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they do not have a common boundary, as in the case of ten stones. For if you count five and five, they do not have a common boundary joining them; for if you put something between the five and the five, they become eleven and not ten; and the name itself indicates the continuous and the discrete. Now, under discrete quantity are classified number and speech. And by number here we mean the things numbered; for all things numbered are discrete, as has been shown. And speech is also discrete; for speech, being counted by its words, does not have a common boundary joining its parts. For if speech has ten words and you divide them into five and five, they do not have a common boundary joining them; for if something is inserted in the middle, they become eleven and not ten. Likewise, a word, being counted by syllables, does not have a common boundary joining the syllables, for example, Socrates; between the syllable Sō and the cra there is no common boundary joining them. There are five continuous quantities: body, surface, line, place, time. But one must know that the point is without quantity; for it is neither measured nor numbered, since it has no dimension at all. The line, however, has one dimension, for it is breadthless length; this, therefore, is classified under continuous quantity. For being one, it is measured, and its parts have a common boundary joining them, the point in between. A surface is the outer part of the body, from ‘to appear.’ It has two dimensions, length and breadth. And this, being one, is measured, and its parts have a common boundary joining them, the line in between. But one must know that a smooth and even surface is called a plane, while an uneven and crooked one is simply a surface. The body has three dimensions: length, breadth, depth or thickness; and being one, it is measured, and its parts have a common boundary joining them, the surface. And place is a surface of the air; for your place is a surface, that is, the limit of the air containing you, and as a surface it is classified under continuous quantity. And time is measured into the past and the future, and its parts have a common boundary joining them, the now; but the now is without quantity. Behold, then, there are three things without quantity: the unit, the point, and the now. And properly speaking, these seven are called quantities: number, speech, time, place, line, surface, body. But accidentally we also call quantities the things considered in them, action, motion, color and such things; for example, if the action and the motion happen in a