tired and need to rest to restore their energies. And what is this movement compared to the movement of the earth, which is immense compared to theirs? However, the earth moves in three contradictory and disturbingly different ways! Who could say such a thing but one who swore in his defense?

In this case, too, there is no usage in Copenic to say that because this motion is natural to the earth and not forced, it produces effects opposite to those of forced motions; and that things given an impulse are destined to disintegrate and cannot long exist, while those created by nature remain in their ideal arrangement. This answer, I say, is not good; falls before our answer. For the animal is also a natural body, not an artificial one; and its movement is natural, derived from the soul; that is, from an inner principle, while that movement is forced whose principle lies outside and to which what is moved contributes nothing. However, if the animal continues its movement for too long, it will become exhausted and even die if it persistently tries to force itself.

So you see how everywhere in nature there are traits contrary to Copernicus' position, and never one in favor of it. And so that I don't have to slip into his opponent's shoes again, hear what he has to say against Kepler (with whom he disagrees) about what this Kepler has to say about those who find it inappropriate or even impossible to do so expand stellar sphere as far as the Copernican position requires. Kepler objects to this saying: "It is harder to determine the size of matter by accident than to increase matter without accident: that is why Copernicus makes it more probable that the fixed star sphere increases without motion than Ptolenweza, that the motion increases fixed stars. Stars with immense speed."("It is more difficult to extend the property beyond the thing's model than to enlarge the thing without enlarging the property. Copernicus is therefore more likely to be on his side by magnifying the sphere of stars as motionless than Ptolemy who is the motion of the fixed stars increased by a tremendous speed.") The author resolves this objection and marvels at the fact that Kepler was so deceived as to say that the Ptolemaic hypothesis increases motion beyond the subject's model, for it seems to him that this the case is only increasing in proportion to the model, and that according to this the speed of movement increases.He proves this by imagining a millstone making one revolution in twenty-four hours, the movement of which is to be called very slow, supposes that its Radius extended to the Sun; the velocity of its end will be equal to that of the Sun; extending it to the stellar sphere, wi r be equal to the speed of the fixed stars, and the millstone will be very slow. Next, applying this reflection on the millstone to the star sphere, imagine a point on the radius of this sphere as near to its center as the radius of the grinding wheel. The same motion that is very fast on the star sphere will be very slow at this point. The size of the body makes it very fast or very slow, and so the speed does not increase beyond the subject's model, but rather increases with the subject and its size, quite contrary to what Kepler thinks.

OINTMENT. I do not believe that this author had such a bad and low opinion of Kepler that he could persuade himself that Kepler did not understand that the furthest point of a line drawn from the center to the starry sky moves faster than a point up the emerge. the same line no more than two meters from the centre. Hence he must have seen and fully understood that Kepler meant that it was less unreasonable to magnify an immovable body to an enormous size than to ascribe excessive speed to an already huge body, respecting proportionality (Module), that is, following the pattern and example of other natural bodies, which can be seen to decrease in velocity as the distance from the center increases; that is, the period of rotation for them requires a longer time. But in the state of rest, which can neither be increased nor decreased, body size does not matter. So if the author's answer is to have anything to do with Kepler's argument, this author must believe that for the motive principle it is the same whether a very small body or a huge body is moved at the same time, the increase in velocity is a direct consequence the increase in size. However, this contradicts the architectural law of nature observed in the model of smaller spheres, just as we see with planets (and even more clearly with Jupiter's satellites) that smaller spheres spin at shorter times. Because of this, Saturn's orbital period of 30 years is longer than the period of any smaller sphere. Now, going from this to a much larger sphere and rotating it in twenty-four hours can truly be said to be beyond the rule of the model. So that, if we think things over carefully, the author's answer does not go against the spirit and idea of ​​the argument, but against its expression and way of speaking. And here, too, the author is wrong; he cannot deny that he has in any way distorted the meaning of the words, accusing Kepler of gross ignorance. But the swindle is so gross that, despite all the censorship, it could not lessen the impression that Kepler's teachings made on the minds of scholars.

Then the objection to the constant movement of the earth, drawn from the impossibility of maintaining it without getting tired, since animals, moving naturally and from an inner principle, get tired and need rest to stretch their limbs relax.

SAGR. I seem to hear Kepler reply that there are also animals which refresh themselves from weariness by rolling on the ground, and that therefore there is no weariness of the earth to be feared; It can even be reasonably said to enjoy an eternal and tranquil repose, holding itself in an eternal roll.

OINTMENT. Sagredo, you are very scathing and sarcastic. Let's put all jokes aside because we are dealing with serious matters.

SAGR. Excuse me, Salviati, but what you just said is not as relevant to me as you might make it out to be. For a movement designed to rest and remove the fatigue of a travel-weary body can serve to remove it much more easily, just as preventative remedies are easier than curative ones. And I'm sure if the movement of animals happened as it is attributed to the earth, they wouldn't get tired. For the fatigue of the animal body arises, in my opinion, from moving only one part and the rest of the body. For example, when you walk, you only use your thighs and legs to support yourself and everything else, but on the other hand you see the movement of the heart as restless because it's moving on its own.

Also, I don't know how true it is that animal movement is natural and unrestricted. Rather, I believe it can truly be said that the soul naturally moves the animal's limbs with supernatural movements. Because if the upward movement is unnatural for heavy bodies, lifting such heavy bodies as the thigh and leg to walk cannot be done without force and therefore not without motor fatigue. Climbing a ladder carries a heavy body up against its natural inclination, with fatigue resulting from the weight's natural reluctance to such movement. But if a moving body has a motion to which it has no aversion, what fatigue or diminution of strength and power is to be feared on the part of the mover? And why waste power where it's not being used?

POTATOES. The author raises his objection to the opposite movements by which the globe is said to be moving.

SAGR. It has already been said that they are not opposed at all, and that the author is sorely mistaken in this that the force of his objection turns against the opponent himself, if he so choosescell phone firstit carries with it all the lower spheres, as opposed to the movement they constantly apply simultaneously. So it's hercell phone firstthat it has to get tired, because apart from the movement it has to take with it many other spheres, which also oppose it with a counter-movement. Hence the last conclusion reached by the author, that in the study of the effects of nature one always finds things favorable to Aristotelian and Ptolemaic opinion, and never anything which does not contradict Copernicus merits careful consideration. It is better to say that if one of these positions is true and the other necessarily false, it is impossible that any right reason, experiment, or argument can be found to favor the false one, since none of these things can contradict the true Position. There must therefore be a great discrepancy between the reasons and arguments put forward by one side and the other for and against these two opinions, the strength of which I leave to you, Simplicius, to judge.

OINTMENT. Impressed by the agility of your wit, Sagredo, you took the words right out of my mouth as I was about to respond to the author's last argument; and although you have answered more than adequately, I would certainly like to add what I more or less had in mind.

He considers it a very unlikely thing that a mortal and ephemeral body like the earth can continually move with a regular movement, especially when we see that animals eventually become exhausted and need rest. And for him this improbability is increased by the fact that this movement is immeasurably larger compared to that of animals. Now I do not understand why the speed of the earth should bother him now, when the much larger stellar sphere does not bother him more than what he ascribes to the speed of a millstone, which works but one revolution every 24 hours. If the speed of rotation of the earth, because it corresponds to the millstone model, does not imply a consequence of a larger momentum, then the author can stop worrying about the exhaustion of the earth; for not even the most sluggish and sluggish animal - not even a chameleon, I say - would be exhausted by not moving more than 15 or 20 feet every 24 hours. But if he intends to consider velocity absolutely, and no longer according to the pattern of this millstone, then, since the moving body must traverse a very large space in twenty-four hours, he must be much less willing to concede that to the starry sphere which with at a speed incomparably greater than that of the earth, must carry thousands of bodies, each much larger than the globe.

It remains for us now to see the evidence by which this author concludes that the new stars of 1572 and 1604 had a sublunar position, and were not celestial, as the astronomers of the day were commonly believed; really a big undertaking. But as these writings are new to me, and long because of so many calculations, I thought it more convenient to go over them as best I could between this evening and tomorrow morning; and then tomorrow, back to our usual discussions, I'll tell you what I took from it. Then, when there is enough time, we will discuss the annual movement attributed to the earth.

Meanwhile, if there is anything else you wish to say, especially to you, Simplicio, on matters pertaining to this diurnal movement which I have been investigating for myself for so long, we have a little time to speak of it.

POTATOES. I have nothing more to say, except that today's discussions certainly seem to me full of the sharpest and most ingenious ideas put forward by the Copernican side in support of earthmoving. But I'm not entirely convinced to believe them; after all, the things that have been said prove nothing, except that the reasons for the country's stability are not necessary reasons. However, this does not deliver an opposite side that necessarily convinces anyone and proves the mobility of the earth.

OINTMENT. I have never attempted, Simplicio, to change your mind; much less do I wish to make a final judgment on such an important dispute. My only intention was, and still will be, in our next debate, to make it clear to you that those who believed that very rapid movement every 24 hours affects only the earth and not the entire universe with just one exception of the earth, isn't it, they were blindly convinced of the possibility and necessity of it. Rather, they watched, listened, and questioned the reasons for the opposite opinion very closely and did not dismiss them lightly. With the same intention, if it is your wish and that of Sagredo, we can proceed to consider that other movement attributed to the same globe, first by Anistarco de Samos and later by Nicolaus Copernicus, who I think is, you know, him rotates under the zodiac in the period of a year around the sun, which stands motionless in the center of the zodiac.

POTATOES. The question is so great and noble that I will be listening to its discussion with great interest, hoping to hear everything that can be said on the subject. Then I go alone and relaxed into the deepest reflections on what I have heard and what has been heard. And if I'm not winning anymore, it's no small matter to have a firmer argument.

SAGR. In order not to tire Salviati any longer, we will end today's discussions and continue speaking as usual tomorrow, hoping to hear great new things.

POTATOES. I'll leave the book on the new stars, but I'll return to this little thesis booklet to review what's being written against the annual motion that will be the subject of tomorrow's discussion.

end of the second day

Dialogue about the two great world systems

THE THIRD DAY

Sagredo. I've been waiting impatiently for your arrival to hear new opinions on the annual rotation of this globe of ours. Last night and this morning the hours seemed very long to me because of this, although I didn't pass them by idly. On the contrary, I lay awake most of the night, mentally going over yesterday's arguments and pondering the reasons put forward by each side in favor of these two opposing positions - the former by Aristotle and Ptolemy and the latter by Anistarchus and Copernicus. And it really seems to me that each of these theories is wrong, the arguments in their favor so plausible that they deserve to be forgiven - so long as we stop at those produced by their authoritative authors. Because of its antiquity, however, the Peripatetic opinion had many adherents while the other had few, partly because of its difficulty and partly because of its novelty. And among the adherents of the former, especially in modern times, I seem to recognize some who give very childish, not to say ridiculous, reasons for the opinion which they believe to be true.

OINTMENT. The same impressed me even more than you. I have heard such things being said that I should blush to repeat them--not so much to avoid discrediting their authors (whose names might always be omitted) as to not so belittle the honor of the human race. Over time, my observations have convinced me that some people, in arguing absurdly, first draw a conclusion in their head that impresses them, either because it is their own or because it was obtained from someone who has their full confidence has. so deep it's impossible to get it out of your head. Such arguments in support of your obsession, as they are presented or made by others, however simple and silly, win your approval and immediate applause. On the other hand, they take everything that is brought against them, no matter how ingenious and conclusive, with contempt or with burning anger - if it doesn't offend them. Furious, some of them would not even hesitate to plot to suppress and silence their opponents. I have had some experience in this regard myself.

SAGR. I know; such people do not derive or reason their conclusion from their premises, but adjust (I should have said confuse and distort) the premises and reasons of a conclusion which is already established and established for them. Dealing with these people cannot be good, especially since their company can be not only unpleasant but also dangerous. So let us continue with our good Simplicio, who has long been known to me as a man of great ingenuity and entirely without guile. Moreover, he is well acquainted with the peripatetic doctrine, and I am sure that what he does not think in support of Aristotle's opinion is unlikely to occur to anyone.

But here, out of breath, comes the very person that has been sought for so long today. We only slandered you.

POTATOES. Please don't scold me; Blame Neptune for my long delay. For this morning's low tide it drew back the water so much that the gondola I was riding in, after it entered a dirt canal not far from here, became high and dry. I had to wait there for over an hour for the tide to come back. And while I was there, unable to get off the boat (which ran aground almost immediately), I began to observe an event that struck me as quite remarkable. As the water subsided, it could be seen flowing down several streams very quickly, exposing the mud in many places. Observing this effect, I saw this movement along a line stop, and without a moment's pause, the same water began to return, the sea went from retreating to advancing without stopping for a moment. It's an effect I've never seen before in all the time I've been in Venice.

SAGR. So they can't be stuck between small fillets. Since they have almost no gradient, the rise or fall of the open sea by only the thickness of a sheet of paper is sufficient to cause water to flow back and forth through such bays for a long distance. On some coasts, sea level rise of just a few meters causes water to spread across the plains over many thousands of hectares.

POTATOES. I know this very well, but I have to think that there should be a noticeable pause between the bottom of the descent and the first point of the ascent.

SAGR. This will appear to you when you think of walls or poles over which this change occurs vertically. But in reality there is no hibernation.

POTATOES. It seems to me that since these two movements are opposites, according to the teaching of Aristotle that proves this, they should pause halfway between themat the point of return mediates the rest. (Note: A rest break at the moment of retreat.)

SAGR. I remember the passage well, and I also remember being unconvinced by Aristotle's proof during my philosophy studies. In fact, I've had many opposite experiences. I can mention them now, but I don't want us to slide further down the abyss. We are gathered here to discuss our business without interruption, as we have done for the past two days.

POTATOES. It will still be good, if not to break it, then at least to lengthen it a bit. For on my return home last night I began to re-read this little book of thesis where I found some very convincing evidence against this annual movement attributed to the earth. And since I didn't dare to quote them exactly, I brought the notebook with me. (Note: This is the flyerOf the three new stars that appeared in the years 1572, 1600, 1609 (1628).by Scipio Chiaramonti, to whom Simplicius referred on the first day (seep. 14).)

SAGR. did you do well But if we're to continue our discussion according to yesterday's agreement, we first need to hear what Salviati has to say about the book about the new stars. So, without further interruption, we can look at the annual movement.

Well, Salviati, what do you have to say about these stars? Were they really drawn down to these lower regions from heaven by this author's calculations made by Simplicius?

OINTMENT. Last night I undertook to study their procedures, and this morning I looked over them again, wondering if what I thought I had read the night before was actually written there, or if I was a victim of the spirits and fantasies of the night. To my great regret I actually found there written and printed what I did not want for the sake of this philosopher's reputation. It seems impossible to me that he should not see the vanity of his undertaking, both because it is so obvious and because I remember our academic friend praising it. It also seems to me very difficult to believe that, out of consideration for others, he could be persuaded to disregard his own reputation so much that he was induced to publish a work for which only scholarly criticism could be expected.

SAGR. You may add that it will be far fewer than one in a hundred to balance those who will celebrate it and exalt it above all the most learned men that exist now or ever were. A man capable of defying an army of astronomers with the perennial immutability of the heavens, and one who, to his great shame, fought it with his own weapons! And if there are half a dozen in a province who notice their trifles, what are they compared to the innumerable crowds who are gripped by all the cries (can neither discover nor understand them) and applaud as much as they least understand? And even the few who understand contempt to respond to such pointless and inconclusive gibberish. Also for good reason; for those who understand have no need of it, and to those who do not understand it is wasted effort.

OINTMENT. Indeed, silence would be the most appropriate reprimand for their uselessness, unless other reasons practically compelled them to refuse. One reason is that we Italians are ignorant and ridiculous towards foreigners, especially those who have broken with our religion; I could show you some very famous ones who make fun of our academic and the many mathematicians in Italy for abandoning the follies of a certain Lorenzini (Note: A critique of Kepler.) appear in print and are unchallengedly maintained as their views. But this, too, may be overlooked in comparison with another and greater cause for laughter that may be mentioned, namely, the hypocrisy of scholars toward the frivolity of such opponents in matters they do not understand.

SAGR. I could not wish for a better example of their irritation, or of the unfortunate position of a man like Copernicus, who is under the censure of those who do not even understand the rudiments of the position against which they have declared war.

OINTMENT. You will be no less surprised as you refute astronomers who claim that new stars are above the orbits of planets and perhaps even below the fixed stars themselves (not firmament).

SAGR. But how did you get through this whole book in such a short amount of time? It's certainly a large volume and there must be numerous demos in it.

OINTMENT. I stopped after these first refutations of his, in which, with twelve demonstrations based on the observations of twelve of the astronomers who believed that the new star of 1572 (which appeared in Cassiopeia) was in the firmament, he proved that in the contrary it was sublunar. To do this, he compares in pairs the meridian heights measured by different observers at locations at different latitudes, and proceeds as you will now understand. And it seems to me that in examining this first of his procedures I discover in this author a great inability to prove anything against the astronomers or in favor of the Peripatetic philosophers, and that he really only more conclusively confirms their opinion. I did not, therefore, wish to devote myself to examining your other methods with the same patience; After a cursory glance at her, I'm sure that the hesitation that pervades her first rebuttal would be present in the others as well. And the fact is (as you will soon see) that very few words suffice to refute this work, even though it is constructed with so many laborious calculations as you have noticed.

That's why you need to hear how I proceeded. The author, I say, in order to attack his opponents with their own weapons, needs a large number of observations made by themselves, these authors are twelve or thirteen in number. He bases his calculations on part of this and concludes that such stars lay under the moon. Well, since I really enjoy interrogating and the author himself isn't here, you, Simplício, will answer the questions I'm going to ask and say what you think he would say.

Assuming we are dealing with the 1572 nova that appeared in Cassiopeia, tell me, Simplicius, whether you think it could have been in different places at the same time. That is, could it be below the elements and also below the orbits of the planets, and also above these among the fixed stars, besides being infinitely higher?

POTATOES. Without a doubt it must be said that it was in a single place at a unique and definite distance from Earth.

OINTMENT. Then, if the observations made by the astronomers were correct, and if the calculations made by this author were not wrong, both the first and the second would necessarily give exactly the same distance; Not true?

POTATOES. As far as I can see it would necessarily be so, and I don't think the author would disagree either.

OINTMENT. But if many calculations don't even match two, what would you think?

POTATOES. I would say they were all wrong, either because of a glitch in the computer or because of an error on the part of the observers. The most I can say is that a single and can no longer be right; but I shouldn't know which one to choose.

OINTMENT. But do you want to derive a questionable conclusion and justify it as true on false basis? Certainly not. Well, the calculations of this author are such that none of them agrees with the other; See, so have a lot of faith that you can put in her.

POTATOES. If so, it really is a serious deficiency.

SAGR. I want to help Simplicio and its author by telling you, Salviati, that his case would indeed have been conclusive if the author had taken it upon himself to find out definitively how far the star is from Earth. But I don't think that was his intention; he just wanted to show that the star was under the moon. If it can always be concluded from the observations mentioned and from all the calculations made on them that the height of the stars was always lower than that of the moon, then it would suffice for the author to condemn with the most crass ignorance all astronomers who, when they err in geometry or arithmetic, could draw no true conclusions from their own observations.

OINTMENT. So I had better turn MY attention to you, Sagredo, since you are so perceptive in representing the author's doctrine. And let's see if I can also convince Simplício (although he is inexperienced in calculations and demonstrations) that this author's demonstrations are inconclusive, to say the least. First, consider that both he and all the astronomers with whom he conflicts agree that the new star had no motion of its own, merely rotating with the star's diurnal motion.cell phone first. But they disagree on its place, astronomers place it in the celestial regions (i.e. above the moon) and perhaps among the fixed stars, while judging it as near-Earth; that is, under the arc of the moon's orbit. And since the location of the new star we are talking about was in the north and not far from the pole, so it never set for us northerners, determining its meridian heights with astronomical instruments was a simple matter. its minimum below the pole and its maximum above the pole. By combining them, the distance to the star could be calculated from observations made at different locations on Earth and at different distances from the north (i.e., locations that differed in polar elevation). For if he were standing in the firmament between the other fixed stars, his meridian heights, taken at different pole heights, would have to differ from one another in the same way as these pole heights. So, for example, if the star's elevation above the horizon is thirty degrees when taken from a location where the pole elevation is say forty-five degrees, then the star's elevation would need to be increased by four or five degrees. in those countries farther north where the pole is four or five degrees higher. But if the star's distance from Earth was very small compared to the firmament, then its meridian elevations should have increased significantly more than the polar elevations as it approached the pole. From such a larger increase, i.e. the excess of the increase in height of the star over the increase in pole height, the so-called parallax difference, the distance of the star from the center of the earth can be calculated quickly. through a clear and safe method.

Now this author takes the observations made by thirteen astronomers at different polar altitudes and compares a portion of them (which he chooses) and using twelve pairs calculates that the altitude of the new star was always below the moon. But he does it by expecting such gross ignorance from anyone who might lay their hands on his book that it turns my stomach. I can hardly see how the other astronomers are silent. Especially Kepler, against whom this author rails against; he would not shut up unless he considered the matter below his attention.

Now, for your information, I have transcribed in these pages the conclusions he draws from his twelve investigations.

(Galileo produces the data on which Chiaramonti relied. There are twelve pairs of observations that produce observed parallaxes that place the comet at distances from one-fifth of the radius (the radius is approximately 3,800 miles) of Earth to twenty-five times that radius. Sulviati notes that Chiaramonti immediately discarded all data that the results obtained placed the comet well beyond most estimates of the stellar sphere's distance.

Salviati explains that it is undoubtedly true that the data discarded are in error, but not necessarily more so than the sets used by the author, on the contrary. He reproduces five sets of observations that Chiaramonti ignored and finds them fairly consistent, given that at the extreme distance at which the observations place the comet, the slightest error of even a minute in the observed angle will produce large variations in the results . It shows how little you need to adjust these observations to get the same results. Meanwhile, he notes that the variations found in the data used by Chiaramonti differ wildly over the much shorter distances of his results and would require such large adjustments to achieve consistent results, suggesting some blunders such as ignoring the Refraction suggests . .)

SAGR. It is as if I were watching an unfortunate farmer who, after his entire expected crop has been uprooted and destroyed by a storm, goes about with a pale and contorted face, picking up crumbs so poor they would not feed a hen for a day . .

OINTMENT. Verily this Author arose with very scanty ammunition against the attackers of the immutability of the heavens, and with very frail chains he attempted to draw the new star of Cassiopeia from the highest heavens into these lower and elemental regions. Now that the great difference between the arguments of the astronomers and those of their opponent seems to me to be very clearly shown, we may well leave this point and return to our main subject. Next we will consider the annual motion, which is usually attributed to the Sun, but was later removed from the Sun and transferred to the Earth, first by Aristarchus of Samos and later by Copernicus. Against this position, I know that Simplício is heavily armed, especially with the sword and shield of his little book of thesis or his mathematical dissertations. It is good to start by setting out the objections in this booklet.

POTATOES. If you don't mind, I'll save these for last as they were the most recently discovered.

OINTMENT. Then you better summarize the counter-arguments of Aristotle and the other ancients according to our previous procedure. I will do the same so that nothing is left out or escapes careful scrutiny and scrutiny. In the same way, Sagredo, with his quick thinking, will throw in his thoughts when the spirit moves him.

SAGR. I will do this with my usual lack of tact; and since you asked for it, you will have to forgive him.

OINTMENT. This favor obliges me to give thanks and not to forgive. But now the simpleton begins to uncover the objections that prevent him from believing that the earth, like the other planets, can orbit about a fixed center.

POTATOES. The first and greatest difficulty is the reluctance and incompatibility between being the center of attention and being far from it. Because if the globe has to move around the circumference of a circle, i.e. around the zodiac, in one year, it cannot possibly be in the center of the zodiac at the same time. But the earth is at this center, as Aristotle, Ptolemy and others proved in many ways.

OINTMENT. Very well argued. Undoubtedly, anyone who wants the earth to move on the circumference of a circle must first prove that it is not at the center of that circle. The next thing is to see if the earth is in the center about which I say it revolves and you say it is. And before that we have to explain whether you and I have the same idea about this center or not. So tell me what and where is this center you mean.

POTATOES. By "center" I mean that of the universe; that of the world; that of the star sphere; that the sky.

OINTMENT. Whether there is such a center in nature I could very well dispute, since neither you nor anyone else has yet proved whether the universe is finite and has a form, or whether it is infinite and limitless. However, if you are granted for a moment that it is finite and finite spherical and therefore has its center, it remains to be seen how credible it is that the earth and not some other body is at that center.

POTATOES. Arislotle gives a hundred proofs that the universe is finite, limited and spherical.

OINTMENT. All of which are later reduced to one, and that to none. Because if I deny him his assumption that the universe is mobile, all his proofs will fall by the wayside, as he only proves that it is finite and limited if the universe is mobile. But in order not to multiply our arguments, I must first grant you that the universe is finite, spherical, and has a center. And since such form and center are derived from mobility, it will be more sensible for us to pass from this same circular motion of the bodies of the world to a detailed study of the proper position of the center. Aristotle himself justified and decided this by making that point the center of the universe, around which all the celestial spheres revolve and in which he suspected the terrestrial globe. Now tell me, Simplicio: if Aristotle had been compelled by the most tangible experiences to partially rearrange this order and disposition of the universe, and to admit to having been wrong in either of these statements... to place the earth at the center, or to say that the heavenly spheres revolve around such a center ... which of these admissions do you think he would choose?

POTATOES. I think when that happens, the peripatetics...

OINTMENT. I am not asking the Peripatetics, I am asking Aristotle himself. As for the first, I know very well what they would answer. They would, like Aristotle's most reverent and humble slaves, deny and even refuse to look at all experiences and observations in the world lest they have to admit them, and would say that the universe remains exactly as Aristotle wrote it; not the way nature intended. For take away from them the support of their authority, and with what would you make them appear in the field? So now tell me what you think Aristotle himself would do.

POTATOES. Really, I can't decide which of these two difficulties he would have considered the lesser.

OINTMENT. Please do not apply this term "difficulty" to something that could necessarily be so, for the desire to put the earth at the center of the celestial revolutions was a "difficulty". But since you do not know in which direction he would be inclined, and, like me, consider him a man of brilliant intellect, let us examine which of the two possibilities is the more reasonable, and take one as the one which Aristotle would have embraced . So, to resume our argument from the beginning, let's assume, out of respect for Aristotle, that the universe (the size of which we have no reasonable information beyond the fixed stars) is something spherical and moving in a circle, it necessarily has a center for its form and for its movement. Since we are also sure that within the stellar sphere there are many spheres within each other, the stars of which are also moving in circles, our question is this: what is more reasonable to believe and say; that these trapped spheres revolve around the same center as the universe or around a different center distant from it? Now tell me, Simplicio, what you think of this matter.

POTATOES. If we could stop that assumption and be sure that we wouldn't find anything else to bother us, I would think it would be much more reasonable to say that the container and the things it contains all revolve around a common center , rather than around different centers. . ones.

OINTMENT. Now if it is true that the center of the universe is that point around which all the spheres and bodies of the world (that is, the planets) revolve, then it is quite certain that there is not the earth but the sun will be found in the center of the universe. Hence, in relation to this first general idea, the central place is that of the sun, and the earth is as distant from the center as it is from the sun.

POTATOES. How do you conclude that the sun, not the earth, is at the center of planetary orbits?

OINTMENT. This is derived from the most obvious and therefore the most convincing observations. The most obvious of them, excluding the Earth from the center and placing the Sun here, is that we find all the planets closer to Earth at one point in time and farther away at another. The differences are so great that, for example, Venus at its extreme point is six times further from us than at its closest, and Mars flies almost eight times higher in one state than in the other. So you can see if Aristotle wasn't a little wrong when he thought they were always the same distance from us.

POTATOES. But what are the signs that they move around the sun?

