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All will profess that it is possible to know: therefore, these things which the astronomer considers are neither our works nor our dispositions: therefore, it is deservedly called a speculative science. But immediately the mathematician, wishing to have this astronomy included under his own genus, will contradict, saying that the demonstrations by which the astronomer moves the celestial bodies, and by which he demonstrates their quantities through measuring, are entirely geometrical and mathematical. But the natural philosopher, wishing to maintain what is his, will reply to the mathematician, saying: "Nay, rather, this astronomy itself is placed under the dominion of our genus." This will become clear to you immediately if you bring back to your memory what is placed under our [domain], and if you bring into the middle what is yours. You will know our subject if you read what was said a little before: and what we intend to demonstrate about it, and how. But you may say: "Has he not often spoken in the frequently alleged doctrinal [text], that form and quantity pure, or that which is base quantity, and its dispositions which occur in them, are those which happen to quantity in a definition of which the species of matter is not found, nor the power of motion? Is it not also common among all that mathematics abstracts from matter and motion?" Yes, indeed. Therefore, if you remember what we said above is the substance of astronomy, you will immediately concede that it is natural and not mathematical. For the astronomer himself is a subtle investigator of the motions of the heavens, the planets, and all the stars. From what, then, does he abstract from motion? Furthermore, he minutely scrutinizes the natures of the stars and their influences and impressions upon these inferior things, as upon that which is more receptive, and he also disposes his speculation toward those things which are more proportionate to the impressions themselves, saying that Venus makes a nature in Italy white, but in Ethiopia no less black. How then can he be said not to be a natural philosopher and abstracting from matter? But you said that the astronomer uses geometric demonstrations: I confess this, but I do not doubt that you accept them by your kindness; for you have mutually traded your propositions to him, just as we often see this happen in many other scientific [fields]: for one often uses the propositions of another. But perhaps some man, my master, will say against that which we have said, that astronomy is not about those things which are our works: "The astronomer judges that Mars conjoined to the head of Algol in the nativity of someone will cause the native to be hanged; yet the native will live rightly and will not be hanged. Likewise, the astronomer judges that a native having Mercury so disposed will be neither learned nor wise; yet the native will labor in wisdom and learning and will become wise and learned." There are two things that follow from the judgment, namely, that he is a liar, and that the science itself is about those things which are our works, insofar as they can be changed and varied by our will. To which we reply by denying both: For the place of judicial astronomy is this, that Mars conjoined to the head of Algol impresses such a disposition in the native that either because of robbery, or because of betrayals, or because of any other cause, the anger of a judge is easily provoked against him and he is hanged; not that the thief or the betrayer is hanged, but those who are born for this, that they may be hanged. Likewise, Mercury so disposed effects such an impression in the native that he may acquire wisdom and learning with difficulty; for not everyone who labors in wisdom turns out wise, but he who has this from nature so that he can become wise. But who will say that these impressions are our own work? But that these impressions, which are the effects of the stars and the causes in us, do not follow secondary effects happens because of an impediment arising from the will of him who received the impression; wherefore the astronomer has also judged correctly, and his consideration was about those things which are not our works: [it is because] the effect of the impression about which he rendered judgment did not occur. I say, however, that when the impressions are all strong, it will be very difficult for a man to become accustomed otherwise according to his will. And Haly the commentator believed it to be impossible, because celestial bodies impress a complexion upon the body and its parts, according to which the organs of the soul itself, which ought to serve it, remain disposed in such a way that the soul cannot use them except according to the disposition of the organs serving it. Nevertheless, when the impressions have been refracted, a man can, through exercise and his own will, adhere to and perfect himself in a part other than the one he chose. And hence arises the diversity in all exercises: for in them one excels more than another. And that sometimes one, failing in an initial exercise, attacks another. However, that we may not contradict the faith concerning free will, we believe that the judgments of astronomy can fail in those things in which a man can interpose an impediment through his will: and that it is both easier and more difficult for a man to interpose an impediment, according to whether the impression is strong or weak; nor is the truth of the science removed because of this, nor the speculation. But in those things in which the voluntary power of man does not extend, the judgments can in no way be removed from the truth, for which reason our Ptolemy says in the Centiloquium at the beginning that the judgments of astronomy are between the necessary and the possible; for the astrologer will be able to prevent many evils by disposing him who ought to receive them to the contrary disposition: which disposition, if it does not happen, will infallibly capture that evil for the man. And in the other works of nature also, we see many errors and monsters happening from some impediment occurring: nor is the truth of natural philosophy or its speculation removed because of this. And it is clear that not a few errors occur in medicine and its works; its judgments, likewise, are often rendered void and without truth, as women and children have seen many times; nor is medicine vilified because of this; on the contrary, the physicians themselves are held in highest veneration, so much so that the ancients were not afraid to call physicians gods. Add, if you like, that both in medicine and in astronomy many void judgments are put forward by those who are themselves to be mocked, since they wish to insert themselves among astrologers and physicians, and are altogether alien to these sciences, often having the dispositions of ignorance as their habit. O you fools who rush so insolently and insanely into so famous and divine a science; for if you knew the astronomers whom you vilify, you would call them earthly gods, and you would believe them sent to us from heaven like prophets. For by what science, tell me, can a man be made more like God than by astronomy? Is not predicting the future prophetic and divine? Is not turning future evils away from you, and increasing future goods, beyond human powers? Cease your insanity and exalt astronomy, and worship astronomers as gods. We, however, my master, so that this most famous and noble science, hitherto hidden by the envious, may be made plain to all who desire it, have taken care that Ptolemy, the king of the Alexandrians and prince in astronomy, and Haly Abenrodan, his most faithful and intimate interpreter, be committed to printing by the expense of the most accurate man, Octavianus Scotus of Monza, as corrected as we could make them. We have also added behind them the works of certain other approved men: and with this intention, that we may take care to commit very many other works of approved men to printing, so that this most noble science, however difficult it may be in itself, may yet shine forth to those who desire it through a bounty of books. However, it is our decree that we do not waste time praising either Ptolemy or any others from the rest, lest, believing that we are extolling them, we cause them to grow vile; for they are worthy of much greater and more numerous praises than we could note with a pen or presume to utter with a word. But if anyone wishes to know how much praise Ptolemy deserves, let him understand his book of the Almagest, and this book of the Quadripartitum, and his Centiloquium most excellently. Similarly, by understanding the works of the others, he will perfectly know how he might praise them. Farewell.