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is a limit of the container, by which limit the contained is contained, for instance the air contains the body. The end of the air, therefore, that contains the body is called the place of the body, and not the whole air, so that place is a surface of the air that contains the body and thus it is reduced under continuous quantity as a surface. But the parts of place join at a line as surfaces do. But the parts of time join at the now; for the now, being without quantity, is a limit of the past, and a beginning of the future. It should be known that a surface is the outer part of a body, from its 'appearing' (phainesthai). This, then, is either equal and even and smooth and is called a plane, or curved and unequal and uneven and is called simply a surface. It should be known that body and surface and line are one and simultaneous, while time and place are about them. Place most of all belongs to quantity; of this, some has position, and some is without position. 'With position', then, indicates that the parts lie somewhere and abide one another; and it has a certain continuity and connection to one another. 'Without position' are those that are not such but are the opposite. Under 'with position', then, are reduced line, surface, body, place; for the parts of each of them abide and lie somewhere and have continuity with one another, the parts of a line in the surface, and of the surface in the body, and of the body in the place, and of the place in the body as surfaces. 'Without position' are number, speech, time; number and speech, because their parts have no continuity nor lie somewhere nor do their parts abide. But the parts of time, even if they have continuity, yet they do not abide nor do they lie somewhere. Number is twofold, the one is in the class of numbers, the other in numerable things like a sextarius; the one is the measure, the bronze one, the other is the thing measured, for instance either wine or some other such thing. The number that numbers, then, is not with position, but the numbered thing is with position. And every quantity is both a measure and measurable. It should be known that quantity is the measure itself and the number that measures and that numbers. But speech and time and place and body and surface and line are not quantity but are quantities, as being subjects of quantity and being measured and numbered, likewise also the numbered number, that is, the wine and such things. And some are subject to continuous quantity as being continuously numbered, and others to discrete quantity as being discretely measured and numbered; for which reason they are also called quantities and not quantity. And in the proper sense these seven are called quantities, but incidentally we call quantities the things observed in them, such as action, motion, whiteness and such things; for instance, if the action and the motion occur 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 should be whiteness in a large body, we speak of much white, but if in a small one, little. But Aristotle also reduces motion itself under quantity. And tendency is also reduced under quantity because the greatest degree is observed in it. The property of quantity is the equal and the unequal; but lightness and heaviness are under quality. 4 Concerning Relatives Such things are called relatives, as are said to be, in their very nature, of others, or in some other way in relation to another, that is, all such things as are said to be of others or in relation to another, whether with reference to a genitive or to another case; for this is what 'in some other way' signifies, that is, in whatever case; for relatives are not only spoken of in relation to the genitive, but sometimes also both the reference and the counter-reference are said in the same case, whether genitive or dative, for instance 'the double' is 'double of a half' and 'the half' is 'half of a double', in relation to the genitive, but in relation to the dative 'the similar' is 'similar to a similar', or the reference is in relation to the genitive and the counter-reference in relation to the dative, the reference for instance 'knowledge' is 'knowledge of the knowable', and the counter-reference; the