OINTMENT. This is explained by the discovery of the three outer planets - Mars, Jupiter and Saturn - which are always very near to Earth when in opposition to the Sun and very distant when in conjunction with it. Such is the significance of this convergence and recession that Mars appears sixty times larger nearby than it is farther away. Next it is certain that Venus and Mercury must orbit the Sun because they never stray too far from it and because they are sometimes seen beyond it, sometimes on its side, conclusively proving Venus' shape changes. (Note: Venus has phases like the moon.) As for the moon, it is true that it can never separate from the earth in any way, for reasons that will be explained in more detail below.

SAGR. I hope to hear even more remarkable things resulting from this annual movement of the earth than those that depended on its daily rotation.

OINTMENT. You will not be disappointed, for as to the effect of diurnal movement on the celestial bodies, it was and could not be otherwise than if the universe were rapidly moving in the opposite direction. But this annual movement, mixed with the individual movements of all the planets, produces many curiosities that have puzzled all the greatest men on earth in the past.

Now returning to these first general notions, I repeat that the center of celestial rotation for the five planets Saturn, Jupiter, Mars, Venus and Mercury is the Sun; this will also apply to the earth if we succeed in placing it in the sky. Then the moon has a circular motion about the earth, from which, as I have already said, it cannot be separated; but that does not prevent it from revolving around the sun along with the earth in its annual motion.

POTATOES. I am still not convinced of this arrangement. Maybe I should understand better if I draw a diagram that can facilitate the discussion.

OINTMENT. It will be done. But to your greatest satisfaction and also to your amazement, I want you to draw it yourself. You will see that as much as you think you don't understand, you do so perfectly, and only by answering my questions will you describe it accurately. Then take a sheet of paper and the compass; Let this side be the expanse of the universe in which you must distribute and arrange its parts as reason tells you. And firstly, since you are sure, without me telling you, that the earth is in this universe, mark at will any point where you want to be and designate it with a letter.

POTATOES. Let this be the place marked with A on the globe.

OINTMENT. Very good. Second, I know that you are aware that this earth is not within the body of the sun, not even adjacent to it, but is some distance away from it. So assign the Sun to another location of your choice, as far from Earth as you like, and determine that too.

POTATOES. Here I did it; let this be the position of the sun marked with 0.

OINTMENT. Now that these two are established, I would like you to consider placing Venus so that its position and movement can correspond to what sensory experience is showing us about it. So you must remember what is happening to this star as you know, either from previous discussions or from your own observations. Then assign it any spot that feels right to you.

POTATOES. I assume that the phenomena you reported, which I also read in the dissertation booklet, are correct; that is, this star never moves further from the Sun than a certain interval of forty degrees or more; therefore it not only never attains opposition to the Sun, but never even a quadratic aspect, not even a sextile aspect. (Note: thus 180° 90° and 60°.) Also, I must assume that it appears to us about forty times larger at one time than at another, larger when it is retrograde and approaching nocturnal conjunction with the Sun, and very small when approaching the morning conjunction, and moreover, when it appears very large, it appears horn-shaped, and when it appears very small, it appears perfectly round.

Since these phenomena are correct, I say, I do not see how I can avoid the assertion that this star orbits the sun in a circle, so that it cannot be said that this circle contains and contains the earth, nor is it under the sun (i.e. between the sun and the earth) nor beyond the sun. Such a circle cannot encompass the earth, because then Venus would sometimes be in opposition to the sun; it cannot be under the sun, for then Venus would appear crescent at both conjunctions; and it cannot be beyond the sun, for then it would always look back and never return. Therefore, for your adjustment, I draw the circle CH around the sun, without the earth.

OINTMENT. Assuming Venus, it is correct to consider Mercury, which, as you know, always moves around the Sun and moves much less from it than Venus. Therefore, think about what place you should allocate him.

POTATOES. There is no doubt that the most appropriate location for this will be a smaller circle within the Venusian circle, which is also described over the Sun as it mimics Venus. Part of the reason for this, and primarily for its proximity to the Sun, is Mercury's luminosity, which surpasses that of Venus and all other planets. Based on this, we can draw in your circle here and mark it with the letters BG.

OINTMENT. Next, where should we place Mars?

POTATOES. Since Mars is in opposition to the Sun, it must encircle the Earth in its circle. And I see that you must also embrace the sun; for when it comes into conjunction with the Sun, if it does not transcend it but lags behind, it seems to have a home like Venus and the Moon. But it always looks round; Therefore, your circle must include both the sun and the earth. And since, I recall, you said that it appears sixty times larger in opposition to the Sun than in conjunction, it seems to me that this phenomenon is well catered for by a circle around the Sun, enclosing the Earth, which I draw here and DI mark. When Mars is at point D, it is very close to Earth and opposite the Sun, but when it is at point 1, it is conjunct the Sun and very far from Earth.

And since the same phenomena are observed for Jupiter and Saturn (albeit with less variation on Jupiter than on Mars, and even less on Saturn than on Jupiter), it seems clear to me that we can accommodate these two planets very well too. with two circles, still around the sun. This first, for Jupiter, I mark EL; the other, higher, for Saturn, is called FM.

OINTMENT. So far you've been remarkably well behaved. And since, as you can see, the approach and distance of the three outer planets are equal to twice the distance between Earth and the Sun, this gives more variation on Mars than on Jupiter because Mars' Circle ID is smaller than that EL circle of Jupiter. Also, the EL here is smaller than Saturn's FM circle, so the variation on Saturn is even smaller than on Jupiter, and this is consistent with the appearance. Now it's up to you to come up with a place for the moon.

POTATOES. By the same method (which seems to me very convincing), since we see the Moon entering into conjunction and opposition with the Sun, it must be admitted that its circle orbits the Earth. But she must not embrace the sun either, otherwise she does not look like horns in conjunction, but always round and filled with light. In addition, it would never cause us an eclipse, as it often does, placing itself between us and the sun. So it must be assigned a circle around the earth, which will be this, NP, so that it appears to us here on earth A in P as in conjunction with the sun, which it will sometimes eclipse in this office. Placed in N, it is seen in opposition to the Sun, and in this position it can fall into Earth's shadow and be eclipsed.

OINTMENT. And now, Simplicio, what shall we do with the fixed stars? Do we want to scatter them across the vast abyss of the universe, at different distances from some predetermined point, or do we want to place them on a spherical surface, extending around a proper center, so that each of them is the same distance from that center?

POTATOES. I prefer to take a middle course, associating them with a sphere inscribed about a definite center and enclosed between two spherical surfaces - one very distantly concave and the other nearer and more convex, between which are placed at various heights the innumerable hosts are of stars. This may be called the universal sphere, containing within itself the spheres of the planets which we have already indicated.

OINTMENT. Well, Simplicio, what we've been doing all this time is arranging the bodies of the world according to the Copernican distribution, and now you've done it yourself. Also, you have all but the sun, earth, and stellar sphere assigned their respective motions. They attributed a circular motion around the Sun to Mercury and Venus without involving the Earth. Around the same sun you caused the three outer planets Mars, Jupiter and Saturn to move and envelop the earth in their orbits. Then the moon can only move around the earth and without hugging the sun. And on all these points you also agree with Copernicus himself. It now remains to divide three things between the sun, earth and celestial sphere: the state of rest, which seems to belong to the earth; the annual movement through the zodiac which seems to belong to the sun; and the diurnal movement which seems to belong to the stellar sphere in which all the rest of the universe except the earth participates. And since it is true that all planetary spheres (I mean Mercury, Venus, Mars, Jupiter and Saturn) revolve around the Sun as their center, it seems more reasonable that the resting state belongs to the Sun and not to the Sun. Earth... just as the center of any moving sphere remains fixed, and not some other point remote from the center.

Now as regards the earth placed in the center of a moving object, I mean between Venus and Mars, one of which makes its revolution in nine months and the other in two years, a motion can take a year allotted to it. more elegant than a state of rest left to the sun. And from this it necessarily follows that the diurnal movement also belongs to the earth. For if the sun stood still and the earth did not revolve but only had the yearly motion around the sun, our year would consist of only one day and one night; that is, six months by day and six months by night, as previously observed.

See, then, how cleanly the precipitous movement of every twenty-four hours is taken out of the universe, and how the fixed stars (which are so many suns) agree with our sun in enjoying eternal rest. See, too, what great simplicity is to be found in this sketch, which gives the reasons for so many manifestations of weight in the celestial bodies.

SAGR. I see it really very well. But just as you deduce from this simplicity a high probability of truth in this system, others may, on the contrary, draw the opposite conclusion from it. If this age-old arrangement of the Pythagoreans fits the bill so well, you may (and not without reason) wonder why it has found so few adherents over the centuries; why it was refuted by Aristotle himself and why even Copernicus has had no better luck with it in the last days.

OINTMENT. Sagredo, if you have sometimes suffered, as I have suffered so many times, from hearing the kind of follies designed to make ordinary people stubborn and reluctant to listen to (and even less agree with) this innovation, then find I would greatly diminish your surprise at finding so few men of this opinion. It seems to me that we can pay little heed to imbeciles who take this as conclusive evidence confirming the immobility of the earth, and who hold them firmly to that belief, when they find that they are not in Constantinople and Japan today, or for those who are sure that the earth is too heavy to rise to the sun and then fall back on its head. There is no need to worry about men like these, whose name is Legion, or heed their folly. Nor do we have to try to proselytize people who can't define broadly and make distinctions just to have such companions for our society in very subtle and delicate teachings. And with all the evidence in the world, what do you hope to get into the minds of people too stupid to see their own limitations?

No, Sagredo, my surprise is very different from yours. You marvel that there are so few adherents to the Pythagorean opinion, while I am amazed that there are still some who have accepted and followed it to this day. Nor can I admire enough the extraordinary perspicacity of those who held this opinion and accepted it as true; They perpetrated such violence against their own senses by sheer power of intellect that they preferred what reason told them to what reasonable experience clearly proved them wrong. For, as we have seen, the arguments against the rotation of the earth which have already been examined are very plausible; and the fact that the Ptolemies and Aristotelians and all their disciples found them conclusive is indeed a strong argument for their effectiveness. But the experiences which openly contradict the annual movement are actually so much greater in their apparent power that, I repeat, my astonishment knows no bounds when I think of Aristarchus and Copernicus being able to conquer reason so that she defied reason the latter, the former became master of her faith

SAGR. So are we facing even stronger attacks on this annual movement?

OINTMENT. We are, and so obviously and sane, if there weren't some higher and better than common sense and common sense to join with reason, I wonder very much if I too shouldn't have been a lot more recalcitrant to the Copemican system than me, since brighter than normal light enlightened me.

SAGR. Well then, Salviati, let's get down to business, as they say; for every word otherwise spent seems wasted to me.

OINTMENT. I am at your service...

POTATOES. Gentlemen, please give me a chance to restore harmony to my mind, which is now very troubled by certain things Salviati just touched on. Then, when this storm is over, I can listen to your theories more profitably. For it is useless to have an image in a wavy mirror, as the Latin poet so graciously told us when he wrote:

... the other day I vi no lilore,

When the winds calmed, the sea stopped.

(Note: "On the shore I saw myself the other day, When the sea stood still, undisturbed by the winds." (Virgil, Bucolicians 2.25))

OINTMENT. You're right; tell us your difficulties.

POTATOES. Those who deny the daily movement of the earth because they do not see that they are being transported to Persia or Japan have been called by you as stupid as those who oppose the annual movement because they feel disgusted when they admit it , that the huge and heavy mass of the globe can rise upwards and then sink downwards as it would have to do if it revolved annually around the sun. Now I am not ashamed to be counted among such fools, and feel the same repugnance to the second point against the annual movement, all the more so as I see how much opposition to the movement is offered even across a level of I don't want to say a mountain, but a mere stone; and even the first would only be the smallest fraction of an Alpine chain. I therefore ask you not to ignore such objections entirely, but to resolve them; and not only for me, but also for others to whom they seem quite real. Because I think it's very difficult for some people, no matter how simple they are, to recognize and admit that they are simple just because they know they are viewed that way.

SAGR. The simpler they are, the near impossible it becomes to convince them of their own shortcomings. And so I think it is good to remove this and all similar objections, not only to satisfy Simplicius, but also for other, no less important reasons. Because of course there are many people who are familiar with philosophy and the other sciences, but which, for want of astronomy or mathematics, or any other discipline to sharpen their minds for the penetrating of truth, cling to such foolish doctrines as these. Therefore the situation of poor Copernicus seems miserable to me; he could only count on criticism for his opinion and could not let it fall into the hands of anyone who did not understand his arguments (very subtle and therefore difficult to master) and would convince himself of their falsity from superficial appearances and would consider them false and declare full of errors. If people can't be persuaded by the more obscure arguments, it's good to make them see the invalidity of those objections. With such knowledge comes moderation in their judgment and condemnation of teachings they currently see as wrong. Accordingly, I shall raise two further objections to the diurnal motion made by leading literati not so long ago, and then examine the annual motion.

The first was that if it were true that the Sun and other stars did not rise above the eastern horizon, but that the eastern side of the earth sank beneath them while lying motionless, it would follow that after a short time the mountains , descending downward with the rotation of the globe, would reach such a position that while it would have to climb steeply to its peaks a little earlier, a few hours later it would have to lower and descend to get there.

The other was that if the daily movement was to earth, it had to be so rapid that someone at the bottom of a well would be momentarily unable to see a star directly overhead was to him, but could only see during the briefest instant when the earth flows two or three meters, that is the width of the well. However, experience shows that the apparent passage of such a star through the well takes quite a while - a necessary argument that the mouth of the well is not moving fast enough for daily movement. Hence the earth is immovable.

POTATOES. Of these two arguments, the second seems really convincing to me; but as for the former, I think I can sort that out myself. For I think it is the same that the terrestrial globe moves about its own center and carries with it a mountain to the east, just as the terrestrial globe stands still while the mountain is detached from its base and dragged across the earth. And I don't see that carrying the mountain across the surface of the earth is any different than sailing a ship across the surface of the sea. Therefore, if the mountain's objection were valid, it would follow that if the ship continues its voyage and moves a few degrees away from our ports, we would have to climb its mast, not only to climb, but also to get around us in an airplane to move possibly even dismount. Well, that doesn't happen, nor have I ever heard of any sailor, even among those who have circumnavigated the world, who found a difference in such actions (or others performed on board the ship) by the fact that the ship was in one was place and not as another.

