We say ‘already’ (46) for any time close enough to the indivisible ‘now’ of the absolute present. “When do you take your walk?’ ‘I am starting already,’ or ‘I have already taken it.’ But the phrase only applies to the near future or past; so that we should not say ‘’Troy has already fallen.’ Another term for the near past is ‘just now’ (αν δ), ‘When did you arrive?’ ‘ Just now,’ if it was near to the instantaneous ‘now’ at which you speak; but ‘some time ago’ (palai) if the interval is con- siderable; and ‘suddenly ὦ (exaiphnés) if the passage of time is so short as to be imperceptible.
= 4 In the Greek there is a rather faint etymological play upon the ἐξ (‘out’ or ‘away from’) of ἐξαίφνης, fairly represented by the etymological suggestion of ‘sudden’ from «the Latin sub-it-aneus, ‘going stealthily.” Cf keat).
ARISTOTLE 2a2b Μεταβολὴ δὲ πᾶσα φύσει ἐκστατικόν. ἐν δὲ τῷ χρόνῳ πάντα γίνεται καὶ φθείρεται" διὸ καὶ οἱ μὲν σοφώτατον ἔλεγον, ὁ δὲ ᾿Τυθαγόρειος ΠΠάρων ἀμαθέστατον, ὅτι καὶ ἐπιλανθάνονται ἐν τούτῳ, λέγων ὀρθότερον. δῆλον οὖν ὅτι φθρρᾶς μᾶλλον 0 ἔσται καθ᾽ αὑτὸν αἴτιος ἢ γενέσεως, καθάπερ ἐλέχθη καὶ πρότερον (ἐκστατικὸν γὰρ ἡ μεταβολὴ καθ᾽ αὑτήν), γενέσεως δὲ καὶ τοῦ εἶναι κατὰ συμ- βεβηκός. σημεῖον δὲ ἱκανὸν ὅτι γίνεται μὲν οὐδὲν ἄνευ τοῦ κινεῖσθαί πως αὐτὸ καὶ πράττειν, φθεί- ρεται δὲ καὶ μηδὲν κινούμενον: καὶ ταύτην μάλιστα a5 λέγειν εἰώθαμεν ὑπὸ τοῦ χρόνου φθοράν. οὐ μὴν ἀλλ᾽ οὐδὲ ταύτην ὃ χρόνος ποιεῖ, ἀλλὰ συμβαίνει ἐν χρόνῳ γίνεσθαι καὶ ταύτην τὴν μεταβολήν. "Ore μὲν οὖν ἔστιν ὁ χρόνος καὶ τί, καὶ ποσαχῶς λέγομεν τὸ νῦν, καὶ τί τὸ ποτὲ καὶ τὸ ἄρτι καὶ τὸ ἤδη καὶ τὸ πάλαι καὶ τὸ ἐξαίφνης, εἴρηται.
α« Nothing is known of any Paron, and Simplicius [754. 9] thinks the word is not a proper name at all, but the ordinary participle that means ‘ being present.’ He quotes Eudemus as telling the tale that Simonides reciting at an Olympic festival extolled Time as the wisest of beings, since all learning and all memory are in him; but a certain unnamed hilosopher (παρόντα τινὰ τῶν σοφῶν) said: ‘ But look ere, Simonides, don’t we forget everything in time as well as learn it?’ Simplicius thinks that Aristotle is referring to this and speaks of the interrupler as ‘The Pythagorean who was there.’ (Diels, More. 16.—C.]
PHYSICS, IV. xm.
