(An Magnitudo et Densitas Corporum Caelestium ex Harmonicis Proportionibus Determinata fuerit)

[I.] This we likewise deny, for the reasons adduced in chapter 8 from number 8 [¶VIII], if what we said of the intervals be applied to the Magnitudes and Densities of the planets — except, however, [that here we lack] the argument a posteriori, taken from sensible experiment, concerning their density; for we have no such experiment by which we could convict of falsity those who might feign the density and rarity of the planets from harmonic proportions. Nor indeed did Kepler (Epitome of Astronomy bk. 4) define those [magnitudes and densities] from harmonic, but only from Geometric, reasons — as is clear from his own pages 484 to 489: he only said that Saturn is twice as high [far] as Jupiter, one-and-a-half times heavier, and one-and-a-half times rarer, and so twice as high as it is heavier, and twice as ample as it is rarer, and proportionally of the rest; but that the Sun is the densest of all. (The proportions of density which he devises we have already reported, bk. 7, sect. 1, ch. 1, num. 7; and his various propositions bearing on it we reviewed, bk. 7, sect. 6, ch. 8, num. 16 — to which we refer the Reader, but so that he also consult Scholium 2 of the same chapter.) The same Kepler, moreover (Harmonics bk. 5, ch. 4), expressly denies that the proportions of the bodies of the planets are harmonic.

But as for what Fr. Anton Maria de Rheita asserts (in his Oculus Enoch et Eliae bk. 4, ch. 2, member 4) — that the Earth is to the Sun as a square root to its square, or as 10 to 100, so that the Sun is a hundredfold greater than the Earth, and the like (of which we treat, bk. 7, sect. 6, ch. 8, schol. 3) — whence Kircher (Musurgia 10, p. 379) says that, if they were true, certain harmonic proportions could be gathered [from them]: this, I say, by no means agrees with the more exact observations of the diameters and distances held by us and by others (as is clear from what was said, bk. 7, sect. 6, from ch. 10). And Kircher himself (same page, and p. 381) holds the observations of Rheita suspect, on which he built those proportions, and says: “But I greatly doubt that Rheita, for the apparent quantity of the said diameters assumed at his pleasure, chose so beautiful and specious a proportion rather than [actually] observed it.”