Moraux (Budé, 1965) · Stocks (1922)
Stocks (1922)
Greek line numbers are exact. The translations carry no Bekker numbers of their own, so those beside the English are aligned to the Greek: upright = fixed (anchored to this point in the text), italic grey = approximate (interpolated estimate).
Book 3,Chapter 1 (298a24–300a19)
298a
Περὶ μὲν οὖν τοῦ πρώτου οὐρανοῦ καὶ τῶν μερῶν, ἔτι δὲ
25 περὶ τῶν ἐν αὐτῷ φερομένων ἄστρων, ἐκ τίνων τε συνεστᾶσι
καὶ ποῖ' ἄττα τὴν φύσιν ἐστί, πρὸς δὲ τούτοις ὅτι ἀγένητα
καὶ ἄφθαρτα, διεληλύθαμεν πρότερον. Ἐπεὶ δὲ τῶν φύσει
λεγομένων τὰ μέν ἐστιν οὐσίαι, τὰ δ' ἔργα καὶ πάθη τούτων
(λέγω δ' οὐσίας μὲν τά τε ἁπλᾶ σώματα, οἷον πῦρ καὶ
30 γῆν καὶ τὰ σύστοιχα τούτοις, καὶ ὅσα ἐκ τούτων, οἷον τόν τε
σύνολον οὐρανὸν καὶ τὰ μόρια αὐτοῦ, καὶ πάλιν τά τε ζῷα
καὶ τὰ φυτὰ καὶ τὰ μόρια τούτων, πάθη δὲ καὶ ἔργα τάς
τε κινήσεις τὰς τούτων ἑκάστου καὶ τῶν ἄλλων, ὅσων ἐστὶν
αἴτια ταῦτα κατὰ τὴν δύναμιν τὴν ἑαυτῶν, ἔτι δὲ τὰς ἀλλοιώσεις
We have already discussed the first heaven and its parts, the moving stars 25within it, the matter of which these are composed and their bodily constitution, and we have also shown that they are ungenerated and indestructible. Now things that we call natural are either substances or functions and attributes of substances. As substances I class the simple bodies-fire, earth, and the other terms of the series-and all things composed of them; 30for example, the heaven as a whole and its parts, animals, again, and plants and their parts. By attributes and functions I mean the movements of these and of all other things in which they have power in themselves to cause movement, and also their alterations and reciprocal transformations.
298b
1 καὶ τὰς εἰς ἄλληλα μεταβάσεις), φανερὸν ὅτι τὴν
πλείστην συμβαίνει τῆς περὶ φύσεως ἱστορίας περὶ σωμάτων
εἶναι· πᾶσαι γὰρ αἱ φυσικαὶ οὐσίαι ἢ σώματα ἢ μετὰ σωμάτων
γίγνονται καὶ μεγεθῶν. Τοῦτο δὲ δῆλον ἔκ τε τοῦ διωρίσθαι
5 τὰ ποῖά ἐστι φύσει, καὶ ἐκ τῆς καθ' ἕκαστα θεωρίας.