All change is in its nature a‘ passing away.’ And it is ‘in time’ that everything begins and ceases to be; so sorne have called it the wisest of things, because it brings all knowledge, but the Pythagorean Paron® said it was the most ignorant, because it is in time too'that everything is forgotten, and he was nearer the mark. Indeed, it is evident that the mere passage of tirne itself is destructive rather than generative, as we said earlier”; because change is primarily a ‘ passing away.’ So it is only incident- ally that time is the cause of things coming into being and existing. A sufficient indication of this may be found in the fact that nothing comes into being without being started by some cause and reacting to it,¢ but things perish without anything being stirred, and it is a kind of perishing without apparent provacation that we especially attribute to time,? But yet, after all, it is not really time itself that destroys things in this way, but the changes that do destroy take place concurrently with time.® That there is such a thing as time, therefore, and what it is, and in how many senses we speak of ‘ now,’ and what ‘ sometime’ and ‘ but now’ and ‘already’ and ‘some time ago’ and ‘suddenly’ mean, has now been said.
® [καὶ πράττειν. Cf, Themust. 159, 9 προσδεῖταί τινος ἐνεργείας ὑφ' ἧς γίνεται, οἷον τέχνης ἣ φύσεως ἢ διδασκαλίας ἢ rpdkews—C.} 2 Not for instance if ἃ man was slain by a sword (Aquinas), ὁ (Or, ‘ but it 1s incidental that this change also occurs in time.’—C.]
ARISTOTLE CHAPTER XIV ARGUMENT Definition of velocity and examination of succession in time.
All change and every moving ae are in time (222 Ὁ 80- Relation of time as hurpiaralinns potential or actual, to consciousness (a 16-29), What kind of succession should time be standardized by? Time is identical as ‘ now’ across all changes everywhere and in every succession, but‘ nows’ and intercepted intervals between them are different from each other as taken along any succession whatever. But all such intervals in whatever Τούτων δ᾽ ἡμῖν οὕτω διηριθμημένων φανερὸν ὅτι πᾶσα μεταβολὴ καὶ ἅπαν τὸ κινούμενον ἐν χρόνῳ. τὸ γὰρ θᾶττον καὶ βραδύτερον κατὰ πᾶσάν ἐστι μεταβολήν' ἐν πᾶσι γὰρ οὕτω φαίνεται. λέγω δὲ θᾶττον κινεῖσθαι τὸ πρότερον μεταβάλλον εἰς τὸ ὑποκείμενον κατὰ τὸ αὐτὸ διάστημα καὶ ὁμαλὴν κίνησιν κινούμενον" οἷον ἐπὶ τῆς φορᾶς, εἰ ἄμφω κατὰ τὴν “περιφερῆ κινεῖται ἢ ἄμφω κατὰ τὴν εὐθεῖαν' ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων. ἀλλὰ μὴν τό γε πρότερον ἐν χρόνῳ ἐστίν" πρότερον “γὰρ καὶ ὕστερον λέγομεν κατὰ τὴν πρὸς τὸ νῦν ἀπό- στασιν, τὸ δὲ νῦν ὅρος τοῦ παρήκοντος καὶ τοῦ μέλλοντος: ὥστ᾽ ἐπεὶ τὰ νῦν ἐν,χρόνῳ, καὶ τὸ πρότερον καὶ ὕστερον ἐν χρόνῳ ἔσται" ἐν ᾧ γὰρ oe © [' homogeneous.’ The two movements compared must be ¢ over the same course ᾽ (κατὰ τὸ αὐτὸ διάστημα) and each ‘of uniform velocity ’ (ὑμαλὴν κίνησιν), for, if either varies in pace, it night be the quicker at some moments, the,slower at others.—C,] PHYSICS, IV. χιν.
CHAPTER XIV ARGUMENT (continued) kind of succession run abreast and are measured by the same time as mutually determining and determined by any one of Advantage of rotation as the form of movement by γ6 787» ence to which to standardize time. Loose ways of speaking of time and temporal things as‘ circulating ’ (Ὁ 12-224 a 2).
An interpolation of no value (a 2-16).