OINTMENT. You argue very well, and if it had ever occurred to the author of this objection to consider how this neighboring eastern mountain of his, if the globe were rotated, would have been carried by this movement in a few hours where today the Olympus or Mount Carmel, he would have seen that he would have been compelled by his own reasoning to believe and admit that it would be necessary to reach the top of these last mountains, in fact in order to descend. These people have the same mindset as those who deny the antipodes on the grounds that one cannot walk with one's head down and one's feet nailed to the ceiling; Develop ideas that are true and that they fully understand, but they do not find it easy to derive the simplest solutions to their difficulties. That is, they understand very well that attracting or descending approaches the center of the globe, and that ascending deviates from it; but they do not understand that our antipodes have no difficulty in supporting themselves or walking because they are like us, with the soles of their feet pointing toward the center of the earth and their heads toward the sky.

SAGR. However, we know that people who are extremely imaginative in other areas are blind to such ideas. This confirms what I just said; It is good to remove all objections, even the weakest. Therefore, the well question must also be answered.

OINTMENT. Indeed, this second argument has an unspeakable semblance of persuasion. However, I think it would be right if someone would question the very person who is experiencing this so that they can express themselves better, and explain exactly what results would follow if someone admitted to the daily rotation of the earth, but they did appear not happen; So, I say, I think he would embarrass himself to explain this question and its implications...perhaps no less than he would unravel it by thinking about it.

POTATOES. To be blunt, I'm pretty sure that would happen, even though I'm in the same mess right now. For at first glance the argument seems to me binding, but on the other hand I am beginning to see what other problems would arise if the argument continued in the same way for that extremely rapid course which is to be perceived in the star if the If the movement belonged to the earth, it would also have to be discovered there if the movement were its own - all the more so since it would have to be a thousand times faster in the star than on earth. On the other hand, the star must get out of sight as it streams through the borehole's mouth, which would be only a few meters in diameter if the borehole follows Earth at more than two million meters per hour. In fact, this seems to be such a glimpse that one cannot even imagine; However, a star can be seen from the bottom of a well for a long time. So I would like some enlightenment on this matter.

OINTMENT. Now I am greatly strengthened in my conviction that the originator of this objection is confused, since you too, Simplicius, are obscuring what you mean and do not quite understand what you are supposed to say. I conclude this mainly because you are omitting a distinction that is a major point in this topic. So tell me, if you did this experiment (I mean the one with the star going through the well's opening), would you make a difference if the well was deeper or shallower; that is, whether the viewer is farther from your mouth or closer to your mouth. Because I didn't hear you mention it.

POTATOES. The fact is that I hadn't thought of it, but your question drew my attention to it and made me understand that such a distinction must be absolutely necessary. I'm already beginning to see that perhaps the depth of the well is no less important than its width in determining transit time.

OINTMENT. Nevertheless, I prefer to ask myself whether the width makes a difference or a big difference for us.

POTATOES. Now it seems to me that it takes ten times as long to walk 10 meters as it does to walk 1 meter. I am sure that a 10-meter boat will pass my view long before a 100-meter galley.

OINTMENT. So we still cling to that ingrained idea of ​​not moving unless our legs can support us.

What you say is true, my dear Simplício, if the object you see is moving while you stop to watch it. But when you are in a well, when the well and you are swept along together by the rotation of the earth, don't you see that not in an hour, not in a thousand, not in all eternity, will you ever be overtaken by the mouth of the well? The way the motion or stillness of the earth in such a situation affects you cannot be seen at the wellhead, but at some other separate object that is not in the same state of motion...or should I say resting state.

POTATOES. So far, so good; but suppose that when I am in the well I am swept up in the daily movement and that the star I see is motionless. The mouth of the shaft (allowing even my sight to pass beyond it) is not more than three yards, of so many millions of yards in balance of the earth's surface obstructing my sight, how can the time of my vision be a fraction? noticeable of mine not see?

OINTMENT. You are still encountering the same problem and you will indeed need someone to help you. It is not the latitude of Node I, Simplício, that measures the time of the star's visibility, because in that case you would see it constantly, just as the well would constantly give way to your sight. No, the measure of that time must be taken from that part of the silent sky that remains visible through the shaft's opening.

POTATOES. Isn't the part of the sky I perceive the same fraction of the whole celestial sphere as the well mouth from the terrestrial globe?

OINTMENT. I want you to answer that for yourself. Tell me if the wellhead is always the same fraction of the earth's surface.

POTATOES. There is no doubt that it is always the same.

OINTMENT. What about the part of the sky that the person at the well sees? Is that always the same fraction of the entire celestial sphere?

POTATOES. Now I'm beginning to clear the darkness of my mind and understand what you hinted to me a moment ago...that the depth of the well has something to do with this matter. For I have no doubt that the farther the eye is from the mouth of the well, the less part of the sky it will see, and the sooner it will have passed and lost sight of whoever happened to be there. looked at him from below.

OINTMENT. But is there any place in the well from which he would see exactly that fraction of the celestial sphere that is the mouth of the well from the surface of the earth?

POTATOES. It seems to me that if the well were dug to the center of the earth, perhaps a part of the sky could be seen from there which would be to him what the well is to the earth. But as one moved away from the center and rose to the surface, more and more of the sky would be revealed.

OINTMENT. And finally, if you put your eye to the mouth of the well, you would see half the sky, or very little less, which would take twelve hours assuming we were at the equator. I have just given you an outline of the Copernican system, against the truth of which the planet Mars launches a savage attack. For if it were true that distances from Mars to Earth vary from minimum to maximum as much as the distance from Earth to the Sun, then its disk, when it were closest to us, would have to appear sixty times larger than when it is the So on. However, this difference should not be seen. Instead, when it faces the sun and is close to us, it shows up only four or five times larger than when hidden behind the sun's rays in conjunction.

Another and greater difficulty is presented to us by Venus, which, if it orbited the Sun, as Copernicus says, would be sometimes beyond it, sometimes on this side, moving away and approaching us as close as the diameter of the Sun. circle it describes. So when it is in the sun and very close to us, its disc must appear to us a little less than forty times larger than when it is beyond the sun and close to the conjunction. However, the difference is hardly noticeable.

Add to this one more difficulty; for if the body of Venus is intrinsically dark, and she shines like the moon only by the light of the sun, which seems reasonable, then she must appear curved when standing in the sun, like the moon when she is also near the Sun. This is a phenomenon not evident on Venus. It is for this reason that Copernicus explained that Venus was inherently luminous, or that its substance was such that it could receive sunlight and transmit it through its entire thickness, making it appear radiant to us. In this way Copernicus forgave Venus her invariable form but said nothing about her slight variation in size; let alone the requirements of Mars. I believe this was because he could not save to his own satisfaction an appearance so contradictory to his view, but being persuaded by so many other reasons he held that view and believed it to be true.

In addition to these things, to make all the planets move together with the earth, with the sun being the center of their rotations, then the moon alone disturbs this order and has its own movement around the earth (in a year around the sun around with the earth and the entire elemental sphere) seems to somehow mess up the whole order and make it improbable and wrong.

These are the difficulties that make me think of Aristarchus and Copernicus. You couldn't overlook them without being able to solve them; However, they were confident that reason told them it should be so, given many other notable observations. So they confidently asserted that the structure of the universe could have no other form than that which they had described. Then there are other very serious but beautiful problems, not easy for ordinary minds to solve, but which Copernicus examined and explained; this we shall defer until we have answered the objections of people hostile to this position.

Turning now to the explanations and responses to the three serious objections mentioned, I say that the first two not only do not contradict the Copernican system, but that they are absolutely and very much in favor of it. For both Mars and Venus show variable proportions, and Venus appears to have one lobe when under the sun, and changes shape just like the moon.

SAGR. But if this was hidden from Copemicus, how is it revealed to you?

OINTMENT. These things can only be understood through the sense of sight, which nature has not bestowed on man so perfectly that he can discern such differences. Rather, the viewing instrument itself introduces an obstacle. But in our day it has pleased God to grant to human ingenuity an invention so wonderful that it has power to magnify vision four, six, ten, twenty, thirty, and forty times, and also an infinite number of objects that were invisible because of their distance or extreme smallness, they became visible through the telescope.

SAGR. But Venus and Mars are not invisible objects because of their distance or small size. We perceive them through simple natural vision. Why then do we not see differences in their sizes and shapes?

OINTMENT. The impairment of our eyes plays an important role here, as I have just indicated to you. For this reason, distant luminous objects are not presented to us simply and flatly, but are covered with random and strange rays, so long and dense that naked bodies are represented as sprawling tens, twenty, hundreds, or thousands. times more than it would appear to us if the small radiant crown that does not belong to them were removed.

SAGR. Now I remember reading something like that, but I don't remember if it was in theSolar lettersor inthe samplerfrom our friend. (Note: Galileo.) It would be good both to refresh his memory and to inform Simplício, who may not have read these works, if he would explain to us in more detail what it is about. Because I think that knowledge of this would be essential for understanding what is now being discussed.

POTATOES. Everything Salviati is currently presenting is really new to me. To be honest, I had no interest in reading these books and I have not yet put my faith in the newly introduced optical device. Instead, following in the footsteps of other peripatetic philosophers in my group, I have regarded as errors and fallacies of the lens those things which other people have admired as wondrous achievements. If I'm wrong, I'm glad to be gotten out of it; and delighted with the other news I have heard from you, I will be listening very carefully to the rest.

OINTMENT. The confidence which men of this kind have in their own shrewdness is as unreasonable as the little regard they have for the judgments of others. Remarkably, they feel better able to judge such an instrument without ever having tested it. than those who have done thousands and thousands of experiments with it and do it every day. But let's forget those wayward people who cannot even be blamed without giving them more credit than they deserve.

Coming back to our purpose, I say that bright objects, either because their light is refracted in the moisture covering the pupil, or because it is reflected from the rims of the eyelids and these reflected rays are scattered about the pupil, or for another reason, our eyes seem surrounded by new rays. Therefore, these bodies appear much larger than they would be if we saw them without such radiations. This enlargement occurs in ever-increasing proportions as these luminous objects grow smaller and smaller, just as if we suppose a growth of lustrous hair, say four inches long, added to a circle four inches in diameter will. , which would increase its apparent size nine times; but ...

POTATOES. I think you meant "three times" since four inches added to each side of a four inch diameter circle would triple its size, not increase it nine times.

OINTMENT. A bit of geometry, simplicio; The diameter increases threefold, but the surface area (that we are talking about) increases ninefold. For the areas of circles, Simplicio, are to one another as the squares of their diameters, and a circle of four inches in diameter is to a circle of twelve inches in the same proportion as a square of four is to a square of twelve; that is, 16 to 144. So it will be nine times larger, not three times. This is for your information, Simplicio.

Now, to continue, if we add this four inch hairstyle to a circle only two inches in diameter, the diameter of the crown will be ten inches and the ratio of the circle to the naked body will be 100 to 4 (for such the squares are of 10 and 2), then the increase would be twenty-five times. And finally, the four inches of hair added to a small circle one centimeter in diameter would do it eighty-one times. Thus, the magnification is made proportionally larger and larger as the actually magnified objects become smaller and smaller.

SAGR. The question that worried Simplício didn't bother me too much, but there are other things I'd like a clearer explanation about. In particular, I want to gather the basis on which you claim that such growth is always the same for all visible objects.

OINTMENT. I've already partially explained it by saying that only luminous objects increase; not dark. Now I add the rest. Of the bright objects, those that are brightest in light make the largest and strongest reflections on our pupils and therefore appear much more magnified than the less bright ones. And not to dwell too long on this detail, let's go back to what is shown to us by our greatest Master; tonight, when the sky is well darkened, let's contemplate Jupiter; we shall see him very bright and great. Then we pass our vision through a tube or even a small opening that we can leave between the palm and the fingers, close the fist and bring it to the eye; or through a hole made in a card by a fine needle. We will see Jupiter's disk, which is rayless and, in fact, so small that we will think it to be less than one-sixtieth what used to appear to us with the naked eye as a large flare. Then we can look at the Dog Star, a very beautiful star and larger than any other fixed star. To the naked eye it does not appear to be much smaller than Jupiter, but if one removes its headdress in the manner described above its disc will appear so small that it would be judged to be no more than one-twentieth the size. from Jupiter. In fact, a person without perfect vision will find it very difficult to find it, from which it is reasonable to conclude that this star is much brighter than Jupiter and emits greater radiation.

Next, the rays from the sun and moon are nothing because of the size of these bodies, which themselves occupy so much space in our eye that they leave no room for incidental rays, so that their discs appear shaved. and delimited.

We may ascertain the same fact by another experiment which I have made many times, namely, to ascertain that bodies which shine with the most vivid light emit far more rays than those which have only a faint light. I often saw Jupiter and Venus together, twenty-five or thirty degrees from the sun, the sky was very dark. Venus would appear eight or even ten times larger than Jupiter when viewed with the naked eye. But later viewed through a telescope, Jupiter's disk would be four or more times larger than Venus. However, the vividness of Venus' glow was incomparably greater than Jupiter's faint light, which is only because Jupiter is very far from the Sun and us, while Venus is close to us and the Sun.

Having explained these things, it will not be difficult to see how it can be that Mars, when opposed to the Sun and therefore seven times or more closer to Earth than when near the conjunction, us only four or more five should appear in the first state times larger than in the second. Nothing but radiation is the cause of this. For if we deprive it of the incidental rays, we shall find it magnified in just the right proportion. And to remove your hair, the telescope is the only and best tool. Magnifying its disk nine hundred or a thousand times, it can be seen naked and delineated like that of the moon, and in the two positions that vary in just the right proportion.

