Chapter X.—Theory of Stellar Motion and Distance in Accordance with Harmony.

Concerning the Moon, however, a statement has been previously made. The distances and profundities of the spheres Archimedes thus renders; but a different declaration regarding them has been made by Hipparchus; and a different one still by Apollonius the mathematician. It is sufficient, however, for us, following the Platonic opinion, to suppose twofold and threefold distances from one another of the erratic stars; for the doctrine is thus preserved of the composition of the universe out of harmony, on concordant principles171    Aristotle considers that Anaxagoras was the first to broach the existence of efficient causes in nature. He states, however, that Hermotimus received the credit of so doing at an earlier date.    The Abbe Cruice thinks that the word should be “tones,” supporting his emendation on the authority of Pliny, who states that Pythagoras called the distance of the Moon from the Earth a tone, deriving the term from musical science (see Pliny’s Hist. Nat., ii. 20). in keeping with these distances. The numbers, however, advanced by Archimedes,172    Or, Hegesephontus.    These numerical speculations are treated of by Archimedes in his work On the Number of the Sand, in which he maintains the possibility of counting the sands, even on the supposition of the world’s being much larger than it is (see Archimedes, τὰ μεχρὶ νῦν σωζόμενα ἅπαντα, Treatise ψαμμίτης, p. 120, ed. Eustoc. Ascalon., Basil, 1544). and the accounts rendered by the rest concerning the distances, if they be not on principles of symphony,—that is, the double and triple (distances) spoken of by Plato,—but are discovered independent of harmonies, would not preserve the doctrine of the formation of the universe according to harmony. For it is neither credible nor possible that the distances of these should be both contrary to some reasonable plan, and independent of harmonious and proportional principles, except perhaps only the Moon, on account of wanings and the shadow of the Earth, in regard also of the distance of which alone—that is, the lunar (planet) from earth—one may trust Archimedes. It will, however, be easy for those who, according to the Platonic dogma itself, adopt this distance to comprehend by numerical calculation (intervals) according to what is double and triple, as Plato requires, and the rest of the distances. If, then, according to Archimedes, the Moon is distant from the surface of the Earth 5,544,130 stadii, by increasing these numbers double and triple, (it will be) easy to find also the distances of the rest, as if subtracting one part of the number of stadii which the Moon is distant from the Earth.

But because the rest of the numbers—those alleged by Archimedes concerning the distance of the erratic stars—are not based on principles of concord, it is easy to understand—that is, for those who attend to the matter—how the numbers are mutually related, and on what principles they depend. That, however, they should not be in harmony and symphony—I mean those that are parts of the world which consists according to harmony—this is impossible. Since, therefore, the first number which the Moon is distant from the earth is 5,544,130, the second number which the Sun is distant from the Moon being 50,272,065, subsists by a greater computation than ninefold. But the higher number in reference to this, being 20,272,065, is (comprised) in a greater computation than half. The number, however, superior to this, which is 50,817,165, is contained in a greater computation than half. But the number superior to this, which is 40,541,108, is contained in a less computation than two-fifths. But the number superior to this, which is 20,275,065, is contained in a greater computation than half. The final number, however, which is 40,372,065, is comprised in a less computation than double.