Περὶ μὲν οὖν τοῦ πρώτου τῶν στοιχείων εἴρηται, καὶ ποῖόν τι
τὴν φύσιν, καὶ ὅτι ἄφθαρτον καὶ ἀγένητον· λοιπὸν δὲ περὶ
τοῖν δυοῖν εἰπεῖν. Ἅμα δὲ συμβήσεται περὶ τούτων λέγουσι
καὶ περὶ γενέσεως καὶ φθορᾶς διασκέψασθαι· γένεσις γὰρ
10 ἤτοι τὸ παράπαν οὐκ ἔστιν, ἢ μόνον ἐν τούτοις τοῖς στοιχείοις
καὶ τοῖς ἐκ τούτων ἐστίν. Αὐτὸ δὲ τοῦτο πρῶτον ἴσως θεωρητέον,
πότερον ἔστιν ἢ οὐκ ἔστιν. Οἱ μὲν οὖν πρότερον φιλοσοφήσαντες
περὶ τῆς ἀληθείας καὶ πρὸς οὓς νῦν λέγομεν ἡμεῖς
λόγους καὶ πρὸς ἀλλήλους διηνέχθησαν. Οἱ μὲν γὰρ αὐτῶν
15 ὅλως ἀνεῖλον γένεσιν καὶ φθοράν· οὐθὲν γὰρ οὔτε γίγνεσθαί
φασιν οὔτε φθείρεσθαι τῶν ὄντων, ἀλλὰ μόνον δοκεῖν ἡμῖν,
οἷον οἱ περὶ Μέλισσόν τε καὶ Παρμενίδην, οὕς, εἰ καὶ τἆλλα
λέγουσι καλῶς, ἀλλ' οὐ φυσικῶς γε δεῖ νομίσαι λέγειν·
τὸ γὰρ εἶναι ἄττα τῶν ὄντων ἀγένητα καὶ ὅλως ἀκίνητα
20 μᾶλλόν ἐστιν ἑτέρας καὶ προτέρας ἢ τῆς φυσικῆς σκέψεως.
Ἐκεῖνοι δὲ διὰ τὸ μηθὲν μὲν ἄλλο παρὰ τὴν τῶν αἰσθητῶν
οὐσίαν ὑπολαμβάνειν εἶναι, τοιαύτας δέ τινας νοῆσαι πρῶτοι
φύσεις, εἴπερ ἔσται τις γνῶσις ἢ φρόνησις, οὕτω μετήνεγκαν
ἐπὶ ταῦτα τοὺς ἐκεῖθεν λόγους. Ἕτεροι δέ τινες ὥσπερ
25 ἐπίτηδες τὴν ἐναντίαν τούτοις ἔσχον δόξαν. Εἰσὶ γάρ τινες οἵ
φασιν οὐθὲν ἀγένητον εἶναι τῶν πραγμάτων, ἀλλὰ πάντα
γίγνεσθαι, γενόμενα δὲ τὰ μὲν ἄφθαρτα διαμένειν, τὰ δὲ
πάλιν φθείρεσθαι, μάλιστα μὲν οἱ περὶ Ἡσίοδον, εἶτα καὶ
τῶν ἄλλων οἱ πρῶτοι φυσιολογήσαντες. Οἱ δὲ τὰ μὲν ἄλλα
30 πάντα γίνεσθαί φασι καὶ ῥεῖν, εἶναι δὲ παγίως οὐθέν, ἓν
δέ τι μόνον ὑπομένειν, ἐξ οὗ ταῦτα πάντα μετασχηματίζεσθαι
πέφυκεν· ὅπερ ἐοίκασι βούλεσθαι λέγειν ἄλλοι τε
πολλοὶ καὶ Ἡράκλειτος ὁ Ἐφέσιος. Εἰσὶ δέ τινες καὶ οἳ
πᾶν σῶμα γενητὸν ποιοῦσι, συντιθέντες καὶ διαλύοντες εἰς
1It is obvious, then, that the greater part of the inquiry into nature concerns bodies: for a natural substance is either a body or a thing which cannot come into existence without body and magnitude. This appears plainly from an analysis of the character of natural things, and equally from an inspection of 5the instances of inquiry into nature. Since, then, we have spoken of the primary element, of its bodily constitution, and of its freedom from destruction and generation, it remains to speak of the other two. In speaking of them we shall be obliged also to inquire into generation and destruction. For if there is generation anywhere, it must be in these elements and things composed 10of them.
