Chapter XI.—Theory of the Size of the Heavenly Bodies in Accordance with Numerical Harmonies.
These (numerical) relations, therefore, the greater than ninefold, and less than half, and greater than double, and less than two-fifths, and greater than half, and less than double, are beyond all symphonies, from which not any proportionate or harmonic system could be produced. But the whole world, and the parts of it, are in all respects similarly framed in conformity with proportion and harmony. The proportionate and harmonic relations, however, are preserved—as we have previously stated—by double and triple intervals. If, therefore, we consider Archimedes reliable in the case of only the first distance, that from the Moon to the Earth, it is easy also to find the rest (of the intervals), by multiplying (them) by double and treble. Let then the distance, according to Archimedes, from Earth to Moon be 5,544,130 stadii; there will therefore be the double number of this of stadii which the Sun is distant from the Moon, viz. 11,088,260. But the Sun is distant from the Earth 16,632,390 stadii; and Venus is likewise distant from the Sun 16,632,390 stadii, but from the Earth 33,264,780 stadii; and Mercury is distant from Venus 22,176,520 stadii, but from Earth 55,441,300 stadii; and Mars is distant from Mercury 49,897,170 stadii, and from Earth 105,338,470 stadii; and Jupiter is distant from Mars 44,353,040 stadii, but from Earth 149,691,510 stadii; Saturn is distant from Jupiter 149,691,510 stadii, but from Earth 299,383,020 stadii.
[11] Οὗτοι δὴ οἱ λόγοι ὅ τε πλείω[ν] ἢ [ἐννεαπλάσιος καὶ] ἐλάττων ἢ ἥμισυς καὶ πλείων ἢ διπλάσιος καὶ ἐλάττων ἢ ἐπιτέταρτος καὶ πλείων ἢ ἥμισυς καὶ ἐλάττων ἢ διπλάσιος ἔξω πασῶν εἰ[σι] συμφωνιῶν: ἐξ ὧν οὐκ [ἂν] ἐναρμόνιόν τι καὶ σύμφωνον σύστημα γένοιτο, ὁ δ' ἅπας κόσμος καὶ τὰ τούτου μέρη κατὰ πάντα ὁμοίως ἐναρμονίως καὶ συμφώνως σύγκειται. οἱ δὲ ἐναρμόνιοι καὶ σύμφωνοι λόγοι σῴζονται, καθάπερ προειρήκαμεν, τοῖς διπλασίοις καὶ τριπλασίοις διαστήμασιν. εἰ δὴ πιστὸν τὸν Ἀρχιμήδην ἡγησάμεθα ἐν μόνῳ τῷ πρώτῳ ἀποστήματι τῷ ἀπὸ σελήνης μέχρι γῆς, ῥᾴδιον καὶ τὰ λοιπὰ κατὰ τὸ διπλάσιον καὶ τριπλάσιον αὔξοντα[ς] εὑρεῖν. ἔστω δὴ κατὰ τὸν Ἀρχιμήδην τὸ ἀπὸ γῆς μέχρι σελήνης ἀπόστημα σταδίων μυρι(ά)δ(ας) φνδʹ, μονάδ(ας) ͵δρλʹ: ἔσται μὲν δὴ τούτου διπλάσιος ἀριθμός, ὃν ἀφέστηκεν ὁ ἥλιος τῆς σελήνης, σταδίων μυρι(ά)δ(ας) ͵αρηʹ καὶ [σταδίους] ͵ησξʹ: ἀπὸ δὲ τῆς γῆς ἀφέστηκεν ὁ ἥλιος σταδίων [μυριάδας] ͵αχξγʹ καὶ [σταδίους] ͵βτϘʹ: καὶ Ἀφροδίτη δὲ ἀφέστηκεν ἀπὸ μὲν ἡλίου σταδίων μυρι(ά)δ(ας) ͵αχξγʹ καὶ σταδίους ͵βτϘʹ, ἀπὸ δὲ γῆς μυρι(ά)δ(ας) ͵γτκϚʹ, σταδίους ͵δψπʹ: Ἑρμῆς δὲ Ἀφροδίτης μὲν ἀφέστηκε σταδίων μυριάδας ͵βσιζʹ, σταδίους ͵Ϛφκʹ, ἀπὸ δὲ γῆς μυρι(ά)δ(ας) ͵εφμδʹ, σταδίους ͵ατʹ: Ἄρης δὲ Ἑρμοῦ μὲν ἀφέστηκε σταδίων μυρι(ά)δ(ας) ͵δϠπθʹ, σταδίους ͵ζροʹ, ἀπὸ δὲ γῆς μυρίας μυριάδας καὶ φλγʹ, σταδίους ͵ηυοʹ: Ζεὺς δὲ Ἄρεως μὲν ἀφέστηκε [σταδίων] μυρι(ά)δ(ας) ͵δυλεʹ, σταδίους ͵γμʹ, ἀπὸ δὲ γῆς [μυρίας] μυρι(ά)δ(ας) καὶ ͵δϠξθʹ, σταδίους ͵αφιʹ: Κρόνος [δὲ] ἀπὸ μὲν Διὸς ἀφέστηκε σταδίων μυρίας μυριάδας καὶ ͵δϠξθʹ, σταδίους ͵αφιʹ, ἀπὸ δὲ γῆς μυρίας μυριάδας [βʹ] καὶ ͵θϠληʹ, σταδίους ͵γκʹ.