§5.6#2ἔτι δὲ ἓν λέγεται ὅσων ὁ λόγος ὁ τὸ τί ἦν εἶναι λέγων ἀδιαίρετος πρὸς ἄλλον τὸν δηλοῦντα τὸ πρᾶγμα (αὐτὸς γὰρ καθʼ αὑτὸν πᾶς λόγος διαιρετός).
Further, 'one' is said of those things of which the formula that states the essence is indivisible in relation to another formula that clarifies the thing (for every formula in itself is divisible).
οὕτω γὰρ καὶ τὸ ηὐξημένον καὶ φθῖνον ἕν ἐστιν, ὅτι ὁ λόγος εἷς, ὥσπερ ἐπὶ τῶν ἐπιπέδων ὁ τοῦ εἴδους.
For in this way even that which has increased and that which has decreased are one, because their formula is one, just as in the case of planes the formula of their form is one.
ὅλως δὲ ὧν ἡ νόησις ἀδιαίρετος ἡ νοοῦσα τὸ τί ἦν εἶναι, καὶ μὴ δύναται χωρίσαι μήτε χρόνῳ μήτε τόπῳ μήτε λόγῳ, μάλιστα ταῦτα ἕν, καὶ τούτων ὅσα οὐσίαι·
And in general, those things of which the thought which thinks the essence is indivisible, and cannot separate them either in time or in place or in formula, are most of all 'one', and of these, especially those which are substances.
καθόλου γὰρ ὅσα μὴ ἔχει διαίρεσιν, ᾗ μὴ ἔχει, ταύτῃ ἓν λέγεται, οἷον εἰ ᾗ ἄνθρωπος μὴ ἔχει διαίρεσιν, εἷς ἄνθρωπος, εἰ δʼ ᾗ ζῷον, ἓν ζῷον, εἰ δὲ ᾗ μέγεθος, ἓν μέγεθος.
For in general, whatever does not have division, in so far as it does not have it, is called one in this respect; for instance, if it does not have division in so far as it is man, it is one man; if in so far as it is animal, it is one animal; and if in so far as it is magnitude, it is one magnitude.
τὰ μὲν οὖν πλεῖστα ἓν λέγεται τῷ ἕτερόν τι ἢ ποιεῖν ἢ ἔχειν ἢ πάσχειν ἢ πρός τι εἶναι ἕν, τὰ δὲ πρώτως λεγόμενα ἓν ὧν ἡ οὐσία μία, μία δὲ ἢ συνεχείᾳ ἢ εἴδει ἢ λόγῳ·
Most things, then, are called 'one' by doing or having or suffering something else, or by being related to something that is one; but those which are called 'one' in the primary sense are those of which the substance is one, and it is one either by continuity or by form or by formula.
καὶ γὰρ ἀριθμοῦμεν ὡς πλείω ἢ τὰ μὴ συνεχῆ ἢ ὧν μὴ ἓν τὸ εἶδος ἢ ὧν ὁ λόγος μὴ εἷς.
For indeed we count as many either those which are not continuous, or those of which the form is not one, or those of which the formula is not one.
ἔτι δʼ ἔστι μὲν ὡς ὁτιοῦν ἕν φαμεν εἶναι ἂν ᾖ ποσὸν καὶ συνεχές, ἔστι δʼ ὡς οὔ, ἂν μή τι ὅλον ᾖ, τοῦτο δὲ ἂν μὴ τὸ εἶδος ἔχῃ ἕν· οἷον οὐκ ἂν φαῖμεν ὁμοίως ἓν ἰδόντες ὁπωσοῦν τὰ μέρη συγκείμενα τοῦ ὑποδήματος, ἐὰν μὴ διὰ τὴν συνέχειαν, ἀλλʼ ἐὰν οὕτως ὥστε ὑπόδημα εἶναι καὶ εἶδός τι ἔχειν ἤδη ἕν·
Further, in one sense we say that anything whatever is 'one' if it is a quantity and continuous, but in another sense we do not, unless it is a whole, and this means if it does not have one form; for instance, if we saw the parts of a shoe put together in any way whatsoever, we would not say they were one in the same way, unless because of their continuity, but only if they were so put together as to be a shoe and already to have a certain single form.
διὸ καὶ ἡ τοῦ κύκλου μάλιστα μία τῶν γραμμῶν, ὅτι ὅλη καὶ τέλειός ἐστιν.
Hence also the line of a circle is most of all one among lines, because it is whole and complete.
—τὸ δὲ ἑνὶ εἶναι ἀρχῇ τινί ἐστιν ἀριθμοῦ εἶναι· τὸ γὰρ πρῶτον μέτρον ἀρχή, ᾧ γὰρ πρώτῳ γνωρίζομεν, τοῦτο πρῶτον μέτρον ἑκάστου γένους· ἀρχὴ οὖν τοῦ γνωστοῦ περὶ ἕκαστον τὸ ἕν.