This is indeed the first question we have to ask: is generation a fact or not? Earlier speculation was at variance both with itself and with the views here put forward as to the true answer to this question. Some removed generation and destruction from the world altogether. Nothing that is, they said, is generated or destroyed, and our conviction to the contrary is an 15illusion. So maintained the school of Melissus and Parmenides. But however excellent their theories may otherwise be, anyhow they cannot be held to speak as students of nature. There may be things not subject to generation or any kind of movement, but if so they belong to another and a higher inquiry than the study of nature. They, however, had no idea of any form of being other than 20the substance of things perceived; and when they saw, what no one previously had seen, that there could be no knowledge or wisdom without some such unchanging entities, they naturally transferred what was true of them to things perceived. Others, perhaps intentionally, maintain precisely the contrary opinion to this. It has been asserted that everything in the world was subject to 25generation and nothing was ungenerated, but that after being generated some things remained indestructible while the rest were again destroyed. This had been asserted in the first instance by Hesiod and his followers, but afterwards outside his circle by the earliest natural philosophers. But what these thinkers maintained was that all else has been generated and, as they said, 'is 30flowing away, nothing having any solidity, except one single thing which persists as the basis of all these transformations. So we may interpret the statements of Heraclitus of Ephesus and many others. And some subject all bodies whatever to generation, by means of the composition and separation of planes.
This is indeed the first question we have to ask: is generation a fact or not? Earlier speculation was at variance both with itself and with the views here put forward as to the true answer to this question. Some removed generation and destruction from the world altogether. Nothing that is, they said, is generated or destroyed, and our conviction to the contrary is an 15illusion. So maintained the school of Melissus and Parmenides. But however excellent their theories may otherwise be, anyhow they cannot be held to speak as students of nature. There may be things not subject to generation or any kind of movement, but if so they belong to another and a higher inquiry than the study of nature. They, however, had no idea of any form of being other than 20the substance of things perceived; and when they saw, what no one previously had seen, that there could be no knowledge or wisdom without some such unchanging entities, they naturally transferred what was true of them to things perceived. Others, perhaps intentionally, maintain precisely the contrary opinion to this. It has been asserted that everything in the world was subject to 25generation and nothing was ungenerated, but that after being generated some things remained indestructible while the rest were again destroyed. This had been asserted in the first instance by Hesiod and his followers, but afterwards outside his circle by the earliest natural philosophers. But what these thinkers maintained was that all else has been generated and, as they said, 'is 30flowing away, nothing having any solidity, except one single thing which persists as the basis of all these transformations. So we may interpret the statements of Heraclitus of Ephesus and many others. And some subject all bodies whatever to generation, by means of the composition and separation of planes.
299a
1 ἐπίπεδα καὶ ἐξ ἐπιπέδων. Περὶ μὲν οὖν τῶν ἄλλων ἕτερος
ἔστω λόγος· τοῖς δὲ τοῦτον τὸν τρόπον λέγουσι καὶ πάντα
τὰ σώματα συνιστᾶσιν ἐξ ἐπιπέδων ὅσα μὲν ἄλλα συμβαίνει
λέγειν ὑπεναντία τοῖς μαθήμασιν, ἐπιπολῆς
5 ἰδεῖν· καίτοι δίκαιον ἢ μὴ κινεῖν ἢ πιστοτέροις αὐτὰ λόγοις