Next, with Venus, which at her evening conjunction when standing in the sun must appear almost forty times larger than at her morning conjunction and not even doubled, it happens in addition to the effects of irradiation that she is sickle-celled. Shaped like a , its horns are not only very thin, but also receive the sunlight at an angle and are therefore very weak. Being small and faint makes its radiance less abundant and vivid than showing itself to us with its whole hemisphere illuminated. But the telescope shows us clearly that its horns are as finite and distinct as those of the moon, and they are seen to belong to a very large circle, almost forty times larger than the same disk when it is beyond the sun. , at the end of his morning performances.

SAGR. O Nicolaus Copernicus, what a joy it would have been for you to see this part of your system confirmed by so clear an experiment!

OINTMENT. Yes, but how much less would his lofty intellect be celebrated among scholars! For, as I have already said, we can see that, guided by reason, he resolutely proceeded to affirm what sense-experience seemed to contradict. I cannot overcome my amazement that he is constantly willing to say that Venus can revolve around the sun and be more than six times farther from us at one point in time than it is at another and still look the same if it should have appeared must . . . forty times larger.

SAGR. So I believe that you should also see size differences on Jupiter, Saturn, and Mercury that correspond exactly to their different distances.

OINTMENT. On the two outer planets I have observed this closely almost every twenty-two years. No important observations can be made on Mercury since it is only visible at its maximum angles to the Sun, where the inequalities of its distance from Earth are imperceptible. Hence, such differences are unobservable, as are their shape changes, which must surely occur as on Venus. But when we see it, it will necessarily show itself to us in the form of a semicircle, just like Venus at its maximum angles, although its disk is so small and its brightness so bright that the telescope's power is insufficient. Plucking the hair so that it looks completely shaved.

It remains for us to remove what appears to be a major objection to the motion of the earth. This means that although all the planets revolve around the sun, the earth alone is not lonely like the others, but goes together in society. of the moon and the entire elemental sphere around the sun in a year, while at the same time the moon moves around the earth every month. Here we must once more exclaim and extol the admirable wit of Copernicus, and at the same time lament his misfortune to be dead in our day. For now, Jupiter is eliminating this apparent anomaly of the Earth and Moon moving together. We see Jupiter as another earth revolving around the sun in twelve years, accompanied by not one but four moons, along with whatever else may be contained in the orbits of its four satellites.

SAGR. And why are the four Jupiter planets called "moons"?

OINTMENT. This is how they would appear to anyone viewing them from Jupiter. For they are dark in themselves and receive their light from the sun; this can be seen from the fact that they are eclipsed as they enter Jupiter's shadow cone. And since only the hemisphere facing the sun is illuminated by them, they always appear fully illuminated to us, who are out of their orbits and closer to the sun; but for anyone on Jupiter they would appear fully illuminated only when at the highest points of their circles. In the lowest part, that is between Jupiter and the Sun, they would appear as Jupiter's homeland. In a word, they would make the same shape changes on the Jupiters as the moon does on us terrestrials.

Now you see how wonderfully these three tones harmonize with the Copernican system, when at first they seemed so disharmonious. From this, Simplicio will be able to see much better how likely it is that the sun, not the earth, is the center of rotation of the planets. And since this amounts to placing the earth below the bodies of the world which undoubtedly revolve around the sun (above Mercury and Venus, but below Saturn, Jupiter and Mars), why wouldn't it also be probable, or perhaps even necessary? , admit that she also walks around?

POTATOES. These events are so great and so visible that Ptolemy and his followers cannot be aware of them. And having it, they too must have found a way of giving sufficient reasons to explain such reasonable phenomena; congruent and probable reasons since they have been accepted by so many people for so long.

OINTMENT. You argue well, but you must know that the main activity of pure astronomers is just to establish the phenomena of celestial bodies and to fit them and the movements of the stars a structure and an arrangement of circles, which are the calculated result movements corresponding to these phenomena. They aren't too concerned about admitting anomalies that may actually be problematic in other ways. Copernicus himself, in his early studies, writes that he corrected astronomical science to the ancient Ptolemaic assumptions and corrected the movements of the planets so that the calculations agreed much better with the phenomena and vice versa. But that still took them apart, planet by planet. He goes on to say that when he tried to pull together the fabric of all the individual constructions, a monstrous chimera arose, made up of disproportionate members that were incompatible as a whole. So much as the astronomer may be content as a calculator, there was no contentment and peace for the astronomer as a scientist. And as he well understood that although the heavenly phenomena could be saved by essentially false suppositions in nature, it would be much better if he could derive them from true suppositions, he set about eagerly investigating whether it among famous men there is one. Antiquity ascribed to the universe a structure different from that generally accepted by Ptolemy. Finding that some of the Pythagoreans had privately attributed the daily rotation of the earth and others also the annual rotation, under these two new assumptions he began to examine the phenomena and peculiarities of the planetary motions, all of which he readily had in mind. Hand. And when he saw that the whole now corresponded to its parts with wonderful simplicity, he accepted this new arrangement and found inner peace in it.

POTATOES. But what anomalies are there in the Ptolemaic arrangement that do not agree with larger ones in the Copernican?

OINTMENT. Diseases are in Ptolemy and remedies for them in Copernicus. First, do not all philosophical schools consider it a great inconvenience for a body, which has natural circular motion, to move irregularly and regularly about some other point relative to its own center? However, Ptolemy's structure consists of such unequal motions, whereas in the Copernican system each motion is equal about its own center. In Ptolemy it is necessary to ascribe opposite movements to the celestial bodies and to move everything from east to west and at the same time from west to east, while in Copernicus all celestial orbits are in one direction from west to east. And what about a planet's apparent motion, which is so erratic that it not only speeds up one moment and slows down the next, but sometimes stops altogether and even recedes long afterward? To keep up appearances, Ptolemy introduces huge epicycles, adapting them to each planet individually, with specific rules for incongruent moves - all of which can be eliminated by a very simple move of the earth. Don't you find it very absurd, Simplicio, that in Ptolemy's construction, where all the planets are given their own orbits, one above the other, it must be said that Mars, which is above the globe of the Sun, often falls so low? how to break the sphere of the sun, descending beneath it and approaching the earth as the sun's body, and then, a little later, rising immeasurably above it? However, these and other anomalies are healed by a single, simple annual movement of the earth.

SAGR. I want to better understand how these stops, dips, and advances in the Copernican system, which always seem highly unlikely to me, work.

OINTMENT. Sagredo, you will see them fulfilled in such a way that theory alone should be enough to get the assent of the rest of the Teaching from anyone who is neither stubborn nor undisciplined. So I tell you that there will be no change in the movement of Saturn in thirty years, in that of Jupiter in twelve, in that of Mars in two, in that of Venus in nine months, or in that of Mercury in about eighty days. The annual movement of the Earth between Mars and Venus alone causes all of the apparent irregularities of the five named stars. In order to understand this easily and fully, I would like to draw a picture for you. Let us now assume that the sun is at the center 0, around which we will denote the orbit described by the earth with its annual movement BGM. The circle described by Jupiter (for example) in 12 years will be BGM here, and in the star sphere we take the circle of the zodiac as PUA. In addition, we will take some equal arcs in Earth's annual orbit, BC, CD, DE, EF, FG, GH, H1, IK, KL and LK, and in Jupiter's circle we will indicate the other arcs that it is passing at the same time have times when the earth passes them by. These areBC, CD, DR, EF, FG, GH, Hf, IK, KL,eLM, which will be proportionately smaller than those observed in Earth orbit, since Jupiter's movement through the zodiac is slower than annual celestial movement.

Now suppose when the earth is at B, Jupiter is atB, then it appears to us in the zodiac inP, along line BBF. Then let the earth move from B to C and Jupiter from B to C at the same time; Jupiter seems to have reached usQin the zodiac, progressed in the order of the signsPProQ. Earth, then transitioning to D and Jupiter to D, will appear in R in the zodiac; and from E, since Jupiter is in E, it will appear in the zodiac in S and still be moving. But now, when the Earth starts to come right between Jupiter and the Sun (after reaching F and JupiterF), Jupiter seems ready to rotate backwards through the zodiac, because by the time the Earth has passed the EF arc, Jupiter will have decelerated between points S and T and will appear almost stationary to us. Later the earth reaches G, Jupiter inG(as opposed to the sun) is seen in the zodiac inshe, directed backwards over the archTUin the zodiac; but in reality it moved, always following its uniform course, not only in its own circle, but also in the zodiac, relative to the center of the zodiac and the Sun situated there.

Earth and Jupiter then continue moving when Earth is in H and Jupiter is inH, will be seen to have returned along the zodiac throughout the arcuser experience; but the earth reaches me and Jupiter reachesEU, apparently it will have only moved through the small space in the zodiacXYand appears stationary. Then when Earth is advanced to K and Jupiter took, Jupiter will have advanced through the arcNO, in the zodiac; and if it continues on its course, the earth will see Jupiter from EEUat point Z finally Jupiter insideMit is seen from land at M that it has passed into A and is still advancing. And all of your seeming retrograde motion in the zodiac will be as much as the arcTexas, made by Jupiter while passing through the arc in his own circleFH, Earth passes FH on its orbit.

Now what is said here of Jupiter must also be understood of Saturn and Mars. These retrocessions are slightly more frequent on Saturn than on Jupiter because its motion is slower than Jupiter's, allowing Earth to catch up with it in less time. They are rarer on Mars, their movement is faster than Jupiter's, so it takes Earth more time to catch up.

Next, Venus and Mercury, whose orbits are contained within those of Earth, also have stops and retrograde motions appearing in them, not due to any motion actually existing within them, but due to the Earth's annual motion. This is sharply demonstrated by Copernicus, enlisting the help of Apollonius of Perga, in Chapter 35 of Book V in his Book VThe revolution.

You see, gentlemen, how easily and simply the annual movement - when made of the earth - lends itself to giving reasons for the apparent anomalies observed in the movements of the five planets Saturn, Jupiter, Mars, Venus and Mercury will. . He removes them all and reduces these movements to smooth and regular movements; and it was Nicolaus Copernicus who first explained to us the reasons for this wonderful effect.

But another effect, no less marvelous than this, and with a knot perhaps even more difficult to untie, compels the human intellect to allow this annual rotation and grant it to our globe. This is a new and unprecedented theory about the Sun itself. For the Sun has shown that it is reluctant to be left alone to avoid corroboration of such an important conclusion, and instead wants to be invariably the greatest witness of all. Now listen to this powerful new wonder.

(From this follows a theory of the sun's rotation on two axes, based on the movement of sunspots, which Galileo may have been the first to observe with his telescope and which others believed to be possible satellites or moons orbiting the sun.)

... This, Simplicius, is all that my friend and I could think of to explain the apparitions in defense of your views of the Copernicans and the Ptolemies. You can do with it what your own judgment tells you to do.

POTATOES. I acknowledge my own inability to make such an important decision for myself. As for my own ideas, I remain neutral, hoping that a time will come when the mind will be liberated by an enlightenment of contemplations higher than human thought, and all the fogs that obscure it will be swept away.

SAGR. Simplicio's advice is excellent and pious, and worthy of acceptance and heed by all, for only that which comes from supreme wisdom and supreme authority can be accepted with complete certainty. But so far as human reason allows me to penetrate, confining myself to the limits of theory and probable causes, I will say (with a little more boldness than Simplicio shows) that, beneath so many depths that I have already heard have not found anything more marvelous to my intellect or more decidedly conquering my mind (outside of pure geometric and arithmetic proofs) than these two conjectures, one taken from the stops and backwards motions of the five planets, and the other from the peculiarities of the movement of sunspots. And it seems to me that they easily and clearly provide the true cause of such strange phenomena, showing the reason why such phenomena are a simple movement that blends with many others that are also simple but different from each other. Besides, they show it without introducing any difficulties; instead, they remove all those associated with other viewpoints. So much so that I am quick to conclude that those who remain hostile to this teaching need not have heard or understood these arguments, so numerous and so cogent.

OINTMENT. I do not give these arguments the status of conclusive or inconclusive because (as I said before) my intention was not to clarify anything on this important question, but only to give the physical and astronomical reasons the two sides can give me for explaining . I leave the decision to others, which ultimately must not be ambiguous, since one of the orders must be true and the other false. It is therefore not possible, within the limits of human learning, that the reasons assumed by the Right should be anything but unequivocally conclusive, and that the opposing ones be vain and ineffective.

SAGR. Now it's time to hear the other side of this little book of theses or dissertations that Simplício brought with him.

POTATOES. Here is the book, and here is the place where the author first briefly describes the system of the world from the Copernican point of view, saying:Copernicus therefore washed the earth together with the moon and this elementaletc. ("So the earth including the moon and this whole elementary world, Copernicus", etc.)

OINTMENT. Wait a little, Simplicio; for it seems to me that this author declares himself a priori very ignorant of the position he undertakes to refute when he says that Copernicus causes the earth, together with the moon, to trace the orbis Magnnus from east to west in a year. ; a thing which, being false and impossible, was never uttered by Copernicus. In fact, he makes it go in the opposite direction (I mean west to east; that is, in the order of the signs of the zodiac) so that it seems as if the yearly movement belongs to the sun, which "stands still." motionless in the center of the zodiac. .

You see the overconfidence of this man who is preparing to refute another's doctrine while ignorant of the fundamental foundations on which the greatest and most important parts of the entire structure rest. This is a bad start to gain the reader's trust, but let's move on.

POTATOES. After the system of the universe is explained, he begins to state his objections to the annual movement. The first of these he utters ironically, in derision of Copernicus and his followers, and writes that in this fantastic arrangement of the world one must assert the loftiest follies: that the Sun, Venus and Mercury are under the earth; that heavy material naturally rises and light material descends; that Christ, our Savior and Redeemer, ascended into hell and descended into heaven as he drew near the sun. That when Joshua commanded the sun to stand still, the earth stood still...or the sun moved in opposition to the earth; that when the Sun is in Cancer, the earth passes through Capricorn, so that the signs of winter form summer and spring form autumn; that the stars do not rise and set for the earth, but the earth for them; and that the east begins in the west while the west begins in the east; in a word that almost the whole course of the world will be turned upside down.