All this being so established, it becomes clear that all changes and everything that moves are con- ditioned by time. For it is a patent fact that every change may be quicker or slower, And what I mean by one change being quicker than another is that, of two homogeneous * change-movements (either both on a periphery, for instance, or both on a straight line, if it be a local movement, and mutatis mutandis in other kinds of change), that one is the quicker which reaches a certain determined stage or point in its course ‘ before’ the other reaches the point at the same distance from the starting-point in its course. Now this ‘ before’ means before ‘ in time,’ for both ‘ before’ and ‘ after’ are expressions of an interval between the ‘ nows’ of arrival;® and since the ‘ now’ is a boundary between past and future, it follows that the two ‘ nows ’ (of the former and latter arrival, namely) being both phenomena of time, so must their ‘ before’ and ‘ after’ be. For, whatever > (Literally, ‘ we use the terms “ earlier” and “later” with respect to the distance (from the event so described) to the present moment.’—C. ] VoL. I Qn 417 ARISTOTLE ~ lot ~ LJ? A. 22aa7d νῦν, Kal ἡ τοῦ νῦν ἀπόστασις. (ἐναντίως δὲ , λέγεται τὸ πρότερον κατά TE τὸν παρεληλυθότα ta " a Arr > \ Ν “ λ 10 χρόνον καὶ τὸν μέλλοντα’ ἐν μὲν γὰρ τῷ παρελη- λυθότι πρότερον λέγομεν τὸ πορρώτερον τοῦ νῦν, ὕστερον δὲ τὸ ἐγγύτερον, ἐν δὲ τῷ μέλλοντι πρότερον μὲν τὸ ἐγγύτερον, ὕστερον δὲ τὸ πορρώ- τερον) ὥστ᾽ ἐπεὶ τὸ μὲν πρότερον ἐν χρόνῳ, ὔ Ἄ > ~ ra A ta A πάσῃ δ᾽ ἀκολουθεῖ κινήσει τὸ πρότερον, φανερὸν 1 φ Fol x " lol, ᾽ν a ὅτι πᾶσα μεταβολὴ καὶ πᾶσα κίνησις ἐν χρόνῳ εστιν.
"Αξιον δ᾽ ἐπισκέψεως καὶ πῶς ποτε ἔχει ὁ χρόνος πρὸς τὴν ψυχήν, καὶ διὰ τί ἐν παντὶ δοκεῖ εἶναι ὁ χρόνος, καὶ ἐν γῇ καὶ ἐν θαλάττῃ Kal ἐν οὐρανῷ. ἢἣ ὅτι κινήσεώς τι πάθος ἢ ἕξις, ἀριθμός 20 γε ὦν, ταῦτα δὲ κινητὰ πάντα (ἐν τόπῳ γὰρ x Ξε, κ ς ra Y nd: πάντα), 6 δὲ χρόνος Kal ἡ κίνησις dua κατά τε δύναμιν καὶ κατ᾽ ἐνέργειαν. Πότερον δὲ μὴ οὔσης ψυχῆς εἴη ἂν 6 χρόνος ἢ οὔ, ἀπορήσειεν ἄν τις" ἀδυνάτου yap ὄντος εἶναι τοῦ ἀριθμήσοντος ἀδύνατον καὶ ἀριθμητόν τι εἶναι, ὥστε δῆλον ὅτι οὐδ᾽ ἀριθμός" ἀριθμὸς yap ἢ ai τὸ ἠριθμημένον ἢ τὸ ἀριθμητόν. εἰ δὲ μηδὲν ἄλλο πέφυκεν ἀριθμεῖν ἢ ψυχὴ καὶ ψυχῆς νοῦς, ἀδύνατον PHYSICS, IV. xiv.
PHYSICS, IV. xiv.
it be that the ‘ now’ pertains to, to that must the interval determined by it pertam. (But note that ‘before ’ has opposite meanings according to whether it refers to past or future time; for in the past we regard the eyent that is farther from the present as ‘before’ the other and the nearer event as ‘ after’ it, but in the future the nearer as ‘ before’ and the farther as ‘after’ thé other.) So, inasmuch as ‘ before ᾿ pertains to time, and may be a‘ before ἡ of arrival at a point of any kind of change-movement, it follows that every change or movement takes place ‘in time.’