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πέρας ἐστὶ τοῦ περιέχοντος, καθὸ πέρας περιέχεται τὸ περιεχόμενον, οἷον ὁ ἀὴρ περιέχει τὸ σῶμα. Τὸ οὖν τέλος τοῦ ἀέρος τὸ περιέχον τὸ σῶμα λέγεται τόπος τοῦ σώματος, καὶ οὐχ ὅλος ὁ ἀήρ, ὥστε ὁ τόπος ἐπιφάνειά ἐστι τοῦ ἀέρος τοῦ περιέχοντος τὸ σῶμα καὶ οὕτως ὑπὸ τὸ συνεχὲς ποσὸν ἀνάγεται ὡς ἐπιφάνεια. Τὰ δὲ μόρια τοῦ τόπου συνάπτουσι πρὸς γραμμὴν ὡς ἐπιφανείας. Τὰ δὲ μόρια τοῦ χρόνου πρὸς τὸ νῦν συνάπτουσι· τὸ γὰρ νῦν ἄποσον ὂν πέρας μέν ἐστι τοῦ παρῳχημένου, ἀρχὴ δὲ τοῦ μέλλοντος. Ἰστέον δέ, ὅτι ἐπιφάνειά ἐστι τὸ ἔξω μέρος τοῦ σώματος, παρὰ τὸ φαίνεσθαι. Αὕτη οὖν ἢ ἴση ἐστὶ καὶ ὁμαλὴ καὶ λεία καὶ λέγεται ἐπίπεδος, ἢ καμπύλη καὶ ἄνισος καὶ ἀνώμαλος καὶ λέγεται ἁπλῶς ἐπιφάνεια. Ἰστέον δέ, ὅτι τὸ μὲν σῶμα καὶ ἡ ἐπιφάνεια καὶ ἡ γραμμὴ ὑφ' ἕν εἰσι καὶ ἅμα, ὁ δὲ χρόνος καὶ ὁ τόπος περὶ αὐτά. Μάλιστα ὁ τόπος ἐστὶ τοῦ ποσοῦ· τὸ μέν ἐστι θετόν, τὸ δὲ ἄθετον. Τὸ μὲν οὖν θετὸν δηλοῖ τὸ κεῖσθαί που καὶ τὸ ὑπομένειν ἄλληλα τὰ μόρια· ἔχει δὲ καί τινα συνέχειαν καὶ ἀλληλουχίαν πρὸς ἄλληλα. Ἄθετα δέ εἰσι τὰ μὴ τοιαῦτα ἀλλ' ἐναντίως ἔχοντα. Ἀνάγονται οὖν ὑπὸ μὲν τὸ θετὸν γραμμή, ἐπιφάνεια, σῶμα, τόπος· ἑκάστου γὰρ αὐτῶν τὰ μόρια μένουσι καὶ κεῖνταί που καὶ συνέχειαν ἔχουσι πρὸς ἄλληλα, τὰ μὲν μόρια τῆς γραμμῆς ἐν τῇ ἐπιφανείᾳ, τῆς δὲ ἐπιφανείας ἐν τῷ σώματι, τοῦ δὲ σώματος ἐν τῷ τόπῳ, τοῦ δὲ τόπου ἐν τῷ σώματι ὡς ἐπιφανείας. Ἄθετα δέ εἰσιν ἀριθμός, λόγος, χρόνος· ὁ μὲν ἀριθμὸς καὶ ὁ λόγος, διότι τὰ μόρια αὐτῶν οὐδὲ συνέχειαν ἔχουσιν οὐδὲ κεῖνταί που οὐδὲ ὑπομένουσι τὰ μόρια αὐτῶν. Τὰ δὲ τοῦ χρόνου μόρια, εἰ καὶ συνέχειαν ἔχουσιν, ἀλλ' οὐδὲ ὑπομένουσιν οὐδὲ κεῖνταί που. Ὁ δὲ ἀριθμὸς διττός ἐστιν, ὁ μὲν ἐν τῇ τῶν ἀριθμῶν, ὁ δὲ ἐν τοῖς ἀριθμητοῖς ὡς ξέστης· ὁ μὲν ὁ μετρῶν ὁ χαλκοῦς, ὁ δὲ ὁ μετρούμενος οἷον ἢ οἶνος ἢ ἕτερόν τι τοιοῦτον. Ὁ μὲν οὖν ἀριθμῶν οὐκ ἔστι θετός, ὁ δὲ ἀριθμούμενος θετός ἐστι. Καὶ πᾶν δὲ ποσὸν καὶ μέτρον ἐστὶ καὶ μετρητόν. Ἰστέον, ὡς ποσότης μέν ἐστιν αὐτὸ τὸ μέτρον καὶ ὁ ἀριθμὸς ὁ μετρῶν καὶ ὁ ἀριθμῶν. Ὁ δὲ λόγος καὶ χρόνος καὶ τόπος σῶμά τε καὶ ἐπιφάνεια καὶ γραμμὴ οὔκ εἰσι ποσότης ἀλλὰ ποσὰ ὡς ὑποκείμενα τῇ ποσότητι καὶ μετρούμενα καὶ ἀριθμούμενα, ὁμοίως καὶ ὁ ἀριθμὸς ὁ ἀριθμούμενος ἤγουν ὁ οἶνος καὶ τὰ τοιοῦτα. Καὶ τὰ μὲν ὑπόκεινται τῇ συνεχεῖ ποσότητι ὡς συνεχῶς ἀριθμούμενα, τὰ δὲ τῇ διωρισμένῃ ὡς διωρισμένως μετρούμενά τε καὶ ἀριθμούμενα· διὸ καὶ ποσὰ λέγονται καὶ οὐ ποσότης. Καὶ κυρίως μὲν ποσὰ ταῦτα τὰ ἑπτὰ λέγονται, κατὰ συμβεβηκὸς δὲ ποσὰ λέγομεν τὰ ἐν αὐτοῖς θεωρούμενα οἷον πρᾶξιν, κίνησιν, τὸ λευκὸν 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 λευκόν, εἰ δὲ ἐν ὀλίγῳ, ὀλίγον. Ὁ δὲ Ἀριστοτέλης καὶ τὴν κίνησιν καθ' ἑαυτὴν ὑπὸ τὸ ποσὸν ἀνάγει. Ἀνάγεται δὲ ὑπὸ τὸ ποσὸν καὶ ἡ ῥοπὴ διὰ τὸ θεωρεῖσθαι ἐν αὐτῇ τὸ μάλιστα. Ἴδιον τοῦ ποσοῦ τὸ ἴσον καὶ ἄνισον· ἡ δὲ κουφότης καὶ ἡ βαρύτης ὑπὸ τὸ ποιόν. 4 Περὶ τῶν πρός τι Πρός τι τὰ τοιαῦτα λέγεται, ὅσα αὐτά, ἅπερ ἐστίν, ἑτέρων εἶναι λέγεται ἢ ὁπωσοῦν ἄλλως πρὸς ἕτερον ἤγουν ὅσα ἑτέρων εἶναι λέγεται ἢ πρὸς ἕτερον εἴτε πρὸς γενικὴν εἴτε πρὸς ἑτέραν πτῶσιν· τοῦτο γὰρ σημαίνει τὸ ὁπωσοῦν ἄλλως ἤγουν καθ' ὁποίαν πτῶσιν· τὰ γὰρ πρός τι οὐ μόνον πρὸς γενικήν, ἀλλ' ἔστιν ὅτε καὶ πρὸς τὴν αὐτὴν πτῶσιν, εἴτε γενικὴν εἴτε δοτικήν, λέγεται καὶ ἡ ἀπόδοσις καὶ ἡ ἀνταπόδοσις, οἷον τὸ διπλάσιον ἡμίσεος διπλάσιον καὶ τὸ ἥμισυ διπλασίου ἥμισυ πρὸς γενικήν, πρὸς δὲ δοτικὴν τὸ ὅμοιον ὁμοίῳ ὅμοιον, ἢ ἡ ἀπόδοσις μὲν πρὸς γενικὴν καὶ ἡ ἀνταπόδοσις πρὸς δοτικὴν, ἡ μὲν ἀπόδοσις οἷον ἐπιστήμη ἐπιστητοῦ ἐπιστήμη, καὶ ἀνταπόδοσις· τὸ