OINTMENT. All of this suffices me, except that he mixed passages from the ever-venerable and powerful Scriptures into these monkey-like ridicules, and he attempted to use sacred things to offend anyone who could philosophize without assertion or denial in jest and in jest, certain have made assumptions and want to discuss them among friends.

POTATOES. Verily, he has also angered me, and not a little; especially later when he adds that if the Copernicans do in fact answer this and other arguments in some distorted way, they still fail to answer satisfactorily some later things.

OINTMENT. Oh, that's worst of all, for he pretends to have things more effective and persuasive than the authority of Scripture. But for our part, let us bow before him and move on to physical and human arguments. However, if he doesn't add questions to his physics arguments that make more sense than those presented so far, we may be able to abandon him altogether. I'm certainly not in favor of wasting words in replying to such petty nonsense. And what he says about the Copernicans answering these objections is completely wrong. I can't believe any man would devote himself to such a useless waste of time.

POTATOES. I also agree with that decision, so let's hear your other objections, which have more support. Well here, as you can see, using very precise calculations, he deduces whether the orbit in which Copernicus travels from Earth

To make the sun in a year scarcely perceptible in relation to the immensity of the stellar sphere, as Copernicus says, must be assumed, then it must be explained and asserted that the fixed stars are at an unimaginable distance from us, and so the smallest of them would be much larger than this entire orbit, while others would be larger than Saturn's orbit. However, such volumes are really very voluminous and incomprehensible and unbelievable.

OINTMENT. I've actually seen something similar argued by Tycho against Copernicus, so this isn't the first time I've pointed out the fallacy...or rather fallacies...of this argument, which is based on utterly wrong assumptions. It is based on a saying of Copernicus, which is taken strictly literally by his opponents, as are those quarrelsome people who, being wrong on the main point, pick up a single word accidentally uttered by their opponents and make a great fuss. about it without ever giving up.

For your better understanding, you should know that Copernicus first explains the remarkable consequences for the various planets resulting from the Earth's annual motion; especially the forward and backward motions of the three outer planets. Then he adds that these apparent mutations, perceived as greater on Mars than Jupiter because Jupiter is more distant, and even less on Saturn because it is more distant than Jupiter, because of their in the Fixed stars remain imperceptible enormous distance. . from us compared to the distance of Jupiter or Saturn. Here the opponents of this opinion rise up and hold that what Copernicus called “imperceptible” is real and absolutely non-existent. From the observation that even the smallest fixed star is still discernible as soon as it reaches our sense of sight, they go to work (introducing still further wrong assumptions) and conclude that in the Copernican doctrine it must be admitted that a fixed star is much is larger than Earth's orbit.

Now, in order to reveal the folly of his whole method, I must show that, supposing that a star of the sixth magnitude cannot be larger than the Sun, it can be deduced by correct demonstrations that the distance of the fixed stars from us is great enough to make them imperceptible to the annual movement of the earth, which in turn causes such large and observable fluctuations in the planets. At the same time, I will make clear to you a gigantic error in the assumptions of Copernicus' opponents.

First of all, like Copernicus and his opponents, I assume that the radius of the earth's orbit, i.e. the distance from the sun to the earth, contains 1208 of the earth's radii. Secondly, I suppose with equal agreement and consonance with truth, that the apparent diameter of the Sun at its mean distance is about half a degree, or 300 minutes; that's 1,800 seconds, or 108,000 third-order divisions. And since the apparent diameter of a fixed star of the first magnitude is no more than 5 seconds or 300 thirds, and the diameter of one of the sixth magnitude is 50 thirds (and here lies the greatest error of Copernicus' opponents), then the diameter of the Sun contains 2,160 times the diameter of a fixed star of the sixth magnitude. So assuming that a sixth magnitude fixed star is really equal to the sun and not larger, this is tantamount to saying that the sun would recede until its diameter was 1/2160 of what it appears to be seems now his distance should be 2,160 times what he actually is now.

This is equivalent to saying that the distance to a sixth-magnitude fixed star is 2160 radii of the Earth's orbit. And since the distance from the earth to the sun normally contains 1208 earth radii and the distance from the fixed star is, as said, 2160 orbital radii, the radius of the earth relative to that of its orbit is much larger than (almost twice) the radius of this orbit relative to star ball. Therefore, the difference in the aspect of the fixed star caused by the diameter of the Earth's orbit would be scarcely more noticeable than that observed on the Sun due to the Earth's radius. (Note: Galileo's numbers are imprecise but serve the purpose of his argument; He seriously underestimated the stellar distance, but still placed the stars well above the more typical estimates of those he further mentions.)

SAGR. For the first step, this is an ugly fall.

OINTMENT. In fact, it is false, because according to this author, a sixth magnitude star would have to be as large as Earth's orbit to justify the Copernican maxim. However, if one assumes that it corresponds only to the Sun, which in turn is a little less than one ten-millionth of that orbit, the stellar orb becomes so large and distant that this alone is sufficient to remove this objection to Copernicus.

SAGR. Please do this calculation for me.

OINTMENT. The calculation is very short and simple. The diameter of the Sun is 11 Earth radii, and the diameter of the Earth's orbit contains 2416 such radii, both parties agree. So the diameter of the orbit contains about 220 times that of the Sun, and since the spheres are related as the cube of their diameters, we take the cube 220 and we have the orbit 10,648,000 times larger than the Sun. The author would say that a sixth magnitude star should correspond to this orbit.

SAGR. So their mistake is that they were very wrong in assuming the apparent diameter of the fixed stars.

OINTMENT. That's the bug, but not the only one. And indeed I am quite astonished at the number of astronomers, and famous astronomers too, who have been rather wrong in their estimates of the magnitudes of the fixed and moving stars, with the exception of the two great ones. Among these men are al-Fergani, al-Battani, Thabit ben Korah, and more recently Tycho, Clavius, and all the predecessors of our academician. Because they didn't care about the random radiation that deceptively makes stars appear a hundred times or larger than they are viewed without halos. Nor can these men be excused for their negligence; it was in his power to see the naked stars at will, for it is enough to look at them when they first appear at night or just before they disappear at dawn. And Venus should not have been the last thing to warn her about her mistake, as she is often seen so small during the day that it takes keen eyes to see her, although the next night she appears as a large flare. I don't think they thought the true disk of a torch was as it appears in deep darkness, not as it is perceived in bright surroundings; for our lights, seen at night from afar, appear great, but at close range their true flames are small and circumscribed. That alone might have been enough to make her suspicious.

To be honest, I firmly believe that none of them - not even Tycho himself, who was precise with astronomical instruments and despite the fact that he built such large and precise instruments without thinking of their enormous cost - ever set their minds to destiny made and measure the diameter visible from every star except sun and moon. I believe that some of the older astronomers held arbitrarily, and as a general rule so to speak, that such and such was the case, and later adhered without further experiment to what the first had declared. For if any of them had taken the time to examine the matter, they would undoubtedly have discovered the error.

SAGR. But if they didn't have the telescope (for you have already said that our friend saw the truth through that instrument) they should be forgiven, not charged with negligence.

OINTMENT. That would be true if they couldn't get the result without the telescope. It is true that the telescope, by showing the stellar disc bare and magnified many times over, makes the operations much easier, but we could do them without it, although not with the same accuracy. I did and this is the method I used. I hung a light rope in the direction of a star (I used the Vega that rises between North and Northeast) and then, moving towards and away from this rope placed between me and the star, I found the point at which it was wide only hid the star from me. After this I found the distance between my eye and the cord equal to one of the sides including the angle formed in my eye and extending through the width of the cord.

(Salviati begins by describing his method of measuring a star's angular diameter by attempting to remove the halo surrounding it. Through this method, he claims to have discovered that stars have a significantly smaller angular diameter than Eve normally considers. This leads to a brief excursion into the optical properties before returning to the question of star distance.)

OINTMENT. Simplicio, I would ask you to put aside your affection for the followers of your teachings for a moment, and tell me frankly whether you think you comprehend in your own mind the greatness that you later decide you want to give to the universe cannot be attributed because of immensity. I don't think so myself. It seems to me that this is very similar to the gathering of numbers when you reach thousands of millions and the imagination is confused and unable to form a concept. The same happens in understanding the magnitude of immense distances; There is a similar effect on our thinking as on a quiet night when I look at the stars and judge by seeing that their distance is only a few miles or that the fixed stars are not a little further away than Jupiter, Saturn or even the moon .

But all that aside, consider these earlier disputes between astronomers and peripatetic philosophers over considerations of the distances of the new stars in Cassiopeia and Sagittarius, which astronomers placed among the fixed stars and which philosophers believed were nearer than the moon. How incapable are our senses of distinguishing great distances from extremely great distances, when in reality the latter are many thousands of times greater!

And finally, I ask you, o fool, does your imagination first grasp a size for the universe, which you then think is very large? If so, would you like to imagine that your understanding is beyond divine power? Would you like to imagine greater things than God can accomplish? And if you don't understand that, then why are you judging things you don't understand?

POTATOES. These arguments are very good, and no one denies that the size of heaven can be beyond our imagination, since God could have made it even a thousand times larger than it is. But don't we have to admit that nothing in the universe was created in vain or is useless? Now if we see this beautiful order among the planets, spaced about the earth at intervals proportional to the production of their effects to our benefit, to what end would there be an interposition between the highest of their orbits ( d from Saturn)? , and the star sphere, a vast space with nothing in it, superfluous and vain? For whose use and convenience?

OINTMENT. It seems to me that we are too busy, Simplicio, if we want mere concern for ourselves to be the appropriate work of divine wisdom and power, and the limit beyond which nothing creates and commands nothing.

I don't want us to tie your hand like that. We should be quite content to know that God and nature are so occupied with the government of human affairs that they could not be more devoted to us even if they had no other concerns to attend to than those of the human race. I think I can explain what I mean by a very fitting and noble example derived from the action of sunlight. Because if the sun extracts any fumes here or warms a plant there, it attracts and heats it up as if it had nothing else to do. Even with the ripening of a bunch of grapes, or perhaps just a single bunch of grapes, he works so effectively that he could not do more even if the aim of all his business was the ripening of that bunch. Now, if this cluster receives from the sun all it can receive and is not deprived of the least bit of the sun, simultaneously producing thousands upon thousands of other results, then this cluster would be guilty of pride or envy if they believe or desire would that the effect of the sun's rays should be applied only to himself.

I am sure that Divine Providence omits nothing concerning the government of human affairs, but I cannot believe that there can be no other things in the universe that depend upon the infinity of their wisdom, at least as far as my reason informs me ; However, if the facts were otherwise, I could not resist believing the reasoning I have borrowed from a higher understanding. However, when I am told that a vast space between the planetary orbits and the stellar sphere would be useless and vain, being idle and starless, and that any immensity beyond our comprehension would be superfluous to accommodate the fixed stars, I say that it is for ours It is unwise to try to judge the reason for God's actions and to dismiss as vain and superfluous everything in the universe that does not serve us.

SAGR. Rather say, and I think you say more precisely, "what we do not know, to serve us." I think one of the greatest pieces of arrogance. or rather, the madness one can imagine is to say, "Since I don't know how Jupiter or Saturn can serve me, they are superfluous and don't even exist." For, oh deluded man, I do not know how my arteries serve me, nor my cartilage, spleen, or bile, I should not even know that I have bile, or spleen, or kidneys, had they not been shown to me in many dissected corpses . Still, I could only understand what my spleen would do for me if it were removed. In order to understand how a celestial body has acted on me (since you want all your actions to be directed at me), it would be necessary to remove that body for a while and say that the effect I may be missing, depends on this star.

Besides, what does it mean to say that the space between Saturn and the fixed stars, which these men call very vast and useless, is void of the bodies of the world? Maybe we don't see them? So did the four satellites of Jupiter and Saturn's companions reach the sky when we began to see them and not before? Were there not innumerable other fixed stars before man began to see them?

OINTMENT. There is no need, Sagredo, to deepen your fruitless exaggerations. Let's proceed with our plan, which is to examine the validity of the arguments put forward by both sides without deciding anything, leaving the decision to those who know more than we do.

Coming back to our natural and human reason, I say that these terms 'big', 'small', 'immense', 'tiny' etc. are not absolute but relative; the same can be called either "immense" or "imperceptible", let alone "small" in comparison to several others. In view of this, I ask: compared to what can the stellar sphere of Copernicus be called too large? As far as I can see it cannot be compared or considered very extensive except in relation to something else of the same kind. Now let's take the smallest thing of the same type, which will be the moon's orbit. If the stellar orb is to be regarded as very gigantic in relation to that of the moon, then every other magnitude which exceeds every other of its kind by a like or greater proportion must also be regarded as very gigantic; and likewise, from the same reasoning, it must be said that it does not exist in the universe. Then the elephant and the whale will be mere chimeras and poetic fictions, because the former are very large compared to ants (as land animals) and the latter compared to gudgeons (as fish). And if they were actually found in nature, they would be immeasurably large; for the elephant and the whale are certainly superior to the ant and the gudgeon to a far greater extent than the stellar globe exceeds that of the moon, bringing the stellar globe to the size required by the Copernican system.

Furthermore, how great is the sphere of Jupiter, and how great is that attributed to Saturn as the receptacle of a single star, though the planet itself is small compared to a fixed star! Certainly if every fixed star as large as a portion of space were called its container, this sphere, containing an innumerable quantity of them, would have to be made many thousands of times larger than was sufficient for Copernicus' needs. Don't you also call a fixed star very small - I mean, even one of the most conspicuous ones, let alone the ones that elude our sight? And we call it that in comparison to the surrounding space. Now if the whole sphere of stars were a single luminous body, who does not understand that in an infinite space one could assign such a great distance that from there such a luminous sphere would now appear as small or even smaller than a fixed star appears in our eyes from the earth? Hence, from such a point, we must judge as small the very things that we now call immeasurably large.

SAGR. To me there is great incompetence on the part of those who want God to have created the universe in proportion to the small capacity of his reason rather than to his immense, infinite power.

