ON THE PREFACE TO THE READER

Author’s Notes.

(1) To those (five bodies) the number of the heavens, the proportions and the ratio of motions, etc. Although all things are coherent with one another, the number of the six primary Orbs is properly derived from the five Bodies of the Sun original: "Corporibus Solis"; Kepler is referring to the spatial arrangement of the planetary spheres around the Sun: the proportion is indeed taken for the most part from the five Geometric Bodies, but it yielded in the smallest details to the motions, as the final cause received into the Idea of the work right from the start. And this must be understood regarding the single slowest and the single fastest motions of each planet—that is, regarding the Motions considered for the sake of their own property. But the periodic Motions: that is, the number of days derived in the circuit of each Planet, have receded further from the 5 bodies, as much from the proportion of the orbs as from the Eccentricities (which were established from the Harmonies).

(2) The dispute concerning the primary motion, that it happens by the rotation of the earth. You have that discussion fully provided in the first book of the Epitome Astronomiæ|Epitome of Copernican Astronomy, Kepler's influential textbook published between 1617 and 1621.

(3) The Solar motion [attributed] to the Earth. This dispute was inserted into my Commentaries on the motion of Mars The Astronomia Nova (1609), especially in the Introduction; it is found accurately in book IV of the Epitome, page 542. Plainly demonstrative arguments, shaped from the restored innermost depths of Astronomy, are gathered there.

(4) Which similarity I shall pursue in the Cosmography. Indeed, I have published no book under the title of "Cosmography" since that time: but that similarity was related by me in Book I of the Epitome, page 42, where I discuss the outermost figure of the World, and in Book IV of the same, pages 437 and 448, where I dispute concerning the three primary members of the World. Nor is it to be held as an empty similarity; but it should be counted among the causes, as the form and Archetype|The original model or 'blueprint' upon which God designed the universe of the World.

(5) Between Jupiter and Mars I interposed a new Planet. Not one that would run around Jupiter, like Galileo’s Medicean stars|The four largest moons of Jupiter (Io, Europa, Ganymede, and Callisto), discovered by Galileo in 1610; let you not be deceived, I never thought of those; but one which, like the primary planets themselves, would encircle the Sun placed in the center of the System in its own course.

(6) Nor by [the power] of any Number. See, even then I rejected "counting numbers," as they call them. I held it among the most important things in that Work to likewise cast them out from Harmonic foundations.

(7) Dignity from things posterior to the world. The senarius|The number six, however, has something abstract from created things, because it is the first among the perfect numbers|A number equal to the sum of its proper divisors (e.g., 1+2+3=6): for a thing is held to be perfect if there are as many units in its parts as in the whole. Does this property, therefore, procure some dignity for a "counting number"? Let it be considered both what kind of dignity this is, and how it applies to Number. First, this dignity seems to be nothing. For if there were any dignity, the discipline of Harmony would seem to have provided testimony for all perfect numbers. But that discipline receives none besides the six. For the remaining perfect numbers are multiples of primes, as is clear from the last proposition of Euclid’s Book IX. Therefore (by Axiom III of my Book III of the Harmonices|The Harmonies of the World (1619), where Kepler linked geometry, music, and astronomy, page 11, and by Proposition VIII of Book IV, page 145, which rely on propositions 45, 46, and 47 of Book I), all so-called perfect numbers, except the six, are exiled from the terms that constitute concordances; even the sense of hearing attests to this; and this is because of the Primes, such as the number seven, etc., from which they are derived. For the Harmonic sections in Book III, proposition 19, page 26, are numbered as seven, which is a prime number: but that number seven gives to none of them the quality of being Harmonic; rather, each is Harmonic by itself first, and only afterwards does it happen to them, once all are established, that they are seven in number. But neither does this condition itself, by which perfect numbers are defined, have anything of dignity when considered in itself: namely, that all the numbers which measure one specific number, when fused into one, should equal the thing measured. Equality is indeed something beautiful, but this equality is accidental to the numbers themselves by reason of each individual one; it brings nothing to their constitution, but results by Geometric necessity from things already established; nor does it give this to them, that they be more articulated; even though it is occupied with this very articulation and is in some way defined by it: rather, he who is ordered to affect this so-called perfection is by that very fact restricted from being able to take the most articulated ones. And as we previously reasoned about sections, so now we can also speak about numbers measuring a specific one: namely, that first each of them for its own sake measures the proposed number, not receiving this nature from a pretended equality, but only afterwards does it happen to them individually that as a whole they equal the thing measured. See a similar place in my Book III of the Harmonies, near the end of chapter III, page 31; concerning the occurrence of the number three, for which there is here an occurrence of equality. Therefore, this equality confers no more virtue or skill upon numbers than the discovery of a treasure does to a farmer; as is believable