TO THE READER.

is half of the circumscribed radius. The proportion between each circle appeared to the eye to be nearly similar to that which exists between Saturn [♄] and Jupiter [♃]; and the triangle was the first figure drawn, just as Saturn and Jupiter are the first planets In the 16th century, Saturn and Jupiter were the "first" planets because they were the furthest from the Sun, moving inward toward the center.. I immediately tried a square for the second distance between Mars and Jupiter, a pentagon for the third, and a hexagon for the fourth. Since even my eyes rebelled against the second distance—that between Jupiter and Mars—I joined a square to the triangle and the pentagon. It would be an endless task to follow every single attempt.

And the end of this futile effort was the beginning of the final and successful one. Specifically, I thought that by this path, if I wished to preserve the order among the figures, I would never reach as far as the Sun, nor would I have a reason why there should be six moving spheres moving spheres|In the Copernican system, the planets were Mercury, Venus, Earth, Mars, Jupiter, and Saturn, totaling six. rather than twenty or a hundred. And yet, the figures pleased me, as they are quantities—and things prior to the heavens. (8) For Quantity was created at the beginning along with the body; the heavens only on the second day Kepler is referencing the Genesis creation narrative to argue that mathematical laws (Geometry) are the fundamental blueprint used by God before the physical universe was shaped.. But if (I thought) instead of the quantity and proportion of the six Heavens established by Copernicus, only Five figures could be found among the infinite others, which might have certain peculiar properties beyond the rest, then the matter would be exactly as desired. Yet again, I persisted. Why use flat figures among solid spheres? Solid bodies should rather be sought. Behold, Reader, this discovery and the subject matter of this entire little work! For if anyone even slightly skilled in Geometry were prompted with these very words, the Five regular bodies These are the "Platonic Solids": the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. They are the only 3D shapes where every face is an identical regular polygon. would immediately come to his mind, along with the proportion of their circumscribed spheres to those inscribed within them; that famous scholium explanatory note in Euclid, at Proposition 18 of Book 13, would immediately appear before his eyes. In which...

A geometric diagram showing the conjunctions of Saturn and Jupiter over time. It consists of a circular border marked with the twelve zodiac signs. Inside, a series of straight lines connect different points on the circumference to form a sequence of overlapping triangles that rotate, creating a star-like pattern around the center. Numerous small numbers (1 through 40) are printed within the segments. In the center, a text box contains the title translated above.