κινεῖν τῶν ὑποθέσεων. Ἔπειτα δῆλον ὅτι τοῦ αὐτοῦ λόγου
ἐστὶ στερεὰ μὲν ἐξ ἐπιπέδων συγκεῖσθαι, ἐπίπεδα δ' ἐκ
γραμμῶν, ταύτας δ' ἐκ στιγμῶν· οὕτω δ' ἐχόντων οὐκ
ἀνάγκη τὸ τῆς γραμμῆς μέρος γραμμὴν εἶναι· περὶ δὲ τούτων
10 ἐπέσκεπται πρότερον ἐν τοῖς περὶ κινήσεως λόγοις, ὅτι
οὐκ ἔστιν ἀδιαίρετα μήκη. Ὅσα δὲ περὶ τῶν φυσικῶν σωμάτων
ἀδύνατα συμβαίνει λέγειν τοῖς ποιοῦσι τὰς ἀτόμους
γραμμάς, ἐπὶ μικρὸν θεωρήσωμεν καὶ νῦν· τὰ μὲν γὰρ
ἐπ' ἐκείνων ἀδύνατα συμβαίνοντα καὶ τοῖς φυσικοῖς ἀκολουθήσει,
15 τὰ δὲ τούτοις ἐπ' ἐκείνων οὐχ ἅπαντα διὰ τὸ τὰ
μὲν ἐξ ἀφαιρέσεως λέγεσθαι, τὰ μαθηματικά, τὰ δὲ φυσικὰ
ἐκ προσθέσεως. Πολλὰ δ' ἐστὶν ἃ τοῖς ἀδιαιρέτοις οὐχ
οἷόν τε ὑπάρχειν, τοῖς δὲ φυσικοῖς ἀναγκαῖον. [Οἷον εἴ τί
ἐστιν ἀδιαίρετον·] ἐν ἀδιαιρέτῳ γὰρ διαιρετὸν ἀδύνατον ὑπάρχειν,
20 τὰ δὲ πάθη διαιρετὰ πάντα διχῶς· ἢ γὰρ κατ' εἶδος
ἢ κατὰ συμβεβηκός, κατ' εἶδος μὲν οἷον χρώματος τὸ
λευκὸν ἢ τὸ μέλαν, κατὰ συμβεβηκὸς δέ, ἂν ᾧ ὑπάρχει
ᾖ διαιρετόν, ὥστε ὅσα ἁπλᾶ τῶν παθημάτων, πάντ'
ἐστὶ διαιρετὰ τοῦτον τὸν τρόπον. Διὸ τὸ ἀδύνατον ἐν τοῖς τοιούτοις
25 ἐπισκεπτέον. Εἰ δὴ τῶν ἀδυνάτων ἐστὶν ἑκατέρου μέρους
μηδὲν ἔχοντος βάρος τὰ ἄμφω ἔχειν βάρος, τὰ δ' αἰσθητὰ
σώματα ἢ πάντα ἢ ἔνια βάρος ἔχει, οἷον ἡ γῆ καὶ τὸ
ὕδωρ, ὡς κἂν αὐτοὶ φαῖεν, εἰ ἡ στιγμὴ μηδὲν ἔχει βάρος,
δῆλον ὅτι οὐδ' αἱ γραμμαί, εἰ δὲ μὴ αὗται, οὐδὲ τὰ ἐπίπεδα·
30 ὥστ' οὐδὲ τῶν σωμάτων οὐθέν. Ἀλλὰ μὴν ὅτι τὴν στιγμὴν
οὐχ οἷόν τε βάρος ἔχειν, φανερόν. Τὸ μὲν γὰρ βαρὺ
ἅπαν καὶ βαρύτερον καὶ τὸ κοῦφον καὶ κουφότερον ἐνδέχεταί
1Discussion of the other views may be postponed. But this last theory which composes every body of planes is, as the most superficial observation shows, in many respects in plain contradiction with mathematics. It is, however, wrong to remove the foundations of a science unless you can replace them with others 5more convincing. And, secondly, the same theory which composes solids of planes clearly composes planes of lines and lines of points, so that a part of a line need not be a line. This matter has been already considered in our discussion of movement, where we have shown that an indivisible length is impossible. But with respect to natural bodies there are impossibilities involved in 10the view which asserts indivisible lines, which we may briefly consider at this point. For the impossible consequences which result from this view in the mathematical sphere will reproduce themselves when it is applied to physical bodies, but there will be difficulties in physics which are not present in mathematics; for mathematics deals with an abstract and physics with a more concrete 15object. There are many attributes necessarily present in physical bodies which are necessarily excluded by indivisibility; all attributes, in fact, which are divisible. There can be nothing divisible in an indivisible thing, but the attributes of bodies are all divisible in one of two ways. They are divisible into kinds, as colour is divided into white and black, and they are 20divisible per accidens when that which has them is divisible. In this latter sense attributes which are simple are nevertheless divisible. Attributes of this kind will serve, therefore, to illustrate the impossibility of the view. It is impossible, if two parts of a thing have no weight, that the two together should have weight. But either all perceptible bodies or some, such as earth and 25water, have weight, as these thinkers would themselves admit. Now if the point has no weight, clearly the lines have not either, and, if they have not, neither have the planes. Therefore no body has weight. It is, further, manifest that their point cannot have weight. For while a heavy thing may always be heavier than something and a light thing lighter than something, a thing which 30is heavier or lighter than something need not be itself heavy or light, just as a large thing is larger than others, but what is larger is not always large.
