Ingenious Designs of Various Mills

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Preface to the Kind Reader.

Among the ancients, Mathematics was always held in such great and high honor—and not without reason—that even Pythagoras, as one reads of him, had these words written over his school: Let no one ignorant of mathematics enter here original: "Nemo Mathematices ignarus ingrediatur". This meant that no one should enter there who did not already know something of mathematics and was not to some extent practiced in it. As a wise and sensible philosopher, he did this with the opinion and firm belief that, just as this science uniquely and wonderfully sharpens the understanding and provides guidance and advancement for all other arts and sciences, he also held it for certain that one to whom mathematics is unknown could not grasp or understand the others—if not entirely, then at least in part. Such a person would be quite unfit for all other arts.

This was also the meaning of Alcinous the Platonist when he said: One ignorant of mathematics is more naked than a bare child original: "Mathematices ignarus, Liberide nudior"; likely a rhetorical comparison suggesting that a mind without mathematical training is as vulnerable and unequipped as a newborn.. That is to say, one to whom mathematics is unknown can grasp and understand less than a naked and bare child who cannot cover herself anywhere.

This was further demonstrated by Aristippus the Socratic Aristippus of Cyrene (c. 435–356 BCE), a pupil of Socrates and founder of the Cyrenaic school of philosophy.. After suffering a shipwreck, he came ashore on the island of Rhodes with several of his companions. There, he saw several mathematical circles original: "Mathematische Circulos"; likely geometric diagrams drawn for study. in the sand on the seashore. Upon seeing them, he told his companions to take heart, for he saw that civilized people lived in that land, and it was difficult to consider them anything but rational human beings.

The dignity and excellence of mathematics consists in this: it not only usefully involves itself in almost all other arts, but it also makes a person capable of everything. It elevates him with great wonder even up to the heavens, so that he can perceive and grasp their nature to some extent. It shows him the course of the planets and other stars, and the movement of the entire firmament original: "Firmament"; in historical astronomy, this refers to the sphere of the fixed stars or the vast curve of the sky.. It guides him upon the wild and monstrous sea and shows him how he may travel upon it from one land to another. On land, it accompanies him as if through the entire world and shows him every feature and occasion of the same. It leads the human being in all kinds of arts, both delightful and necessary, all of which are imperfect without mathematics. Even all craftsmen receive their certain measure and proportion from mathematics.