Euclid's Elements

with the help of Mechanics itself, which fabricates admirable machines for attacking or resisting, as Archimedes did against Marcellus, who (for I pass over Ctesibius, Archytas, Priscus, Eudoxus, and Diogenetus) when he was once preaching this so wonderful art before Hiero, the King, having admired the geometer, asked that he make a trial with such confidence. Wherefore Archimedes, having bought one ship from the royal vessels, and drawn it onto dry land, and having loaded it more heavily, pulled it to himself alone with his machines, no differently than if it were being driven on the sea with oars and sails. Afterwards, he later drew the same king's ship from the shore into the sea at Alexandria, which all the forces of Sicily could not do. Those, therefore, who are equipped with this art can protect the walls of a city and elude the attacks of enemies. And the enterprise, begun with such impetus, would have had good fortune (says Livy, when he speaks of Marcellus besieging Syracuse) had not one man been in Syracuse at that time. That was Archimedes, a unique spectator of the sky and the stars, yet more wonderful as an inventor and machinist of war engines and works, by which he mocked those things which the enemies were doing with huge mass in a light moment. It has pleased me to bring forward such a distinguished testimony of an illustrious historian about Archimedes, so that by his example, men may understand how much utility and advantage they can acquire for themselves and their country, if they cultivate the noble faculty of Mathematics with diligent care and study. Moreover, I cannot conceal that I am much more grievously perturbed by the impudent audacity of certain philosophers (as they seem to themselves to be) (For why should I not bear more grievously that mathematics are slandered by them, whose duty it should be to cultivate and defend them, than by men whom the evil desire for riches holds bound in the tightest snares?) But against this class of philosophers I will say nothing else now, because I know that these Aristippuses and Epicureans, as Peter Ramus, a man of great erudition, truly and elegantly names them, say such things more out of a certain pain and desire to cover their own ignorance, than because they truly think that the knowledge of mathematics brings no utility, no help to all the disciplines of the liberal arts, and especially to the monuments of Plato and Aristotle, who it is clearly established were greatly delighted by this kind of doctrine. For those who think this, when they find many things daily that are primarily necessary and most beautiful to know among them, which because they are handed down in the mathematical manner, they are forced to avoid like certain rocks. Hence they do not touch the Timaeus as a fabulous book of no value. Hence they are reluctant to explain the seventh book of the Physics, and many other Aristotelian works to their students because, as they say, they are useless. But perhaps more has been said about this matter than was necessary. For the utility of true mathematics, its excellent fruits, and incredible pleasures are placed in the sole knowledge of truth, for which we were born. By this alone we show ourselves to be truly human, and truly participants in the divine light. The rest present a terrestrial and fragile condition. But let us come to those things which pertain to our geometer. And first let us speak of Euclid himself; then of the inscription and the scope. Finally, of his demonstrations, as we had promised from the beginning. Let us therefore free many from that error by which they are persuaded to believe that our Euclid is the same as the philosopher of Megara, and let us explain this whole matter briefly. The elder Euclid was from the town of Megara, which lies by the isthmus, a student of the books of Parmenides above all, and the head of the Megarian sect, to whom, after the death of Socrates, Plato and almost all the Socratics fled for fear of the thirty tyrants. He wrote six dialogues, which Laertius enumerates. He used proofs not those which are made by assumptions, but which are made by conclusions, and are more dialectical. He had Eubulides as a successor. The younger Euclid, however, who was called στοιχειωτης author of the elements and geometer, flourished in the time of the First Ptolemy, and diligently cultivated the academy, and having been egregiously educated by the almost daily habit of Plato's disciples, he approached Mathematics, which was then especially flourishing in the Academy by the teacher's institution, with such excellent impetus of mind that he made admirable progress, and progress most worthy of eternal memory in it; and by the constant testimony of all scholars, he claimed the first place for himself. But let no one think it unknown to me that Valerius Maximus writes that Plato referred those who were contracting for the sacred altar to Euclid, as to the primary mathematician. But we follow Hero and Proclus, who were distinguished in the study of mathematics, or rather Eudoxus and Theophrastus from the Peripatetics, the most noble after the teacher. For these committed to memory in those books, which were written about geometric history, which we do not ignore have perished with great grief and to the inconvenience of the learned. Therefore our Euclid, after Hippocrates, Leo, Theudius, and Hermotimus, who had written geometric elements one after another, wove this truly golden work with the greatest labor and excellent judgment of mind. Many things had indeed been discovered by those earlier men with a certain excellent and almost divine sharpness of wit. A few things had been added by Theaetetus and Eudoxus, who associated with Plato. And so Euclid

The right margin contains faint ink sketches; the top shows cloud-like shapes, the middle displays the profile of a bearded man's head, and the bottom features abstract swirls.