And to be one is to be a certain principle of number; for the first measure is a principle, since that by which we first know is the first measure of each genus; the principle, then, of what is knowable concerning each thing is the one.
οὐ ταὐτὸ δὲ ἐν πᾶσι τοῖς γένεσι τὸ ἕν. ἔνθα μὲν γὰρ δίεσις ἔνθα δὲ τὸ φωνῆεν ἢ ἄφωνον· βάρους δὲ ἕτερον καὶ κινήσεως ἄλλο.
But the one is not the same in all genera; for in one case it is a quarter-tone, in another a vowel or a mute; and in weight it is another thing, and in motion another.
πανταχοῦ δὲ τὸ ἓν ἢ τῷ ποσῷ ἢ τῷ εἴδει ἀδιαίρετον.
But everywhere the one is indivisible either in quantity or in form.
τὸ μὲν οὖν κατὰ τὸ ποσὸν ἀδιαίρετον, τὸ μὲν πάντῃ καὶ ἄθετον λέγεται μονάς, τὸ δὲ πάντῃ καὶ θέσιν ἔχον στιγμή, τὸ δὲ μοναχῇ γραμμή, τὸ δὲ διχῇ ἐπίπεδον, τὸ δὲ πάντῃ καὶ τριχῇ διαιρετὸν κατὰ τὸ ποσὸν σῶμα·
That, then, which is indivisible according to quantity, if it is so in every way and without position, is called a unit; if in every way and having position, a point; if in one dimension, a line; if in two, a plane; and that which is divisible according to quantity in every way and in three dimensions is a body.
καὶ ἀντιστρέψαντι δὴ τὸ μὲν διχῇ διαιρετὸν ἐπίπεδον, τὸ δὲ μοναχῇ γραμμή, τὸ δὲ μηδαμῇ διαιρετὸν κατὰ τὸ ποσὸν στιγμὴ καὶ μονάς, ἡ μὲν ἄθετος μονὰς ἡ δὲ θετὸς στιγμή.
And conversely, indeed, that which is divisible in two dimensions is a plane, that in one dimension a line, and that which is in no way divisible according to quantity is a point and a unit, the one without position being a unit, and that with position a point.
ἔτι δὲ τὰ μὲν κατʼ ἀριθμόν ἐστιν ἕν, τὰ δὲ κατʼ εἶδος, τὰ δὲ κατὰ γένος, τὰ δὲ κατʼ ἀναλογίαν, ἀριθμῷ μὲν ὧν ἡ ὕλη μία, εἴδει δʼ ὧν ὁ λόγος εἷς, γένει δʼ ὧν τὸ αὐτὸ σχῆμα τῆς κατηγορίας, κατʼ ἀναλογίαν δὲ ὅσα ἔχει ὡς ἄλλο πρὸς ἄλλο.
Further, some things are one in number, others in form, others in genus, others in analogy; in number those of which the matter is one, in form those of which the formula is one, in genus those which have the same scheme of category, and in analogy those which are related as one thing is to another.
ἀεὶ δὲ τὰ ὕστερα τοῖς ἔμπροσθεν ἀκολουθεῖ, οἷον ὅσα ἀριθμῷ καὶ εἴδει ἕν, ὅσα δʼ εἴδει οὐ πάντα ἀριθμῷ· ἀλλὰ γένει πάντα ἓν ὅσαπερ καὶ εἴδει, ὅσα δὲ γένει οὐ πάντα εἴδει ἀλλʼ ἀναλογίᾳ· ὅσα δὲ ἀνολογίᾳ οὐ πάντα γένει.
And always the latter follow from the former; for instance, whatever is one in number is also one in form, but that which is one in form is not all one in number; but whatever is one in form is all one in genus, while that which is one in genus is not all one in form, but in analogy; and what is one in analogy is not all one in genus.
φανερὸν δὲ καὶ ὅτι τὰ πολλὰ ἀντικειμένως λεχθήσεται τῷ ἑνί· τὰ μὲν γὰρ τῷ μὴ συνεχῆ εἶναι, τὰ δὲ τῷ διαιρετὴν ἔχειν τὴν ὕλην κατὰ τὸ εἶδος, ἢ τὴν πρώτην ἢ τὴν τελευταίαν, τὰ δὲ τῷ τοὺς λόγους πλείους τοὺς τί ἦν εἶναι λέγοντας.
It is also clear that 'many' will be spoken of in senses opposite to 'one'; for some things are called many because they are not continuous, others because they have their matter divisible in form, whether the first or the last, and others because the formulae which state their essence are plural.