Aristotle, On Indivisible Lines

LCL 307: 416-417

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968 a1. Ἆρά γ᾿ εἰσὶν ἄτομοι γραμμαί, καὶ ὅλως ἐν ἅπασι τοῖς ποσοῖς ἐστί τι ἀμερές, ὥσπερ ἔνιοί φασιν;

Εἰ γὰρ ὁμοίως ὑπάρχει τό τε πολὺ καὶ τὸ μέγα 5καὶ τὰ ἀντικείμενα τούτοις, τό τε ὀλίγον καὶ τὸ μικρόν, τὸ δ᾿ ἀπείρους σχεδὸν διαιρέσεις ἔχον οὐκ ἔστιν ὀλίγον ἀλλὰ πολύ, φανερὸν ὅτι πεπερασμένας ἕξει τὰς διαιρέσεις τὸ ὀλίγον καὶ τὸ μικρόν· εἰ δὲ πεπερασμέναι αἱ διαιρέσεις, ἀνάγκη τι εἶναι ἀμερὲς μέγεθος, ὥστε ἐν ἅπασιν ἐνυπάρξει τι ἀμερές, ἐπείπερ καὶ τὸ ὀλίγον καὶ τὸ μικρόν.

10Ἔτι εἰ ἔστιν ἰδέα γραμμῆς, ἡ δ᾿ ἰδέα πρώτη τῶν συνωνύμων, τὰ δὲ μέρη πρότερα τοῦ ὅλου τὴν φύσιν, ἀδιαίρετος ἂν εἴη αὐτὴ ἡ γραμμή, τὸν αὐτὸν δὲ τρόπον καὶ τὸ τετράγωνον καὶ τὸ τρίγωνον καὶ τὰ ἄλλα σχήματα, καὶ ὅλως ἐπίπεδον αὐτὸ καὶ σῶμα· συμβήσεται γὰρ πρότερ᾿ ἄττα εἶναι τούτων.

15Ἔτι εἰ σώματός ἐστι στοιχεῖα, τῶν δὲ στοιχείων μηδὲν πρότερον, τὰ δὲ μέρη τοῦ ὅλου πρότερα, ἀδιαίρετον ἂν εἴη τὸ πῦρ καὶ ὅλως τῶν τοῦ σώματος στοιχείων ἕκαστον, ὥστ᾿ οὐ μόνον ἐν τοῖς νοητοῖς, ἀλλὰ καὶ ἐν τοῖς αἰσθητοῖς ἐστί τι ἀμερές.


On Indivisible Lines

On Indivisible Lines

1. Are there such things as indivisible lines, and must there be in all magnitudes some unit which has no parts, as some say?

If “much” and “big,” and their opposites “few” Proof that indivisible units exist. and “little,” are similarly constituted, and it that which has almost infinite divisions is not small, but big, it is evident that “few” and “little” will have a limited number of divisions; if, then, the divisions are limited, there must be some magnitude which has no parts, so that in all magnitudes there will be some indivisible unit, since in all of them there is a “few” and a “little.”

Moreover, if there is an idea of a line, and the Idea is the first of quantities so called, and if the parts are logically prior to the whole, this unit line must be indivisible, and the same argument will apply to the square, triangle, and other figures, and generally speaking to a plane figure or to any other body; for there must be some unit prior in their case too.

Again, if there are elements in a body, and there is nothing prior to the elements, and if the parts are prior to the whole, fire and, generally speaking, each of the elements of the body would be indivisible, so that there must be a unit without parts, not only in the world of thought, but also in the world of perception.

DOI: 10.4159/DLCL.aristotle-divisible_lines.1936