long time, we speak of a long action and a long motion, but if in a short time, a short one. Likewise also, if there were whiteness in a large body, we speak of much white, but if in a small one, little. Further, of quantity, some is definite, and some indefinite. Definite, then, is that which can be measured or numbered, while indefinite is that which by some excess surpasses every measure and every number; and it is called great and much indefinitely, as we say: Great is the compassion of God, great the mystery of the economy of the Word of God. But one must know that Aristotle places great and small, much and little, and greater and smaller, and less and more, and double and half and such things under the category of relatives. We say, therefore, that it is possible for the same thing to be classified under different categories according to different points of view. For inasmuch as the aforementioned things indicate a number and a measure, they are classified under quantity, but inasmuch as they have a relation to one another and are spoken of in relation to one another, under relatives; for the great is called great in relation to the small, and the double in relation to the half, and likewise the rest. The body, insofar as it is physical, is classified under substance, but insofar as it is mathematical, that is, measured, under quantity. Further, of quantity, some is magnitude, and some multitude. Now, magnitude is measured, while multitude is numbered. And 'how large' follows magnitude, but 'how many'

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ὅρον οὐ συνάπτουσιν ὡς ἐπὶ δέκα λίθων. Ἐὰν γὰρ ἀριθμήσῃς πέντε καὶ πέντε, οὐκ ἔχουσι κοινὸν ὅρον τὸν συνάπτοντα αὐτούς· εἰ γὰρ δώσεις τι μεταξὺ τῶν πέντε καὶ τῶν πέντε, γίνονται ἕνδεκα καὶ οὐ δέκα· καὶ αὐτὸ δὲ τὸ ὄνομα δηλοῖ τοῦ συνεχοῦς καὶ τοῦ διωρισμένου. Ὑπὸ μὲν οὖν τὸ διωρισμένον ποσὸν ἀνάγεται ὁ ἀριθμὸς καὶ ὁ λόγος. Ἀριθμὸν δὲ λέγομεν ἐνταῦθα τὰ ἀριθμούμενα· τὰ γὰρ ἀριθμούμενα πάντα διωρισμένα εἰσίν, ὡς δέδεικται. Καὶ ὁ λόγος δὲ διωρισμένος ἐστίν· ὁ γὰρ λόγος ἀριθμούμενος ταῖς λέξεσιν οὐκ ἔχει κοινὸν ὅρον τὸν συνάπτοντα τὰ μόρια αὐτοῦ. Ἐὰν γὰρ ἔχῃ δέκα λέξεις ὁ λόγος καὶ διέλῃς αὐτὰς εἰς πέντε καὶ πέντε, οὐκ ἔχουσι κοινὸν ὅρον τὸν συνάπτοντα αὐτάς· ἐὰν γὰρ παρεντεθῇ τι ἐν τῷ μέσῳ, γίνονται ἕνδεκα καὶ οὐ δέκα. Ὁμοίως καὶ ἡ λέξις ἀριθμουμένη συλλαβαῖς οὐκ ἔχει κοινὸν ὅρον τὸν συνάπτοντα τὰς συλλαβάς, οἷον Σωκράτης· μεταξὺ τῆς ˉˉΣˉω συλλαβῆς καὶ τῆς ˉκˉρˉα οὐκ ἔστι κοινὸς ὅρος συνάπτων αὐτάς. Συνεχῆ δὲ ποσὰ πέντε· σῶμα, ἐπιφάνεια, γραμμή, τόπος, χρόνος. Χρὴ δὲ γινώσκειν, ὅτι ἡ στιγμὴ ἄποσός ἐστιν· οὐ γὰρ μετρεῖται οὐδὲ ἀριθμεῖται, ἐπειδὴ οὐκ ἔχει οὐδεμίαν διάστασιν. Ἡ δὲ γραμμὴ ἔχει μίαν διάστασιν, ἔστι γὰρ μῆκος ἀπλατὲς οἷον· αὕτη οὖν ὑπὸ τὸ συνεχὲς ποσὸν ἀνάγεται. Μία γὰρ οὖσα μετρεῖται καὶ τὰ μόρια αὐτῆς ἔχουσι κοινὸν ὅρον συνάπτοντα αὐτὰ τὴν μεταξὺ στιγμήν. Ἐπιφάνεια δέ ἐστι τὸ ἔξω μέρος τοῦ σώματος, παρὰ τὸ φαίνεσθαι. Ἔχει δὲ δύο διαστάσεις, μῆκος καὶ πλάτος. Καὶ αὕτη δὲ μία οὖσα μετρεῖται, καὶ τὰ μόρια αὐτῆς ἔχουσι κοινὸν ὅρον συνάπτοντα αὐτὰ τὴν μεταξὺ γραμμήν. Χρὴ δὲ γινώσκειν, ὅτι ἡ μὲν ὁμαλὴ καὶ ἴση ἐπιφάνεια ἐπίπεδος λέγεται, ἡ δὲ ἀνώμαλος καὶ σκολιὰ ἁπλῶς ἐπιφάνεια. Τὸ δὲ σῶμα ἔχει τρεῖς διαστάσεις· μῆκος, πλάτος, βάθος ἤγουν πάχος· καὶ ἓν ὑπάρχον μετρεῖται, καὶ τὰ μόρια αὐτοῦ ἔχουσι κοινὸν ὅρον συνάπτοντα αὐτὰ τὴν ἐπιφάνειαν. Καὶ ὁ τόπος δὲ ἐπιφάνειά ἐστι τοῦ ἀέρος· ὁ γὰρ τόπος σου ἐπιφάνεια ἤγουν τὸ τέλος τοῦ περιέχοντός σε ἀέρος ἐστὶ καὶ ὡς ἐπιφάνεια ὑπὸ τὸ συνεχὲς ποσὸν ἀνάγεται. Καὶ ὁ χρόνος δὲ μετρεῖται εἰς τὸν παρεληλυθότα καὶ εἰς τὸν μέλλοντα, καὶ ἔχουσι τὰ μόρια αὐτοῦ κοινὸν ὅρον συνάπτοντα αὐτὰ τὸ νῦν· τὸ δὲ νῦν ἄποσόν ἐστιν. Ἰδοὺ οὖν τρία εἰσὶν ἄποσα· ἡ μονὰς καὶ ἡ στιγμὴ καὶ τὸ νῦν. Καὶ κυρίως μὲν ταῦτα τὰ ἑπτὰ λέγονται ποσά· ἀριθμός, λόγος, χρόνος, τόπος, γραμμή, ἐπιφάνεια, σῶμα. Κατὰ συμβεβηκὸς δὲ λέγομεν ποσὰ καὶ τὰ ἐν αὐτοῖς θεωρούμενα, πρᾶξιν, κίνησιν, χρῶμα καὶ τὰ τοιαῦτα· οἷον, εἰ ἐν πολλῷ χρόνῳ γένηται ἡ πρᾶξις καὶ ἡ κίνησις, φαμὲν πολλὴν πρᾶξιν καὶ πολλὴν κίνησιν, εἰ δὲ ἐν ὀλίγῳ, ὀλίγην. Ὁμοίως καί, εἰ ἐν πολλῷ σώματι λευκότης εἴη, φαμὲν πολὺ λευκὸν, εἰ δὲ ἐν ὀλίγῳ, ὀλίγον. Ἔτι τοῦ ποσοῦ τὸ μέν ἐστιν ὡρισμένον, τὸ δὲ ἀόριστον. Ὡρισμένον μὲν οὖν ἐστι τὸ δυνάμενον μετρεῖσθαι ἢ ἀριθμεῖσθαι, τὸ δὲ ἀόριστον τὸ ὑπεροχῇ τινι ὑπερβάλλον πᾶν μέτρον καὶ πάντα ἀριθμόν· καὶ λέγεται μέγα καὶ πολὺ ἀορίστως, ὡς λέγομεν· Πολλὴ ἡ εὐσπλαγχνία τοῦ θεοῦ, μέγα τὸ μυστήριον τῆς τοῦ θεοῦ λόγου οἰκονομίας. Χρὴ δὲ γινώσκειν, ὅτι ὁ Ἀριστοτέλης τὸ μέγα καὶ μικρὸν πολύ τε καὶ ὀλίγον καὶ τὸ μεῖζον καὶ τὸ μικρότερον καὶ ὀλιγώτερον καὶ πλείω καὶ διπλάσιον καὶ ἥμισυ καὶ τὰ τοιαῦτα ὑπὸ τὰ πρός τι τίθησι. Λέγομεν οὖν, ὅτι δυνατὸν τὸ αὐτὸ πρᾶγμα κατ' ἄλλον καὶ ἄλλον σκοπὸν ὑπὸ ἄλλην καὶ ἄλλην κατηγορίαν ἀνάγεσθαι. Ὡς μὲν γὰρ ἀριθμὸν καὶ μέτρον δηλοῦντα τὰ προειρημένα ὑπὸ τὸ ποσὸν ἀνάγονται, ὡς δὲ σχέσιν ἔχοντα πρὸς ἄλληλα καὶ ὡς πρὸς ἄλληλα λεγόμενα ὑπὸ τὰ πρός τι· τὸ γὰρ μέγα πρὸς τὸ μικρὸν λέγεται μέγα καὶ τὸ διπλάσιον πρὸς τὸ ἥμισυ, ὁμοίως καὶ τὰ λοιπά. Τὸ δὲ σῶμα, καθὸ μὲν φυσικόν ἐστιν, ὑπὸ τὴν οὐσίαν ἀνάγεται, καθὸ δὲ μαθηματικὸν ἤγουν μετρούμενον, ὑπὸ τὸ ποσόν. Ἔτι τοῦ ποσοῦ τὸ μὲν μέγεθος, τὸ δὲ πλῆθος. Τὸ μὲν οὖν μέγεθος μετρεῖται, τὸ δὲ πλῆθος ἀριθμεῖται. Ἀκολουθεῖ δὲ τὸ πηλίκον τῷ μεγέθει, τὸ δὲ ποσὸν