Prolegomena of Federicus Commandinus to the Elements of Euclid.

A large decorative drop-cap initial 'Q' containing a scene of a classical female figure, likely Urania or a muse, holding a celestial globe or armillary sphere.

Just as many interpreters—and especially those who are most praised—are accustomed to deferring certain things to the first place before they begin to unfold the monuments and writings of famous men, which they have undertaken to explain and adorn for the benefit of the literary republic, so too I have thought that the same must be done at the beginning of this most excellent work. For there is no doubt that the mind of a reader, still untutored but warned from the beginning about the matter as a whole, is afterward formed with less labor and in a shorter time to understand each individual part. First, therefore, we shall speak briefly about this noble faculty of the mathematical arts: what is the subject matter for them, both generally and particularly; what is their order and degree of dignity; what is their definition; and what is their origin. Next, we shall narrate, in a very few words, their wonderful suitability for human use. Afterward, we shall touch upon matters by no means useless concerning the author—namely, Euclid himself—concerning the inscription of the work, its purpose, its demonstrations, and the arrangement and method of those things which he has encompassed in these books. Finally, we shall add a summary of the whole στοιχειώσεως Elements with this intention: that not only may whatever Euclid teaches about this genre be understood more easily, but also that it may be kept more faithfully committed to memory.

Thus, they have handed down to us all philosophy that resides in contemplation, distributed by the most illustrious of philosophers into three parts, guided by the reasoning that some things exist and are understood solely by themselves, free from the stain and filth of matter. Others, having obtained a nature entirely different from these, so lean upon matter that they can in no way exist without it. Finally, others hold a place intermediate between these in nature and dignity: both because they are devoid of all matter, if you look more accurately at their true condition, and because they seem in a certain way to be endowed with matter, because they cannot be known without some conjunction of it, due to the weakness of our intellect. Hence that threefold type of philosophy: Divine, which excels the other two more than can be said, both in name and in reality; Natural, which is third and holds the last place in order and dignity; and the intermediate, which is called mathematical. Since it alone can be truly called and known, because of the supreme constancy of the subject matter and the certain method of demonstration: this, indeed, as it is inferior to divine substances (for what is so excellent that it can be compared with them?), so it excels and is superior to natural ones, which, deeply immersed in matter, follow its varied and mutable nature. This was first discovered by those men who, before the flood of the earth, enjoyed a happier sky and genius, and noticed the wisdom of celestial things and the admirable order of the world. They erected two columns, one of stone and the other of brick, upon which they most diligently inscribed what they had discovered, lest the knowledge of such great things vanish, either by the inundation of waters or by fire, one of which they knew from the predictions of the ancients would occur. Therefore, even in those first times, which are believed to be so uncultivated, the noble study of mathematics did not lie uncultivated. After the flood of the earth, it flourished among the Chaldeans, adorned and increased especially by the study of Abraham, a man nearly divine. The Egyptians, men born to this kind of science both because of the perpetual serenity of the sky and the great flatness of the lands, cultivated it most highly after receiving it from the Chaldeans. From the Egyptians, it was transferred to the Greeks—to whom you could not deservedly prefer anyone either in keenness of mind or in desire for knowledge—by the industry of Thales of Miletus, Pythagoras of Samos, and other excellent men, whom the love of science compelled both to cross vast seas and to travel through distant regions, especially Egypt, where, if we believe the Greeks, the mathematical disciplines were born and raised. These were later illustrated by both practice and writings by Anaxagoras, Oenopides, Zenodotus, Brito, Antiphon, Hippocrates, Theodorus, Plato, Theaetetus, Archytas, Euclid, Aristarchus, Archimedes, and countless others, who turned nearly all mortals to admiration of themselves through this exceptional and outstanding discipline of mathematics. But enough of these; for it is not my intention to weave a history here. Rather, we have touched upon these few things so that we might, as it were, point with a finger to the ancient nobility of this study. Now, concerning the matter and the chief parts of the mathematical faculty.