The relation of time to consciousness deserves examination, and so does the question why we conceive of time as immanent in everything in earth and seaand sky. As to the latter point, it is because time, being the numerator of motion, pertains to such motion wherever it exists, as an affection or disposi- tion of it (namely, that it is either actually counted in units or potentially countable in such); and all things in the material universe are suscepuble of motion (for they all have position which is subject to change), and time and movement run in pairs both potentially and actually.
The question remains, then, whether or not time would exist if there were no consciousness; for if it were impossible for there to be the factor that does the counting, it would be impossible that anything should be counted; so that evidently there could be no number, for a number is either that which has actually been counted or that which can be counted. And if nothing can count except consciousness, and consciousness only as intellect (not as sensation merely), it is impossible that time should exist if ARISTOTLE 223 8 εἶναι χρόνον ψυχῆς μὴ οὔσης, ἀλλ᾽ ἢ τοῦτο ὅ ποτε 80 σι ὄν ἐστιν 6 χρόνος, οἷον εἰ ἐνδέχεται κίνησιν εἶναι ἄνευ ψυχῆς. τὸ δὲ πρότερον καὶ ὕστερον ἐν κινήσει ἐστίν: χρόνος δὲ ταῦτ᾽ ἐστὶν ἡ ἀριθμητά ἐστιν. ᾿ ᾿Απορήσειε δ᾽ ἄν τις καὶ ποίας κινήσεως ὁ χρόνος ἀριθμός. ἢ ὁποιασοῦν" καὶ γὰρ γίνεται ἐν χρόνῳ καὶ φθείρεται καὶ αὐξάνεται, καὶ ἀλλοιοῦται ἐν χρόνῳ καὶ φέρεται: ἢ οὖν κίνησίς ἐστι, ταύτῃ ἐστὶν ἑκάστης κινήσεως ἀριθμός. διὸ κινήσεώς ἐστιν ἁπλῶς ἀριθμὸς συνεχοῦς, ἀλλ᾽ οὐ σινός.
"AM ἔστι νῦν κεκινῆσθαι καὶ ἄλλα, ὧν ἑκατέρας τῆς κινήσεως εἴη ἂν ἀριθμός. ἕτερος οὖν χρόνος ἔστι, καὶ ἅμα δύο ἴσοι χρόνοι ἂν εἶεν; ἢ οὔ' ὁ αὐτὸς' ἀρ χρόνος εἷς εἷς ὁμοίως καὶ ἅμα!: εἶδει δὲ καὶ οἱ μὴ ἅμα" εἰ γὰρ εἶεν κύνες, οἱ δ᾽ ἵπποι, ἑκάτεροι δ᾽ ἑπτά, ὁ αὐτὸς ἀριθμός. οὕτω καὶ τῶν κινήσεων τῶν ἅμα περαινομένων ὁ αὐτὸς χρόνος" ἀλλ᾽ ἡ μὲν 1 [αὐτὸς: Gras GIL—C.[ ted ὁμοίως καὶ ἅμα F, Bekker: εἷς καὶ ἴσος καὶ πᾶς dua H; εἷς καὶ ἴσος καὶ ἅμα Ἐ).---Ο,] * [τοῦτο ὅ more ὅν ἐστιν ὁ χρόνος is explained by Philo- ponus (755. 17) as ‘the substratum of time, namely move- ment.’ Movement is the objective thing which contains before and after, whether we count these or not. If we count them, then we have tme —C,] 5 (Either, 6 αὐτὸς yap xpdvos πᾶς καὶ els ὁ loos καὶ ἅμα cae Prantl) or ὁ αὐτὸς γὰρ χρόνος πᾶς ὁ ἴσος καὶ ἅμα Carteron) will yield the sense: ‘ For all stretghes of time that are equal and simultaneous are numerically one and the same tine, while (equal) stretches which are not simul- taneous are the same conceptually (though not numerically),’ ég. two successive hours. Ch. Simplic. 764. 3 λύων οὖν τὴν ἀπορίαν οὐχ οὕτως ἔχει, φησίν οὐ γὰρ πλείους ἅμα χρόνοι γίγνονται, PHYSICS, IV. χιν.