SEMP. Everything you say is fine, but what the other side objects to is having to admit that a fixed star must not only be equal to, but much larger than, the sun; for both are still individual bodies located within the star sphere. And it seems to me very pertinent that this author should ask: "For what purpose and use are frames so huge? Perhaps made for the earth? That is, for an insignificant speck? And why so distant that they seem very small? and being too utterly incapacitated on Earth? Why is there such a disproportionately large chasm between these and Saturn? All these things are troubling because, for probable reasons, they cannot be sustained."

OINTMENT. It seems to me to infer from the questions this fellow is asking that if only the sky, the stars, and their distances could maintain the magnitudes and magnitudes he has hitherto believed in (although he certainly never imagined anything intelligible to them Orders of magnitude ) then he would fully understand and be content with the benefits they would emanate for the country, which in itself would no longer be such an insignificant thing. These stars would also no longer be so distant that they appear tiny, but large enough to have an impact on Earth. And the distance between them and Saturn would be in good proportion, and he would have very probable reasons for everything, which I'd love to hear. But seeing how confused and contradictory he is in those few words leads me to believe that he is being too parsimonious or difficult for these probable reasons, and that what he calls reasons are most likely fallacies, even shadows of foolish fantasies. So I ask you, do these celestial bodies really work on earth, and is that why they were placed in such and such a large and such and such a distance, or do they have nothing to do with earthly affairs? If they have nothing to do with Earth, then it is great folly for us Earthlings to want to be arbiters of their magnitudes and regulators of their local dispositions while we are utterly ignorant of all their affairs and interests. But when he says that they are acting and that they aim to do so, it amounts to admitting what he denies elsewhere and praising what he has just condemned when he said that the celestial bodies are moving so far from the Country find that it seems tiny could not affect it in any way. Now, my good man, in the stellar sphere, which may already be at whatever distance, and which, as you have just decided, is well proportioned to have an impact on terrestrial affairs, a multitude of stars appear very small , hundreds of times as many are completely invisible to us, which should look smaller than small. So you must now (contradicting yourself) deny your actions on earth or (still contradicting yourself) admit that your humble appearance does not diminish your agency. Or (and that would be a frank and honest admission) you must admit and freely admit that your judgment of their greatness and distance was folly, not to say presumption or audacity.

POTATOES. Yes, while reading this passage I immediately noticed the obvious contradiction in his statement that the stars of Copernicus could not work on earth, so to speak, because they looked so small, and that he did not realize that he had one on earth Effect has given earth, earth to the stars of Ptolemy and his own, which not only appear small but are mostly invisible.

OINTMENT. But now I come to another point. On what basis does he say the stars look so small? Is it perhaps because they appear that way to us? Doesn't he know that this comes from the instrument we use to look at them - our eyes? Or, as we switch instruments, can we see them get as much bigger and bigger as we want? Who knows; Perhaps they could appear huge to the eyeless earth staring at them and what they really are?

But it's time to leave those little things behind and focus on more important things. I have already shown two things: First, at what distance can the firmament be placed so that the diameter of the earth's orbit undergoes no greater change than the diameter of the earth relative to the sun at a distance from it, and I then showed this, for although we a fixed star appears as large as we see it, it is not necessary to assume that it is larger than the sun. Now I want to know whether Tycho or any of his disciples ever attempted in any way to investigate whether any phenomenon is perceived in the stellar sphere by which the annual motion of the earth may be boldly asserted or denied.

SAGR. I should answer "no" for them as they don't need it since Copernicus himself says there is no such variation there; and they grant it to him, arguing ad hominem. Then, on the basis of this assumption, they show the consequent improbability; That is to say, it would be necessary to make the sphere so huge that, for a fixed star to appear so large, it would have to be of such enormous volume that it would exceed the orbit of the earth - a thing that is, as they say, absolute incredible.OINTMENT. So it seems to me, and I believe they argue against man more in defense of another man than out of a great desire to know the truth. And not only do I believe that none of them ever made such observations, but I am also not sure that any of them knew what variation in the fixed stars would have been produced by the annual motion of the earth if the stellar motion of the spheres were not so distant that any variation in them would vanish due to their small size. For to refrain from such research and resort to the mere dictum of Copernicus may be enough to refute the man, but certainly not to clear up the fact.

Now there may be a variation, but it is not sought; or that it was unknown to Copernicus because of its small size or lack of precise instruments. (Note: stellar parallax is not discovered until 1837.) That wouldn't be the first thing he would unlearn, whether it's because of a lack of instruments or some other disability. However, based on the most solid theories, he asserted what seemed to be contradicted by things he did not understand. Because, as has already been said, it is impossible to understand without a telescope that Mars in one position relative to the other increases sixty times, and Venus increases forty times, and their differences seem to be much smaller than the true ones. Since that time, however, it has been established that such variations by a hair's breadth are exactly what the Copernican system requires. Therefore, it would be good to investigate as closely as possible whether one could really observe a variation as it should be perceived with the fixed stars, assuming an annual movement of the earth.

(There follows a discussion of what types of motion are or are not discernible between the stars, given the Earth's annual rotation about a fixed axis, and Salvian's claim that the stars are not all equidistant from the (assumed) center of the universe.)

POTATOES. To be honest, I have a great reluctance to admit that the distances between the fixed stars are so great that the changes in them that we have just explained should remain quite imperceptible.

OINTMENT. Do not despair entirely, Simplicio; perhaps there is another way to alleviate your difficulties. First, you don't need to feel completely improbable that the apparent size of stars doesn't change visibly when you see that people's estimates of such a matter can be so grossly off, especially when looking at bright objects. For example, if you look at a flaming torch two hundred paces away and then approach it ten or four feet, do you think you would see it larger yourself? For my part, I certainly would not discover it, even if I approached twenty or thirty paces; sometimes it even happened to me to see such a light in the distance and I couldn't decide if it was coming towards me or going away, although it was actually approaching. And now? If the same approach and retreat from Saturn (I mean twice the distance from the Sun to us) is almost imperceptible, and if it's almost imperceptible on Jupiter, what could it mean in the fixed stars, which I don't think you do would ? hesitate to put twice as far away as Saturn? On Mars approaching us. . .

POTATOES. Please do not insist on this point, as I am truly convinced that what you have said about the unchanging appearance of the apparent magnitudes of fixed stars may well be the case. But what shall we say of that other difficulty which arises from seeing no change in its changing aspects?

OINTMENT. Let's say something that can satisfy you on this point as well. In short, would you be happy if those changes in the heavenly bodies were really noticed, which seem so necessary to you if the annual movement is part of the earth?

POTATOES. I really ought to be regarding this particular.

OINTMENT. I wish you had said that if such a variation were noticed, there would be nothing left to cast doubt on Earth's mobility, since no counter could be found for such an event. But even if this is not visible to us, it neither excludes the mobility of the earth nor necessarily proves its immobility. It is possible, Copernicus explains, that the immense distance of the stellar sphere renders these small phenomena unobservable. And as has already been remarked, they may not even have been sought before, or, if they are sought, not as they ought to be; that is, with all the necessary precision and minute precision. It is difficult to achieve this level of accuracy, both because of the imperfections of astronomical instruments, which are subject to many variations, and the shortcomings of those who handle them with less care than is necessary. A compelling reason for giving little confidence to such observations is the disagreement which we find among astronomers in the attribution of the localities, I might say, not only of novae and comets, but also of fixed stars themselves, and even of polar altitudes about which they disagree. usually for many minutes.

Indeed, how would you expect someone with a quadrant or sextant, who typically has a 10 or 15 foot arm, to be sure that they are not in the vertical attitude or alignment for two or three minutes? from alidade? (Note: An instrument for measuring angles.) For in such an extent it will not be more than the thickness of a grain of millet. In addition, it is nearly impossible to construct and maintain the instrument with absolute accuracy. Ptolemy was suspicious of an armillary instrument built by Archimedes himself to determine when the sun entered the equinox.

POTATOES. But when the instruments are suspicious and the observations so doubtful, how can we safely accept and disprove them? I have heard great praise for Tycho's instruments, which were made at enormous expense, and for his remarkable ability to make observations.

OINTMENT. I admit all this, but neither one nor the other fact is enough to give us certainty on such important matters. I want us to use instruments much larger than Tycho's; made precisely and at minimal cost, the sides of which will be four, six, twenty, thirty, or fifty miles long, so that a degree is a mile wide, a minute fifty yards, and a second just under a yard. . In a word, we can have them in the size we want without costing us anything.

While in one of my villas near Florence, I clearly observed the arrival of the sun at the summer solstice and its subsequent departure. For one night it hid behind a cliff in the Pietrapana Mountains some sixty miles away, leaving only a small fragment of itself to the north, the width of which was not one-hundredth of its diameter. But the next night, in the same placement position, she left a similar part of herself visible, visibly thinner. This is conclusive evidence that it has begun to move away from the Tropic; However, the Sun's return between the first and second observations certainly did not amount to one arc second along the horizon. Later observation with a thin telescope that would magnify the sun's disk a thousandfold turned out to be beautifully simple.

My idea now is that we carry out our observations of the fixed stars with similar instruments, using a star where the changes can be seen. These, as I have already explained, are the ones farthest from the ecliptic. Among them, Vega, a very large star near the pole of the ecliptic, would be the most convenient for the way it works, which I will describe to you in a moment, as far as the northernmost countries are concerned, although I will use a different star. I have already looked for a place that is well suited for such observations. The place is an open plain, over which rises to the north a very prominent mountain, on the top of which is built a small chapel, facing west and east so that the pediment of its roof intersects the meridian over a house at right angles can be located in the plain. I want to attach a joist parallel to this joist and about a meter above it. After that I will look in the plane for the place where one of the stars of the Big Dipper is occluded by this ray I placed, exactly when the star crosses the meridian. Or, if the ray is not large enough to hide the star, I find the point from which the star's disk can be seen cut in half by the ray - an effect perfectly seen through a fine telescope can be. It will be very convenient if there is a house on the spot from which this event can be observed, but if not then I will drive a stick firmly into the ground and make a mark to indicate where the eye is placed shall be. whenever the observation is repeated. I will make the first of these observations at the summer solstice to continue month by month or whenever I choose until the next solstice.

Through these observations, one can discern the rising or falling of the star, no matter how small. And if in the course of these operations any variation of this kind should become known, what a great achievement in astronomy! distance from the same star.

SAGR. I understand the whole procedure perfectly, and the operations seem to me so simple and so well adapted to what is desired that it is reasonable to assume that Copernicus himself or some other astronomer actually performed them.

OINTMENT. It seems the opposite to me as it is unlikely that anyone who would have attempted this would not have mentioned the result, regardless of positive opinion. However, no one is known to have used this method for the above purpose or for any other purpose; and without a good telescope it could not be put into practice very well.

SAGR. What you say satisfies me completely. Well, with the night still far away, if you want me to get some rest then, hopefully it won't be too much trouble for you to explain to us these issues that you just asked us to put off until tomorrow. Please give us back the pardon we grant you and, apart from all other arguments, tell us how (assuming the motions Copernicus ascribes to the earth and by keeping the sun motionless and the stars fixed) such Events can occur as far as related to the rising and setting of the sun, the changing of the seasons, and the inequality of nights and days, as is so easily understood in the Ptolemaic system.

OINTMENT. I cannot and must not reject anything that Sagredo advocates. The delay I asked for was only to give me time to rearrange in my mind the premises useful for a clear and comprehensive explanation of how these events occur in the Copernican system as well as the Ptolemaic system . In fact, easier and simpler in the first than in the second, so that it is plain to see that the first hypothesis is as easy for nature to realize as it is difficult for the intellect to understand. However, I hope to make even learning much less obscure by using explanations different from Copernicus'. To do this I will set some assumptions as known and self-evident as follows:

First. I suppose that the earth is a spherical body revolving about its own axis and poles, and that every point on its surface describes the circumference of a circle, larger or smaller according as the point referred is more or less from the poles is removed. Of these circles, the largest is that drawn from a point equidistant from the poles. All of these circles are parallel to each other, and we will denote them asparallel.

Second. Because the earth is spherical and its material is opaque, half of its surface is constantly illuminated and the rest is dark. The border separating the lighted part from the dark part is a big circle, we call it the light border circle.

third party When the limiting circle of light passes through the poles of the earth, it will cut all parallels into equal sections and form a great circle; but if it does not go through the poles, it will cut all into unequal parts, except the central circle; since this is also a great circle, it will be cut into equal parts in any case.

Bedroom. As the earth revolves around its own poles, the length of day and night is determined by the arcs of parallels intersected by the bounding circle of light. The arc left in the illuminated hemisphere determines the length of the day and the rest of the night.

Now that these things have been explained, we might want to draw a diagram to understand more clearly what's next. (Fig. 6) First we indicate the circumference of a circle, which represents for us the orbit of the earth, which is described in the plane of the ecliptic. This we can divide into four equal parts by two diameters; Capricorn, Cancer, Libra and Aries, which here simultaneously represent the four cardinal points; that is, the two solstices and the two equinoxes. And in the center of this circle we signify the sun, oh, fixed and immovable

With the four points Capricorn, Cancer, Libra and Aries as the center, we now draw four circles of equal size, which represent the earth in these four different seasons. The center of the earth moves within a year around the entire orbit of Capricorn-Aries-Cancer-Libra, (Note: Counter-clockwise from top left of page.) in the order of the signs of the zodiac from west to east. It is already clear that when the Earth is in Capricorn, the Sun appears in Cancer, the Earth moves along the arc of

Capricorn to Aries, the Sun seems to move along the arc from Cancer to Libra. In a word, he will cycle through the signs of the zodiac within a year. Thus, with this first assumption, the apparent annual movement of the sun around the ecliptic is fulfilled without a doubt.

Coming now to the other motion—that is, the daily motion of the earth about itself—its poles and axes must be ascertained. These are not to be understood perpendicular to the plane of the ecliptic; That is, not parallel to the axis of Earth's orbit, but inclined at a right angle by about twenty-three and a half degrees, with the North Pole pointing toward the axis of Earth's orbit, when the center of the Earth is at the solstice Capricorn, so that the center of the terrestrial sphere is at that point, let give us the poles and the AB axis, which is inclined twenty-three and a half degrees from the normal in the Capricorn-Cancer diameter, so that A-Capricorn-Cancer angle is equal to the complement, or sixty-six and a half degrees, and this inclination must be considered invariable. We take the upper pole, A, north and the other, B, south.

