ON DEMONSTRATION. BOOK 1.

Peter Ramus’s unfair and ignorant judgment of Euclid.

But our own age has not yet found the time to penetrate such hidden depths. Peter Ramus Petrus Ramus (1515–1572) was a famous French scholar who sought to reform—and often simplify—the teaching of logic and mathematics, frequently attacking established authorities like Aristotle and Euclid. did read the book of Proclus, but as far as the core of its philosophy is concerned, it was despised and thrown away, along with the tenth book of Euclid. Proclus, who had written a commentary on Euclid as if he were writing a defense for him, was rejected and ordered to be silent; indeed, the anger of that hostile Critic was turned against Euclid himself as if he were a criminal. Euclid’s tenth book was condemned with a harsh sentence so that it should not be read—even though, if read and understood, it could reveal the mysteries of philosophy. Please read Ramus’s own words, than which he never uttered anything more unworthy of himself: Mathematical Schools, Book 21. original: "Scholarum Math. lib. 21" The subject matter, he says, presented in the tenth book, is handed down in such a way that I have never found similar obscurity in human literature or arts: I call it obscurity not in understanding what Euclid teaches (for that can be clear even to the unlearned and illiterate, who look only at what is right in front of them), but in perceiving deeply and exploring what the purpose and use of the work might be, or what the types, species, and differences of the subjects are; for I have never read or heard of anything so confused or tangled. Indeed, the Pythagorean superstition seems to have been led into this place like a cave, etc.

But by Hercules, Ramus, if you had not believed this book too easy to understand, you would never have slandered it with such talk of "obscurity." There is a need for greater labor, a need for quiet, a need for care, and a special attention of the mind, until you grasp the author's intent. When a noble mind has struggled toward that goal, then at last, seeing itself moving in the light of truth, it is bathed in incredible pleasure and exults; and from that watchtower, as it were, it perceives the whole World and all the differences of its parts most exactly. But as for you, who here act as the patron of ignorance and of the common mob—those who seek profit from everything, whether divine or human—to you, I say, let those things be "monstrous sophisms." To you, Euclid may have immoderately wasted your leisure; to you, those sharp points of logic may have no place in Geometry. Let it be your lot to pluck at what you do not understand. For me, who investigates the causes of things, no paths have opened toward them except through the tenth book of Euclid.

Lazarus Schoner.

Lazarus Schoner A mathematician and contemporary of Kepler who edited some of Ramus’s works., following Ramus in his own Geometry, confessed that he could see absolutely no use for the five Regular solids in the World until he had 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 were determined by the five Platonic solids.. In that book, I prove that the number and intervals of the Planets are derived from the five Regular solids. See how the teacher Ramus harmed his pupil Schoner! First, having read Aristotle—who had refuted the Pythagorean philosophy regarding the properties of the Elements being deduced from the five solids—Ramus 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 the propositions of all the books refer (except those leading to the Perfect Number), is the five regular solids. From this arose the most confident persuasion in Ramus that the five solids were to be removed from the goal of Euclid’s Elements.

Once the goal of the work was taken away—just as if the design of a building were removed—there remained in Euclid only a formless heap of propositions. Ramus attacks this heap, as if it were some ghost, throughout all twenty-eight books of his Scholarum, saying great—