consciousness did not; unless as the ‘ objective thing ’ which is subjectively time to us, if we may suppose that movement could thus objectively exist without there being any consciousness. For ‘ before’ and ‘ after’ are objectively involved in motion, and these, gua capable of numeration, constitute time.
It may be asked further to what kind of motion- change time does pertaitt. We may answer, ‘ It does not matter.’ For things beg and cease to be, and grow, and change their qualities and their places ἡ in time’; so far, then, as change can be regarded as movement, so far time must be a numerator of every such kind of movement. We conclude, then, that time is the numeration of continuous movement, without any qualification, not only of some particular kind.
But if we take one kind of change and say ‘ now’ with respecl to it, other kinds of change, each of which has a specifically different unit to be counted in, will be at a certain stage of their change at this same ‘now.’ Can each of them have a different time, and must there be more than one time running con- currently? No; for it is the same lapse of time that is counted by two ‘ nows,’ every where at once, whatever the units of movement or change; whereas the one- and-sameness of the units is determined by their kind and not by their ‘ at-once-ness ’;° just as if there were dogs and horses, seven of each, the number would be the same, but the units numbered different. So, too, of all movement-changes determined simultaneously the time is*the same; one may be quick and another ἀλλ᾽ ὁ ἴσος χρόνος πᾶς ἐν τῷ ἐνεστῶτι ὁ αὐτὸς els ἅμα ἐστὶ τῷ ἀριθμῷ, εἴδει δὲ οἱ αὐτοί εἰσι καὶ οἱ μὴ ἅμα, τουτέστιν ὁ παρεληλυθὼς τῷ μέλλοντι.---Ο,] ARISTOTLE 2288 ταχεῖα ἴσως ἡ δ᾽ ov, καὶ ἡ μὲν φορὰ ἡ δ᾽ ἀλλοίωσις' ε, ὰ ΓΝ ΌΝ. » YS dobuds ἢ O μέντοι KPOVOS O QUTOS, εὐπὲρ Καὶ O αριῦμος Loos ww καὶ ἅμα, τῆς Te ἀλλοιώσεως Kal τῆς φορᾶς. καὶ διὰ τοῦτο αἱ μὲν κινήσεις ἕτεραι καὶ χωρίς, ὁ δὲ ~ ω A χρόνος πανταχοῦ ὁ αὐτός, ὅτι καὶ 6. ἀριθμὸς εἷς καὶ ὁ αὐτὸς πανταχοῦ ὁ τῶν ἴσων καὶ ἅμα. 1 JKA 0 Emel δ᾽ dort’ φορὰ καὶ ταύτης ἡ κύκλῳ, apil- μεῖται δ᾽ ἕκαστον ἑνί τινι συγγενεῖ, μονάδες μονάδι, ἵπποι δ᾽ ἵππῳ, οὕτω καὶ 6 χρόνος χρόνῳ 15 τινὶ ὡρισμένῳ, μετρεῖται δὲ (ὥσπερ εἴπομεν) ὅ τε 2 > χρόνος κινήσει καὶ ἡ κινήσις χρόνῳ---τοῦτο δ᾽ ἐστίν, ὅτι ὑπὸ τῆς ὡρισμένης κινήσεως χρόνῳ μετρεῖται τῆς τε κινήσεως τὸ ποσὸν καὶ τοῦ χρόνου---εἰ οὖν τὸ πρῶτον μέτρον πάντων τῶν συγγενῶν, ἡ κυκλοφορία ἡ ὁμαλὴς μέτρον μάλιστα, ὅτι ὁ ἀριθμὸς ὃ ταύτης γνωριμώτατος.
