ON DEMONSTRATION. BOOK I.

Petrus Ramus’s Petrus Ramus (1515–1572) was a famous French humanist and reformer of logic who often criticized traditional academic authorities like Aristotle and Euclid for being impractical. unfair and ignorant criticism of Euclid.

But in our current age, no one has yet found the time to penetrate such deep mysteries. Proclus's book was read by Petrus Ramus, but as far as the core of philosophy is concerned, it was despised and cast aside along with the tenth book of Euclid. Ramus, who had written both a commentary on Euclid and what seemed like a defense of him, was rejected and ordered to fall silent; truly, the anger of this hostile Critic was turned against Euclid as if he were a criminal. The tenth book of Euclid was condemned by a harsh sentence, to the effect that it should not be read—even though, if read and understood, it could reveal the mysteries of philosophy. Read, I pray, the words of Ramus, than which he never produced anything more unworthy of himself: Mathematical Lectures, book 21. The subject matter, he says, proposed in the tenth book, is handed down in such a way that I have never discovered a similar obscurity in human literature or arts. I call it an obscurity not for the purpose of understanding what Euclid teaches (for that alone which is present and before one's eyes might be clear even to the unlearned and illiterate), but for the purpose of looking deeply within and exploring what the intended end and use of the work is, and what the genera, species, and differences of the subjects are; for I have never read or heard of anything so confused or tangled. Indeed, it seems as if Pythagorean superstition has been led into this cave, etc. But by Hercules, Ramus, if you hadn't believed this book was too easy to understand, you would never have slandered it with such "obscurity." Great labor is needed, stillness is needed, care is needed, and a special attention of the mind, until you grasp the intention of the writer. When a noble mind has struggled toward that goal, then at last, seeing itself moving in the light of truth, it is drenched and exultant with incredible pleasure; and from that "watchtower," as it were, it perceives the whole World and all the differences of its parts with the greatest exactness. But as for you, who here act as the patron of ignorance and of the common crowd of men who hunt for profit from everything—divine or human—I say to you: let those things be prodigious sophisms; let Euclid be to you a man who intemperately wasted his leisure; let those sharp points of his have no place in Geometry; let it be your business to pluck at what you do not understand. As for me, who investigates the causes of things, no paths have opened to them except through the tenth book of Euclid.

Lazarus Schonerus Lazarus Schoner (1543–1607) was a German mathematician and follower of Ramus..

Lazarus Schoner, following Ramus in his own Geometry, confessed that he could see absolutely no use for the five Regular Solids The five Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. These are the only shapes where every face is an identical regular polygon. in the World, until he read through my little book, which I titled The Secret of the Universe original: "Mysterium Cosmographicum," Kepler’s 1596 work arguing that the distances between planets are determined by the five Platonic solids.; in that book, I prove that the number and intervals of the Planets are taken from the five Regular Solids. See how the teacher Ramus harmed his student Schoner. First, Ramus, having read Aristotle—who had refuted the Pythagorean philosophy concerning the properties of the Elements being derived from the five solids—immediately conceived a contempt for the whole of Pythagorean Philosophy. Then, since he knew Proclus had belonged to the Pythagorean sect, he did not believe him when he affirmed what was most true: namely, that the ultimate goal of Euclid’s work, to which absolutely all propositions of all the books refer (except those leading to the Perfect Number), is the five regular solids. From this arose in Ramus the most confident persuasion that the five solids were to be removed from the goal of Euclid's Elements.

Once the goal of the work was taken away, as if the design of a building were removed, there remained in Euclid a shapeless heap of propositions, which Ramus attacks as if it were some ghost throughout all twenty-eight books of his Lectures, [with] great [things to be] said—