Forerunner of the Cosmographic Dissertations

ANCIENT PREFACE

Mars to Earth, in the size of the sphere of Mars. But the insertion of not even one planet was enough for the vast gap between Jupiter [♃] and Mars [♂]. For there remained a greater proportion of Jupiter to that new planet than there is of Saturn to Jupiter: and in this way, although I might obtain some sort of proportion, yet there would be no end based on reason, no certain number of moving bodies, neither toward the fixed stars, until they themselves were encountered: nor toward the Sun ever, because the division of the remaining space after Mercury by this proportion would proceed to infinity. (6) Nor indeed could I guess from the nobility of any number why so few moving bodies had existed instead of infinite ones. Nor does Rheticus Georg Joachim Rheticus (1514–1574), the mathematician who first published an account of Copernicus’s heliocentric theory. speak truths in his Narratio original: Narratio Prima, or "First Account." when he argues from the holiness of the number six for the number of the six moving heavens. For he who disputes about the creation of the world itself ought not to derive reasons from those numbers (7) which have attained some dignity from things posterior to the world Kepler argues that "holy" numbers are human inventions created after the world began, and therefore could not have been the blueprint used by God during creation..

Again, I explored in another way whether, in the same quadrant, the distance of any planet might be the remainder from the sine, and its motion might be the remainder from the sine of its complement. Imagine a square AB, described by the radius of the whole universe AC. Therefore, from the angle B opposite the Sun or the center of the world A, let a quadrant CED be drawn with radius BC. Then, on the true radius of the world AC, let the Sun, the Fixed Stars, and the moving bodies be marked according to the ratio of their distances: from which points let straight lines be raised, extending to the quadrant facing the Sun.

A geometric quadrant diagram labeled ABD. The vertical axis AB contains astronomical symbols for the Sun (☉), Mercury (☿), Venus (♀), Earth (♁), Mars (♂), Jupiter (♃), and Saturn (♄), with the word 'Fixed Stars' [Fixæ] at the bottom. A curved line marked with points E, F, G, H, I, K arcs from the vertical axis towards the point D, illustrating planetary distances or motions. The horizontal base is labeled B, and the quadrant arc is labeled C, E, D.

Whatever, then, is the proportion of the parallels, I imagined the same for the moving power motive force: the "virtus movens," a force Kepler believed emanated from the Sun to push the planets. belonging to each planet. In the line of the Sun, it remains infinite, because AD is touched but not cut by the quadrant. Therefore, there is an infinite force of motion in the Sun, indeed nothing but motion in its very act. At Mercury, the infinite line is cut off at K. Therefore its motion is now comparable to the others. In the fixed stars, the line is entirely lost and compressed into a mere point C. Therefore, there is no power for motion there. This was the theorem that had to be examined by calculation. But if someone properly weighs that I lacked two things: first, that I was ignorant of the whole sine The "whole sine" or sinus totus refers to the radius of the circle used in trigonometric calculations., or the size of that proposed quadrant; and second, that the strengths of the motions were not expressed otherwise than in the proportion of one to another—whoever, I say, properly weighs these things, will not undeservedly doubt whether I could have reached my goal to any extent by this difficult way or not. And yet, through continuous labor and infinite alternation of sines and arcs, I achieved enough to understand that this opinion could not hold its place.

You see this in the following diagram.

Almost the entire summer was lost to this torture original: cruce; literally "cross," used here to mean an agonizing mental struggle.. Finally, by a slight occasion, I happened upon the matter itself more closely. I thought it had happened to me by divine providence, that I might obtain by chance what I could never achieve by any labor; and I believed it all the more because I had always prayed to God that if Copernicus had spoken the truth, these things might succeed. Therefore, on the 9th or 19th of July in the year 1595, when I was about to show my students the leaps of the great conjunctions through every eight signs, and how they gradually pass from one trigon trigon: a triangle formed by the positions of planetary conjunctions in the zodiac. to another, I inscribed many triangles, or quasi-triangles, in the same circle, so that the end of one was the beginning of the other. Therefore, at the points where the sides of the triangles intersected each other, a smaller circle was outlined. For the radius of the circle inscribed in the triangle is cir-