1 [ἔστι: πρώτη ἐστὶ Prantl—cC.]
4 [ὑπὸ τῆς ὡρισμένης κινήσεως χρόνῳ, Taking χρόνῳ with ὡρισμένης (of. 221 a 1 μετρεῖ δ' οὗτος (ὁ χρόνος) τὴν κίνησιν τῷ ὁρίσαι τινὰ κίνησιν ἣ καταμετρήσει τὴν ὅλην), the meaning will be: ‘ that is because it is by the movement-determined- by-time that the quantity both of movement and of time is measured.’ The unit of measurement (the day, for in- stance) is a movement determined by a certain time-length. Alexander, and some copies known to Simplicius (769, 15) read τῆς ὡρισμένης κινήσεως χρόνῳ, So also Philoponus, 782. 26 (lemma τῆς KM, ὑπὸ τῆς ὃ), but he paraphrases: διότι ἢ ὑπὸ τοῦ χρόνου πρώτως ὁρισθεῖσα κίνησις, αὕτη καὶ τῆς πάσης ἐστὶ κινήσεως μέτρον καὶ τοῦ xpdvov.—C.} > The unit fixed is the unit of time fixed in reference to some particular motion, and this becomes she measure of all time-lapses, whether of movement, modification, change of size, etc.; for the lapses of ail these different manifesta- tions of time are akin to each other with respect to before and after. 5 * A circumference, being a re-entrant curve, any part of PHYSICS, IV. x1v.
slow, and one a change of place and the other of quality; the time, however, 1s the same, if the counting has reached the same number and been made simultaneously, whether of the qualitive modification, or of the place-movement. So the movements or changes are different and stand apart, but the time is the same everywhere, because the numeration, if made simultaneously and up to the same figure, is one and the same.
And now, keeping local motion and especially rotalion in mind, note that everything is counted by some unit of like nature to itsclf—monads monad by monad, for instance, and horses horse by horse— and so likewise time by some finite unit of time. But as we have said, movement and time mutually determine each other quantitively; and that because the standard of time established by the movement we select is the quantitive measure both of that movement and of time. If, then, the standard once fixed measures all dimensionality of its own order,® a uniform rotation will be the best standard, since it is easiest to count.® which will fit any other part, is uniform all over; and motion upon it (supposing its velocity to be uniform) has ἃ natural spatial unit in each completed circle. It is therefore easy to count, and since its natural unit is easy to divide or multiply into convenient secondary units, it furnishes a, perfect standard by which to determine time. Aristotle does not say what petienley circular motion we are to take as our standard, but the commentators are probably right in sup- posing that for practical purposes he accepted the solar day, though on‘all theoretical grounds he should have taken the stellar day, as registering (in his astronomy) the prime heavenly movement and one that by the science of the day (which recognized differences in the length of the solar day, measured from one southing of the sun to another, at different seasons of the year) would seem to be demonstrably uniform.