[10] Τὰ μὲν οὖν ἀποστήματα καὶ βάθη τῶν σφαιρῶν οὕτως Ἀρχιμήδης ἀποδίδωσιν, ἑτέρως δὲ ὑπὲρ αὐτῶν Ἱππάρχῳ εἴρηται καὶ ἑτέρως Ἀπολλωνίῳ τῷ μαθηματικῷ. ἡμῖν δὲ ἐξαρ(κ)εῖ τῇ Πλατωνικῇ δόξῃ ἑπομένοις διπλάσια μέν[τοι] καὶ τριπλάσια οἴεσθαι τῶν πλανωμένων τὰ ἀπ' ἀλλήλων διαστήματα: σῴζεται γὰρ οὕτως ὁ λόγος τοῦ καθ' ἁρμονίαν συγκεῖσθαι τὸ πᾶν ἐν λόγοις συμφώνοις κατὰ ταῦτα τὰ ἀποστήματα. οἱ δ' ἐκτεθέντες ὑπὸ Ἀρχιμήδους ἀριθμοὶ καὶ [οἱ] ὑπὸ τῶν ἄλλων περὶ τῶν ἀποστημάτων λεγόμενοι λόγοι εἰ μὴ ἐν συμφώνοις εἶεν λόγοις_ τουτέστι τοῖς ὑπὸ Πλάτωνος εἰρημένοις διπλασίοις καὶ τριπλασίοις_, ἔξω δὲ συμφώνων εὑρισκόμενοι, οὐκ ἂν σῴζοιεν τὸ καθ' ἁρμονίαν κατεσκευάσθαι τὸ πᾶν. οὐ γὰρ πιθανὸν οὐδὲ δυνατὸν ἄλογά τε καὶ ἔξω συμφώνων καὶ ἐναρμονίων λόγων εἶναι αὐτῶν τὰ ἀποστήματα, πλὴν ἴσως σελήνης μόνης, ἐκ τῶν λείψεων καὶ τῆς σκιᾶς τῆς γῆς: περὶ ἣν μόνην καὶ πιστεύσαι τις ἂν Ἀρχιμήδῃ [περὶ τῆς] ἀποστάσεως, τουτέστι τῆς σεληνιακῆς ἀπὸ γῆς. ταύτην δὲ λαβοῦσι ῥᾴδιον ἔσται κατὰ τὸ Πλατωνικὸν αὔξοντας κατὰ τὸ διπλάσιον καὶ τριπλάσιον [ὡς ἀξιοῖ Πλάτων] καὶ τὰ λοιπὰ ἀποστήματα ἀριθμῷ περιλαβεῖν. εἰ δὴ κατὰ τὸν Ἀρχιμήδην ἀπὸ τῆς ἐπιφανείας τῆς γῆς ἡ σελήνη ἀφέστηκε σταδίων μυρι(ά)δ(ας) φνδʹ, σταδίους ͵δρλʹ, ῥᾴδιον τούτους τοὺς ἀριθμοὺς αὔξοντας κατὰ τὸ διπλάσιον καὶ τριπλάσιον, [ὡς ἀξιοῖ Πλάτων,] καὶ τὰ τῶν λοιπῶν εὑρεῖν διαστήματα, ὡς μιᾶς μοίρας λαμβανομένης τοῦ τῶν σταδίων ἀριθμοῦ οὓς ἡ σελήνη τῆς γῆς ἀφέστηκεν. Ὅτι δὲ οἱ λοιποὶ ἀριθμοὶ οἱ ὑπ' Ἀρχιμήδους περὶ τῆς ἀποστάσεως τῶν πλανωμένων λεγόμενοι οὐκ ἐν συμφώνοις [εἰσὶ] λόγοις, ῥᾴδιον γνῶναι [τοὺς] πῶς ἔχουσι πρὸς ἀλλήλους καὶ ἐν τίσι λόγοις εἰσὶ κατανοήσαντας: μὴ εἶναι δὲ ἐν ἁρμονίᾳ καὶ συμφωνίᾳ ταῦτα, τ(οῦ) καθ' ἁρμονίαν συνεστῶτος κόσμου ὄντα μέρη, ἀδύνατον. τοῦ μὲν δὴ πρώτου ἀριθμοῦ, ὃν ἀφέστηκεν ἡ σελήνη τῆς γῆς, ὄντος μυρι(ά)δ(ων) φνδʹ, μονάδων ͵δρλʹ, ὁ δεύτερος ἀριθμός, ὃν ἀφέστηκεν [ὁ] ἥλιος τῆς σελήνης, ὢν μυρι(ά)δ(ων) ͵εκζʹ, μονάδ(ων) ͵βξεʹ, ἐν λόγῳ ἐ(στὶ πλ)είον[ι] ἢ ἐ[ννεαπ]λασίῳ: πρὸς δὲ τοῦτον ὁ ἀνωτέρω ἀριθμός, ὢν μυρι(ά)δ(ων) ͵βκζʹ, μονάδ(ων), ͵βξεʹ, ἐν λόγῳ ἐστὶ [ἐλάττονι ἢ ἡμίσει: πρὸς δὲ τοῦτον ὁ ἀνωτέρω ἀριθμός, ὢν μυρι(ά)δ(ων) ͵επαʹ, μονάδ(ων) ͵ζρξεʹ, ἐν λόγῳ ἐστὶ] πλείονι ἢ διπλασίῳ: πρὸς δὲ τοῦτο[ν] ὁ ἀνωτέρω ἀριθμός, ὢν μυρι(ά)δ(ων) ͵δνδʹ, μονάδ(ων) ͵αρηʹ, ἐν λόγῳ ἐστὶν ἐλάττονι ἢ ἐπιτετάρτῳ: πρὸς δὲ τοῦτον ὁ ἀνωτέρω ἀριθμός, ὢν μυρι(ά)δ(ων) ͵βκζʹ, μονάδων ͵εξεʹ, ἐν λόγῳ ἐστὶ πλείονι ἢ ἡμίσει: πρὸς δὲ τοῦτον ὁ ἀνωτάτω ἀριθμός, ὢν μυρι(ά)δ(ων) ͵δλζʹ, μονάδων ͵βξεʹ, ἐν λόγῳ ἐστὶ[ν] ἐλάττονι ἢ διπλασίῳ.