The Harmony of the World

ON THE HARMONY OF FIGURES###

...with a bitterness of speech and a great rashness, most unworthy of such a man.
Lazarus Schöner’s opinion on the five solid figures.

Schöner Lazarus Schöner (1543–1607) was a German mathematician and follower of Ramus., following this persuasion of Ramus, also came to believe that the regular bodies were of no use. Not only this, but he also neglected or despised Proclus, following the judgment of Ramus—the very Proclus from whom he could have learned the use of the five bodies both in Euclid’s Elements and in the construction of the World. Indeed, the student was more fortunate than the Master, because Schöner eventually welcomed with gratitude the use of these bodies in the Construction of the World that I revealed, which Ramus had rejected when Proclus urged it. For what does it matter if the Pythagoreans attributed these figures to the elements The "four elements": Earth, Air, Fire, and Water., and not, as I do, to the Spheres of the World? Ramus should have striven to remove this error of theirs regarding the true subject of the figures, just as I have done; he should not have abolished this entire philosophy with a single tyrannical word. What if the Pythagoreans taught the exact same thing as I do, but covered their meaning in a cloak of words?

A mystical interpretation of the Pythagoreans regarding the five figures.

Does not the Copernican form of the World exist in Aristotle himself, though wrongly refuted by him under other names? For they called the Sun "Fire," and the Moon the "Counter-earth" original: "Antichthona". A hypothetical body in Pythagorean astronomy.. For if the arrangement of the spheres was the same among the Pythagoreans as it is in Copernicus; if the five known Bodies were recognized, along with the necessity of their five-fold number; and if they all constantly taught that the five bodies are the Archetypes for the parts of the World—how much more should we believe that Aristotle read their opinion as a riddle, and refuted it as if the words held their literal sense? For example, Aristotle read "Earth," to which they gave the Cube A six-sided regular solid., when they perhaps actually meant Saturn, whose orbit is separated from Jupiter by the insertion of a Cube. The common people ascribe "rest" to the Earth, but Saturn was allotted the slowest motion, which is closest to rest; for this reason, it even obtained its name from "Rest" among the Hebrews The Hebrew name for Saturn is Shabbathai, sharing a root with Shabbat (Sabbath/Rest)..

Similarly, Aristotle read that the Octahedron An eight-sided regular solid. was given to "Air," when they perhaps meant Mercury, whose orbit is enclosed by the Octahedron; and Mercury is no less swift (being indeed the swiftest of all) than Air is considered mobile. By the word "Fire," perhaps Mars was implied, which otherwise is named Pyroeis original: "Pyroeis", meaning "The Fiery One" in Greek. from fire, and to it was given the Tetrahedron A four-sided regular solid, or pyramid., perhaps because its orbit is enclosed by this figure. And under the cloak of "Water," to which the Icosahedron A twenty-sided regular solid. was attributed, the star of Venus could have been hidden (since its path is contained by the Icosahedron), because the bodily humors are subject to Venus, and she herself is said to have been born from the foam of the sea, which is the origin of the name Aphrodite original: "Αφροδιτη". The name is traditionally derived from the Greek aphros, meaning "foam.". Finally, the word "World" could have signified the Earth, and the Dodecahedron A twelve-sided regular solid. could be ascribed to the "World" because the Earth’s path is contained by this figure, distinguished by twelve parts of length Likely referring to the twelve months or the twelve signs of the Zodiac., just as that figure is contained by twelve planes around its whole circumference. Therefore, the fact that in the Mysteries of the Pythagoreans the five figures were distributed in this way—not among the Elements, as Aristotle believed, but among the Planets themselves—is most strongly confirmed by Proclus. Among other things, Proclus teaches that the goal of Geometry is to show how the heavens received fitting shapes for their specific parts.

Willebrord Snell’s opinion on Binomials.

Nor is there yet an end to the damage Ramus has done us. Look at Snell Willebrord Snell (1580–1626), the Dutch astronomer and mathematician famous for the law of refraction., the most skillful of modern Geometers, clearly supporting Ramus in his preface to the problems of Ludolph van Ceulen Ludolph van Ceulen (1540–1610) was a mathematician famous for calculating pi to 35 decimal places.. First, he says that the division of "irrationals" into thirteen species is useless for practice. I grant this, if he recognizes no use except in common life, and if no con...