a5 δῦ ARISTOTLE ᾿Αλλοίωσις μὲν οὖν οὐδ᾽ αὔξησις οὐδὲ γένεσις οὐκ εἰσὶν ὁμαλεῖς, φορὰ δ᾽ ἐστίν. διὸ καὶ δοκεῖ ὁ χρόνος εἶναι ἡ τῆς σφαίρας κίνησις, ὅτι ταύτῃ μετροῦνται αἱ ἄλλαι κινήσεις καὶ ὁ χρόνος ταύτῃ τῇ κυήσει. διὰ δὲ τοῦτο καὶ τὸ εἰωθὸς λέγεσθαι συμβαίνει" φασὶ γὰρ κύκλον εἶναι τὰ ἀνθρώπινα πράγματα καὶ τῶν ἄλλων: τῶν κίνησιν ἐχόντων φυσικὴν καὶ γένεσιν καὶ φθοράν. τοῦτο δ᾽, ὅτι ταῦτα πάντα τῷ χρόνῳ κρίνεται, καὶ λαμβάνει τελευτὴν καὶ ἀρχὴν ὥσπερ ἂν εἰ κατά τινα περίοδον" καὶ γὰρ ὁ χρόνος αὐτὸς εἶναι δοκεῖ κύκλος τις. τοῦτο δὲ πάλιν δοκεῖ διότι τοιαύτης ἐστὶ φορᾶς μέτρον καὶ μετρεῖται αὐτὸς ὑπὸ τοιαύτης. ὥστε τὸ λέγειν εἶναι τὰ γινόμενα τῶν πραγμάτων κύκλον τὸ λέγειν ἐστὶ τοῦ χρόνου εἶναί τινα κύκλον" τοῦτο δ᾽, ὅτι μετρεῖται τῇ κυκλοφορίᾳ: παρὰ γὰρ τὸ μέτρον' οὐδὲν ἄλλο παρεμφαΐίνεται τὸ μετρούμενον, ἀλλ᾽ ἢ πλείω μέτρα τὸ ὅλον.
[Λέγεται δ᾽ ὀρθῶς καὶ ὅτι ἀριθμὸς μὲν ὁ αὐτὸς ὁ τῶν προβάτων καὶ τῶν κυνῶν, εἰ ἴσος ἑκάτερος" ® That is to say, one part of rotary motion can be fitted on to another and has no distinguishing quality, whereas in a given process of change or growth the stages differ from one another: ὁμαλής does not here mean ‘ uniform’ in the ordinary sense, i.¢. a motion free from acceleration, positive or negative. Aristotle here assumes this kind of uniformity in the rotation which he is about 10 choose as the standard, and, that being assumed, there will be no distinction between two equal sections of the course.
Ἂ [ΟἿ 218 8 84 οἱ μὲν γὰρ τὴν τοῦ ὅλου κίνησιν εἶναί φασιν.
° Motion here includes every kind of successive passing from this to that, whether it be from this to that place, from this to that quality, or from this to that size.
PHYSICS, IV. xiv.
Neither qualitive modification nor growth nor genesis has the kind of uniformity that rotation has; and so time is regarded as the rotation of the sphere,? inasmuch as a}l other orders of motion ὃ are measured by it, and time itself is standardized by reference toit. And this is the reason of our habitual way of speaking; for we say that human affairs and those of all other things that have natural movement and become and perish seem to be in a way circular, because all these things come to pass in time and have their beginning and end. as it were ‘ periodically ’¢; for time itself is conceived as ‘ coming round’; and this again because time and such a standard rotation mutually determine each other. Hence, to call the happenings of a thing a circle is saying that there is ἃ sort of circle of time; and that is because it is measured by a complete revolution, and the whole measurement of a thing is nought clse but a defined number of the units of its measurements.“ [It is correct to say that the number of sheep and of dogs is the same number, if that of the sheep and that of the dogs are equal; but it is not the same 4 ‘Period’ is a Greek word which means ‘ passage round.’