If one assumes that the earth rotates around its AB axis in 24 hours, also from west to east, then parallel circles are described by all points observed on its surface. In this first earth position we shall denote the great circle CD and the two that are twenty-three and a half degrees distant from it—EF above and GN below—and these others at the two extremes, 1K and LM, at a similar distance from it, the poles A and B; and we could have drawn innumerable other circles parallel to these five, traced from innumerable points on the earth. Suppose now that the earth is carried by the annual movement of its center to the other positions already marked and passes to them according to the following laws: that its own axis AB not only does not change its inclination to the plane of the ecliptic , but that it also does not change direction; thus always remaining parallel to itself, it continually points to the same parts of the universe, or shall we say the firmament. This means that if we imagine the axis extended, its top end would describe a circle parallel and equal to the orbit of the earth through Libra, Capricorn, Aries and Cancer, like the top base of a cylinder centered within it self describes annual movement around the lower base, Libra-Capricorn-Aries-Cancer. Because of this invariable inclination, we will therefore draw these other three figures around the centers of Aries, Cancer and Libra, just like the one drawn around the center of Capricorn.

Next, let's look at the first diagram of the earth. Since the axis AB is inclined twenty-three and a half degrees to the sun, and the arc Al is also twenty-three and a half degrees, the sun's light illuminates the sun-exposed hemisphere of the globe (only half of which is shown here), from the dark part through the light boundary IM disconnected. The parallel CD, which is a great circle, is divided equally by these, but all others are cut into unequal parts because the bright boundary W does not pass poles A and B. The parallel IK together with all the others described between it and the pole A will be entirely within the illuminated part, as, on the other hand, the opposites to the pole B and contained in the parallel LM will remain obscure.

Furthermore, since arc Al is equal to arc FD and arc AF is common to IKF and AFD, the last two are equal, each being a quadrant; and since every IFM arc is a semicircle, the MF arc is also a quadrant and equals FKI. Therefore, in this position of the earth, the sun 0 will be perpendicular to everyone. at the point F. But by the diurnal revolution about the fixed axis AB, all points on the parallel EF pass through the same point F, and hence on such a day the midday sun will be over all the inhabitants of the parallel PE; and to them it seems, by its motion, to describe that circle which we call the Tropic of Cancer.

But for the denizens of all parallels above the parallel EF toward the North Pole, A, the sun is below its zenith toward the south. On the other hand, for all inhabitants of the parallels below EF to the CID equator and to the South Pole B, the midday sun stands over the zenith to the North Pole A.

Next you can see how of all the parallels only the great circle CD is cut into equal parts by the boundary of the IM light, while the others above and below are all cut into unequal parts. Of the higher ones, the semidiurnal arcs (that is, those in the sunlit part of the earth) are larger than the semidiurnal ones that remain in darkness. The opposite occurs for the others located below the larger circle CD towards pole B; of these the semi-diurnal arcs are smaller than the semi-nocturnal. You can also clearly see that the differences in these arcs increase as the parallels get closer to the poles, until the IK parallel stays entirely in the lighted part and its occupants have a 24-hour day with no night. In contrast, the parallel LM, which remains completely in the dark, has a 24-hour dayless night.

Then we move on to the third diagram of the Earth, which is placed here with its center at the point of Cancer from which the Sun appears to be at the first point of Capricorn. It's really easy to see that since the AB axis hasn't changed its tilt but has stayed parallel to itself, the Earth's appearance and situation is exactly the same as in the first diagram, except that the hemisphere, the illuminated in the first diagram, by the sun remains in shadow here, and what was previously dark now becomes light. What happened in the first diagram is now reversed in terms of the differences in days and nights and their relative duration or shortness.

The first thing you notice is that the 1K circle was all light in the first image, now it is all dark; and LM, the opposite, is now in full light where it used to be in full shadow. Of the parallels between the great circle CD and the pole A, the semi-diurnal arcs are now smaller than the semi-diurnal arc, which is the opposite of the first; and from the others to pole B the semidiurnal arcs are now longer than the semicircular ones, just like the opposite of what happened in the earth's other position. Now you can see the sun made vertical for the inhabitants of the tropic GN, and for those of the parallel EF it is pushed south through the entire ECG arc; that is, forty-seven degrees. In short, it went from one tropic to the other, past the equator, up and down the meridian in the said forty-seven degree interval. All these changes do not originate in a fall or an uplift of the earth; on the contrary, never descending or ascending, but generally always staying in the same place with respect to the universe, simply revolving around the sun, which is at the center of the same plane that the earth revolves around the annual motion.

A remarkable phenomenon must be noted here, namely that, like keeping the earth's axis in the same direction with respect to the universe (or shall we say in the direction of the highest fixed stars), the sun makes us appear as if it were going to the 40th five seven degrees with no rise or fall of the fixed stars, so if, on the contrary, the earth's axis were constantly held at a certain inclination to the sun (or we might say to the axis of the zodiac), no change in rise or fall seems to be made by the sun. Thus, the inhabitants of a given place would always have the same night and day times and be of the same type or season; i.e. some people would always have Writer, some would always see it, some would spring it up, etc. seven degrees. To understand this, let's return to looking at the Earth's position in the first diagram, where the AB axis can be seen with its top pole A tilted toward the Sun. In the third figure the same axis has retained the same direction to the highest sphere and has remained parallel to itself, so that the upper pole A is no longer inclined towards the Sun but is inclined away from it, being forty-seven degrees from its first position. Thus, to reproduce the same inclination of pole A to the Sun, it would be necessary (by rotating the globe along its circumference ACBD) to bring it forty-seven degrees toward E; and every fixed star observed along the meridian would be raised or lowered by that many degrees. Now let's proceed with an explanation of the rest and consider the Earth placed in the fourth diagram with its center in the first point of Libra, with the Sun appearing at the beginning of Aries. Thus the Earth's axis, which in the first diagram is considered to be inclined to the Capricorn-Cancer diameter and thus in the same plane that perpendicularly intersects the Earth's orbit in the Capricorn-Cancer line, is transferred to the fourth figure (kept always parallel to itself, as we said) happens to be in a plane that is as perpendicular to the plane of Earth's orbit as it is parallel to the one it intersects at right angles along the Capricorn-Cancer diameter. Therefore, the line from the center of the sun to the center of the earth (from 0 to Libra) is perpendicular to the BA axis. But this same line from the center of the sun to the center of the earth is always perpendicular to the limiting circle of light; Therefore, in the fourth figure, the same circle will pass through poles A and B, and the axis AB will lie in its plane. But the great circle going through the poles of the parallels will divide them all into equal parts, hence the arcs IK EF, CD, GN and LM will all be semicircles, and the lighted hemisphere will be the one facing us and the Sun and the limit circle of light will be the same circumference ACBD. And when the earth is in that place, the equinox will come for all her inhabitants.

The same will happen in the second diagram, where the earth, whose illuminated hemisphere faces the sun, shows us its dark side with the nocturnal arcs. These too are all semicircles and consequently also form an equinox. Finally, since the line drawn from the center of the Sun to the center of the Earth is perpendicular to the AB axis, to which the great circle CD between the parallels is also perpendicular, the same line OLibra necessarily passes through the same plane as the parallel CD, which intersects its circumference at the midpoint of the arc CD ; Therefore, the sun is vertical for everyone who is in this section. But all the inhabitants of this parallel, swept along by the rotation of the earth, pass by this way, and have the midday sun directly overhead; Therefore, the sun will appear to all inhabitants of the earth to trace the greatest parallel, called the equatorial circle.

In addition, since the earth is at one of the solstices, one of the arctic circles IK or LM is entirely in light and the other in shadow; but when the earth is at the equinox points, half of each of these polar circles is light and the rest is dark. It shouldn't be hard to see if the earth goes from Cancer (where the IK parallel is totally dark) to Leo, for example, part of the IK parallel towards the I point comes to light and the IM light boundary starts in retreating towards poles A and B and no longer intersects the circle ACBD at I and M, but at two other points lying between the ends I, A, M and B of the arcs IA and MB. Thus, the inhabitants of the IK circle begin to enjoy the light, and those of the LM circle to enjoy the darkness.

So see how two simple, non-contradictory movements ascribed to the earth, performed at times well suited to their size, and also performed from west to east, as is the case with all moving bodies in the world , provide reasonable causes for all visible phenomena. These phenomena can only be reconciled with a solid Earth, by abandoning all symmetry seen between the velocities and sizes of moving bodies, and by ascribing to a giant sphere an unimaginable speed above all others, while the smaller ones move balls very hard. slow. Furthermore, the movement of the first must be opposed to the second, and to increase the improbability the highest sphere must be made to carry all the lower spheres against its own inclination. I leave it to your judgment who is more likely to do so.

SAGR. As far as my senses are concerned, there is a great difference to me between the simplicity and ease of achieving results with the means given in this new arrangement and the variety, confusion and difficulty encountered in the old and generally accepted arrangement are . For if the universe were ordered according to such diversity, it would be necessary to eliminate from philosophy many axioms held in common by all philosophers. It is said that nature does not multiply things unnecessarily; that it uses the simplest and simplest means to achieve its effect; that she doesn't do anything for free and so on.

I must confess that I have heard nothing more admirable, nor can I believe that the human mind has ever penetrated to more subtle speculations. I don't know about Simplicio.

POTATOES. If I have to be honest, it seems to me that these are some of those geometric intricacies that Aristotle criticized in Plato when he accused him of deviating from sound philosophy by studying too much geometry. I have known some great Peripatetic philosophers, and heard them discourage their students from studying mathematics, because it makes the intellect sophistical and unfit for true philosophizing; a doctrine diametrically opposed to that of Plato, who would admit no one to philosophy unless he had first mastered geometry.

OINTMENT. I support the policy of those peripatetics of yours to discourage their students from the study of geometry, as there is no art better suited to propagate their errors. You see how different they are from mathematical philosophers, who prefer to deal with those who are well informed about general philosophy ←-The Third Day 81-→ Peripatetics than with those who lack such information and who, by virtue of this In the absence of being unable to make comparisons of one doctrine and another.

But apart from that, please tell me what absurdities or over-the-top sophistry make this Copernican arrangement less plausible to you.

POTATOES. In fact I didn't quite get it, perhaps because I'm also not very knowledgeable about how Ptolemy produces the same effects...etc. But other than the consequences that flow from the basic assumptions, I have no small difficulty in to exist on these assumptions themselves, and when the assumptions fall to the ground, they will ruin the whole structure. Now that it seems to me that the whole structure of Copernicus is built on a weak foundation (based on the mobility of the earth) then there would be no room for further argument if this were removed. And to remove it, Aristotle's axiom that for a simple body only simple movements can be natural seems to suffice. Here the earth, a simple body, is assigned three, if not four, motions; and they are all quite different from each other. Because in addition to the linear movement towards the center, which cannot be denied as a heavy body, it is assigned a circular movement in a large circle around the sun in one year and a rotation around itself every twenty years and four hours, and (what more extreme, and perhaps for that reason you have been silent about it) another rotation about your own center, which will be completed in a year and is opposed to the 24-hour movement mentioned above. My mind feels a great aversion to it.

(The three characters re-enter the realm of physics, from where they move on to a discussion of William Gilbert's De Wagnele (1600), his theories of magnetism, and the possibility that the earth is a magnet. This ends the third day. The fourth day - by far the shortest segment - is devoted almost entirely to Galileo's theory that the earth's motion is the cause of the tides. In it he criticizes Kepler, who attributed the tides to the influence of the moon. While Kepler was closer to the truth, Galileo distrusted what he saw as the mystery of planetary influence and sought a purely mechanical explanation.)

Those:

Notes on the text:

The full title is "DIALOGUE ABOUT THE TWO MAIN WORLD SYSTEMS: THE PTOLEMIC AND THE COPERNICAN.“The book, published in 1632, summarizes Galileo Galilei's ideas and views on questions in the field of astronomy.

The book discusses the two competing astronomical theories - the Ptolemaic, according to which the earth is the center of the world, and the Copernican, which assumes that the sun is immobile and the planets orbit around it. Galileo examines both theories in terms of their ability to explain phenomena actually observed in the sky and their agreement with known terrestrial phenomena. As part of the astronomical discussion, the book also addresses physical laws such as the laws of motion.

The book was written in Italian as a dialogue, that is, a conversation between three people, Salivati, who takes the position of Galileo, Simplicio, who takes the place of the Aristotelian philosophers who regard the earth as immovable, and Sagrado, a Venetian nobleman who presented as a layman (i.e., non-expert) willing to learn from the other two speakers. The dialogue weighs the plausibility of the two models of the structure of the universe. Its official purpose is to understand and enjoy the debate itself, rather than judging which theory is true. However, it is evident that the book accepts the Copernican theory and rejects the Ptolemaic theory. After the publication of the book, Galileo was accused by the Inquisition of believing and teaching the theory that the earth moves, contrary to what the Church expressly forbade.

The book is divided into four days (chapters). Every day the conversation revolves around a different topic. On the first day, Galileo speaks out against the hitherto accepted Aristotelian physics. According to Aristotle, the supralunar world consists of a special material that differs from terrestrial material. Ether is a very hard material, but lighter than anything known on Earth. The main property of the ether is its circular motion, and therefore all stars naturally move in a circle. Galileo shows that there is no difference between the matter in the heavens and the earth, and thus asserts that the stars are not made of ether. The stars and bodies on earth obey the same laws of nature. Galileo dedicates the second part of the dialogue to the law of inertia, showing that there is no difference between motion and rest, and that therefore the motion of the earth is possible without any sensation of motion. The third part is devoted to the analysis of astronomical phenomena to show that there is creation and destruction in the sky too, and that not everything on the moon is as eternal and permanent as Aristotle claimed. The fourth day is dedicated to the Copernican explanation of the solar system and the tides and ebbs on earth. Interestingly, in this description, Galileo describes the motion of the planets as circular, although twenty years earlier Kepler had shown that the orbits of the stars are elliptical.