Authors/Aristotle/metaphysics/l11/c4

Chapter 4

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ἐπεὶ δὲ καὶ ὁ μαθηματικὸς χρῆται τοῖς κοινοῖς ἰδίως, καὶ τὰς τούτων ἀρχὰς ἂν εἴη θεωρῆσαι τῆς πρώτης φιλοσοφίας. ὅτι γὰρ [20] ἀπὸ τῶν ἴσων ἴσων ἀφαιρεθέντων ἴσα τὰ λειπόμενα, κοινὸν μέν ἐστιν ἐπὶ πάντων τῶν ποσῶν, ἡ μαθηματικὴ δ᾽ ἀπολαβοῦσα περί τι μέρος τῆς οἰκείας ὕλης ποιεῖται τὴν θεωρίαν, οἷον περὶ γραμμὰς ἢ γωνίας ἢ ἀριθμοὺς ἢ τῶν λοιπῶν τι ποσῶν, οὐχ ᾗ δ᾽ ὄντα ἀλλ᾽ ᾗ συνεχὲς αὐτῶν ἕκαστον ἐφ᾽ [25] ἓν ἢ δύο ἢ τρία: ἡ δὲ φιλοσοφία περὶ τῶν ἐν μέρει μέν, ᾗ τούτων ἑκάστῳ τι συμβέβηκεν, οὐ σκοπεῖ, περὶ τὸ ὂν δέ, ᾗ ὂν τῶν τοιούτων ἕκαστον, θεωρεῖ.	Quoniam autem et mathematicus utitur communibus proprie, et horum principia erit utique speculari primae philosophiae. Quod enim ab equalibus equalibus ablatis quae relinquun↵tur equalia, commune quidem est in omnibus quantis. Mathematica autem absumens circa aliquam partem convenientis ƿ materiae facit theoriam, puta circa lineas aut angulos aut numeros aut reliquorum aliquid quantorum, non in quantum autem entia sed in quantum continuum ipsorum unumquodque ad ↵ unum aut duo aut tria. Philosophia autem de hiis quae in parte quidem in quantum horum unicuique aliquid accidit non intendit, circa ens autem in quantum ens talium unumquodque speculatur.	Chapter 4. Since even the mathematician uses the common axioms only in a special application, it must be the business of first philosophy to examine the principles of mathematics also. That when equals are taken from equals the remainders are equal, is common to all quantities, but mathematics studies a part of its proper matter which it has detached, e.g. lines or angles or numbers or some other kind of quantity-not, however, qua being but in so far as each of them is continuous in one or two or three dimensions; but philosophy does not inquire about particular subjects in so far as each of them has some attribute or other, but speculates about being, in so far as each particular thing is.
τὸν αὐτὸν δ᾽ ἔχει τρόπον καὶ περὶ τὴν φυσικὴν ἐπιστήμην τῇ μαθηματικῇ: τὰ συμβεβηκότα γὰρ ἡ φυσικὴ καὶ τὰς ἀρχὰς θεωρεῖ τὰς τῶν ὄντων [30] ᾗ κινούμενα καὶ οὐχ ᾗ ὄντα (τὴν δὲ πρώτην εἰρήκαμεν ἐπιστήμην τούτων εἶναι καθ᾽ ὅσον ὄντα τὰ ὑποκείμενά ἐστιν, ἀλλ᾽ οὐχ ᾗ ἕτερόν τι): διὸ καὶ ταύτην καὶ τὴν μαθηματικὴν ἐπιστήμην μέρη τῆς σοφίας εἶναι θετέον.	Eodem autem habet modo et circa naturalem scientiam mathematice. Naturalis enim accidentia et principia speculatur ↵ entium in quantum mota et non in quantum entia. Primam autem scientiam diximus horum esse secundum quod entia subiecta sunt, sed non alterum aliquid. Propter quod et hanc et mathematicam scientiam partes sapientie esse ponendum.	-Physics is in the same position as mathematics; for physics studies the attributes and the principles of the things that are, qua moving and not qua being (whereas the primary science, we have said, deals with these, only in so far as the underlying subjects are existent, and not in virtue of any other character); and so both physics and mathematics must be classed as parts of Wisdom.