¢ Here in the time of ‘Themistius (fourth century δ) the chapter and book seem to have ended, except perhaps the final summary. The inte:polated passage is worthless. [Themistius, however, (at 162. 23) does mention the ‘ ten sheep’ of this paragraph. It recurs to the statement (223 Ὁ 10) that one universal time is the measure οἱ ‘ number’ of movenents which are distinct from one another and of different sorts (qualitative modification, growth, etc.), although these movements are not ‘ uniform,’ whereas the rotation which measures time is uniform (Ὁ 12-21), A technical explanation 1s now given of how it is that the same * number ’ can serve to measure things of different kinds.—C 1 1 1 ARISTOTLE 1 1 ARISTOTLE a δεκὰς δὲ ody ἡ αὐτὴ οὐδὲ δέκα ταὐτά, ὥσπερ οὐδὲ 5 τρίγωνα τὰ αὐτὰ τὸ ἰσόπλευρον καὶ τὸ σκαληνές. καίτοι σχῆμά γε ταὐτό, ὅτι τρίγωνα ἄμφω" ταὐτὸ γὰρ λέγεται οὗ μὴ διαφέρει διαφορᾷ, ἀλλ᾽ οὐχὶ οὗ διαφέρει" οἷον τρίγωνον τριγώνου διαφορᾷ διαφέρει τ-- τοιγαροῦν ἕτερα τρίγωνα--σχήματος δὲ οὔ, ἀλλ᾽ ἐν τῇ αὐτῇ διαιρέσει καὶ μιᾷ. σχῆμα γὰρ τὸ μὲν τοιόνδε κύκλος, τὸ δὲ τοιόνδε τρίγωνον, τούτου δὲ τὸ μὲν τοιόνδε ἰσόπλευρον, τὸ δὲ τοιόνδε σκαληνές. σχῆμα μὲν οὖν τὸ αὐτὸ καὶ τοῦτο (τρίγωνον γάρ), τρίγωνον δ᾽ οὐ τὸ αὐτό. καὶ ὁ ἀριθμὸς δὴ ὁ αὐτός: οὐ γὰρ διαφέρει ἀριθμοῦ διαφορᾷ ὁ ἀριθμὸς αὐτῶν" δεκὰς δ᾽ οὐχ ἡ αὐτή" ἐφ᾽ ὧν γὰρ λέγεται, διαφέρει" τὰ μὲν γὰρ κύνες, τὰ δ᾽ ἵπποι].
Kat περὶ μὲν χρόνου καὶ αὐτοῦ καὶ τῶν περὶ αὐτὸν οἰκείων τῇ σκέψει εἴρηται.
- a 5 fa 6 ταὐτὸ γὰρ λέγεται κτλ, Literally, ‘(A thing) 18 said to be “ the same as” that from which it does not differ by a differentia (proper to that thing, οἰκείᾳ διαφορᾷ τούτου, Alex. ap. Simpl. 770. 98), and “ not (the same as) * that from which it does (so) differ. Jor ἰρδίβηζο, a (scalene) triangle differs from an (isosceles) triangle by a differentia —so they are ‘not the same’ triangle—but does not so differ from PHYSICS, ΤΥ. xv.
PHYSICS, ΤΥ. xv.
decad in each case, nor are the units of one the same as the units of the other, any more than a sealene and an isosceles are the same triangle, though they are the same figure, both being triangles; for things bear the same name if they do not differ as to the charac~ teristic in virtue of which that name is borne, in this casc the differentia of triangle. They are different as triangles, therefore, ‘but not different as figures, sinee they belong to one and the same figure denom- ination.? For, as a figure, this is a circle and that a triangle, but, as a triangle, this isosceles and that sealene. ‘The two, then, have the same figure conformation (for both are triangular), but not the same triangle formation. So with the animals: the number of each ten-group is the same, for they do not differ in a numerical differentia; but the Len-groups themselves are not the same, for the ten-ness is pre- dicated of different subjects—dogs in the one case and horses in the other.]
This closes our investigation of time and_ its properties, in so far as they are germane to our inquiry.
Figure,’ but (both triangles) are in one and the same Table of Division (headed by the genus ‘ Figure,’ which includes all sorts of triangles, as well as other figures),’—C.]} Printed in Great Britain by Re ὃς Ἐς, Crark, Limirep, Zdindnr gh THE LOEB CLASSICAL LIBRARY VOLUMES ALREADY PUBLISHED LATIN AUTHORS APULEIUS..THE GOLDEN ASS (METAMORPHO- SES). Trans. by W. Adlington (1566). Revised by 5. Gaselee (4th Impression.)
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