Treatise on the Sphere with Commentaries

Calo Calonymos the Hebrew, to the Reverend Lord, Lord Io. Mattheo de Gibertis, Bishop of Verona, greetings.

The ancient philosophers physici, in order to perfect themselves, Reverend Lord, inquiring into the causes of the whole universe, were moved by the greatest wonder when they saw the stars, or rather the planets themselves, involved in their own motions. For sometimes they are swift, sometimes slow, and so it happens that at times they proceed directly, at times they retrograde, and similarly they are found to move now toward the north, now toward the south, in addition to other differences found in them. For it is widely evident to them that the celestial bodies ought to move uniformly, for their substance is free from such variations. Searching for the causes of these in the orbs placed in the highest sphere—for in the highest sphere uniformity is always perceived—they discovered that this proceeds from gyrating motions, called lullabini gyrating/whirling, made indeed by the permission of the motion of the orb on its poles with the motion of the same on the poles of another. Thus, from many motions collected together, one motion is made. This theory, conformable to physical reasons, was valid among all the ancients up to Aristotle, the prince of philosophers, who indeed, with the sharp edge of his intellect, never ceases to inquire into it, as Averroes attests (2 De Caelo, com. 35). Ptolemy, however, stirred by greed or "eagerness" which had existed before, decided that this former theory should be rejected, saying that it was entangled in too many motions, while he had found a simpler and easier one, as he opined, which men indeed greatly cultivate and observe. The ancients, however, passing it over with a certain voluntary oblivion, writing and publishing the book of the Almagest to provide causes for the diversities of the apparent motions, reduced these indeed to two roots: one, an eccentric an orb whose center is offset from the center of the world orb found in every orb of the planets; the other, an epicycle a secondary orb revolving around a point on the primary orb to which the planet itself is affixed. He built that volume upon both these foundations, which were as firm for him as they were weak and fragile for the philosophers, especially for Averroes in his commentaries on Aristotle (especially 2 De Caelo, com. 35 mentioned above, and 12 Metaphysics, com. 45), as well as in the preface to his Almagest, in which he collected in brief words all that Ptolemy placed in the Almagest. For in these places and others, he strives with many demonstrations to attack eccentrics and epicycles, which I cease to recite here for the sake of brevity. Moreover, he truly feels that the old theory is correct, promising furthermore (in com. 35 mentioned above) that if God grants him days, he wishes to inquire into that theory which was cultivated in the time of Aristotle, conformable indeed to physical science. He pursues this same thing in the preface to his Almagest. And in com. 45 mentioned above, he despairs of being able to reach this investigation, being worn out by old age and burdened by occupations, which in his youth he hoped for with a strong spirit. He truly imitates in the aforementioned the footsteps of Alexander and Themistius, the ancient interpreters of Aristotle, as is evident to one looking into their volumes, even if this is assigned to Averroes alone by all as if he were the heir of philosophy. And since he, in the end of the aforementioned com. 45, stirring up men, said, "Perhaps what I have put here will incite later thinkers to investigate these things," I do not know what spirit of divination moved him to predict what would come. Thus, a certain extraordinary man, singularly gifted in the mathematical disciplines among the Arab wise men, whose name is Alpetragius, wrote this short work in which he first attacks the entire Ptolemaic theory with physical reasons; then he explains his own both universal and particular primary orb, and affirms it physically, not differing, however, from Ptolemy in the space of each of the individual motions and the diversities found in them, but rather confessing them. For it is not the role of a wise man to contradict the senses. However, he shrinks from Ptolemy in providing the causes of those things, for Ptolemy attributes that to the eccentric and epicycle, which are indeed something absurd and alien to the nature of things. This wise man, however, assigns that only to the motions of the poles, from which no physical inconvenience follows. The author himself also establishes only nine orbs, while Ptolemy is not ashamed to assign many orbs to each planet, and indeed five to Mercury itself, which is something extraneous to celestial bodies. Furthermore, this wise man judges the motion of individual orbs from east to west to be according to the daily [motion], and the closer one is to the highest, the faster it is; Ptolemy, however, opines their motion to be from west to east, contrary to the daily, and the more remote, the faster it is. Again, what Ptolemy calls the proper motion of the orb in a day from west to east, this wise man calls a defect of the proper motion from east to west from the daily motion. Oh, the basest thing, that an adversity of motions should exist in celestial bodies and that the proper ones should be slower than the first cause due to broken powers! In addition to other inconveniences following the opinion of Ptolemy, explained by this author. Finally, Ptolemy's theory answers to computation, not to the nature of things, as Averroes attests; but this wise man's theory agrees with both computation and the thing itself. Lastly, it must be said, since both theories concur in the same computation and provide the cause of each of the things appearing in the stars, it is not for a wise man to adhere to the theory of Ptolemy, which is alien to the thing itself and to philosophy, and to pass over that original theory conformable to physical and metaphysical science, cultivated by the princes of philosophy, especially Aristotle, the head of all, although it was passed over by the order of Ptolemy, which truly came about from his and his followers' little practice in physical matters. For Ptolemy was a supreme mathematician, not a physicist, and those who came later followed him vehemently, consigning that old theory to oblivion. And since I have labored for many years in the theory of Ptolemy, I call God to witness that I was never able to satisfy myself, perceiving in it so many things so contrary to physical reasons. Therefore, I almost removed myself from it; indeed, many others also pass over the study of astrology, seeing that such absurdities exist in heaven which no one can contemplate. Wherefore, stirred by divine counsel, applying study to this short work together with Elias, my son-in-law, a truly sharp man, I satisfied myself as if repeating from the heights the physical causes of the diversities found in the orbs. And if the book was provided to me corrupted, I corrected it with another copy and excessive vigil, especially the relevant figures. Thus, due to the weakness of my talent, I brought this short work to light, and I translated it into Latin in as many words, clearly and plainly as I could, so that men might reach this knowledge of the motion of the orbs with the consent of physical science and be able to do so, and thus the science of astrology will be illustrated by true, proven demonstrations, whereas that of Ptolemy, as Averroes witnesses in the preface to his Almagest and in the demonstration, is because of the demonstration [defective]—because it is deprived of it. By what then, according to that doctrine in other liberal arts, can astrology itself be concluded? And if this booklet has been translated to the Latins before, that translation is so involved that hardly anything good can be pulled from it; indeed, it sometimes takes away the author's meaning entirely, which is difficult to hear. And since I have seen, Reverend Lord, that your Reverence is greatly delighted by mathematical disciplines, and is doubtful about the motions of the planets arising from the common theory (for they answer less to physical reasons), I have decided to offer and dedicate this short work to you, so that you may be able to enjoy its fruit, and may God Almighty favor you in all things. Farewell.