299b
1 τινος εἶναι. Τὸ δὲ βαρύτερον ἢ κουφότερον ἴσως οὐκ
ἀνάγκη βαρὺ ἢ κοῦφον εἶναι, ὥσπερ καὶ τὸ μὲν μέγα μεῖζον,
τὸ δὲ μεῖζον οὐ πᾶν μέγα· πολλὰ γάρ ἐστιν ἃ μικρὰ
ὄντα ἁπλῶς ὅμως μείζω ἑτέρων ἐστίν. Εἰ δὴ ὃ ἂν
5 βαρὺ ὂν βαρύτερον ᾖ, ἀνάγκη βάρει μεῖζον εἶναι, τὸ
βαρὺ ἅπαν διαιρετὸν ἂν εἴη. Ἡ δὲ στιγμὴ ἀδιαίρετον ὑπόκειται.
Ἔτι εἰ τὸ μὲν βαρὺ πυκνόν τι, τὸ δὲ κοῦφον μανόν,
ἔστι δὲ πυκνὸν μανοῦ διαφέρον τῷ ἐν ἴσῳ ὄγκῳ πλεῖον ἐνυπάρχειν·
εἰ οὖν ἐστι στιγμὴ βαρεῖα καὶ κούφη, ἔστι καὶ
10 πυκνὴ καὶ μανή. Ἀλλὰ τὸ μὲν πυκνὸν διαιρετόν, ἡ δὲ
στιγμὴ ἀδιαίρετος. Εἰ δὲ πᾶν τὸ βαρὺ ἢ μαλακὸν ἢ σκληρὸν
ἀνάγκη εἶναι, ῥᾴδιον ἐκ τούτων ἀδύνατόν τι συναγαγεῖν.
Μαλακὸν μὲν γὰρ τὸ εἰς ἑαυτὸ ὑπεῖκον, σκληρὸν δὲ τὸ μὴ
ὑπεῖκον· τὸ δὲ ὑπεῖκον διαιρετόν. Ἀλλὰ μὴν οὐδ' ἐκ μὴ
15 ἐχόντων βάρος ἔσται βάρος. Καὶ γὰρ ἐπὶ πόσων συμβήσεται
τοῦτο καὶ ἐπὶ ποίων; Ἢ πῶς διοριοῦσι μὴ βουλόμενοι
πλάττειν; καὶ εἰ πᾶν μεῖζον βάρος βάρους βάρει, συμβήσεται
καὶ ἕκαστον τῶν ἀβαρῶν βάρος ἔχειν· εἰ γὰρ αἱ
τέτταρες στιγμαὶ βάρος ἔχουσι, τὸ δ' ἐκ πλειόνων ἢ τοδὶ
20 βαρέος ὄντος βαρύτερον, τὸ δὲ βαρέος βαρύτερον ἀνάγκη
βάρει εἶναι, ὥσπερ καὶ τὸ λευκοῦ λευκότερον λευκῷ, ἔσται
τὸ μεῖζον μιᾷ στιγμῇ βαρύτερον, ὥστε, ἀφαιρεθέντος τοῦ
ἴσου, [ὥστε] καὶ ἡ μία στιγμὴ βάρος ἕξει. Ἔτι εἰ μὲν τὰ ἐπίπεδα
μόνον κατὰ γραμμὴν ἐνδέχεται συντίθεσθαι, ἄτοπον·
25 ὥσπερ γὰρ γραμμὴ πρὸς γραμμὴν ἀμφοτέρως συντίθεται,
καὶ κατὰ μῆκος καὶ κατὰ πλάτος, δεῖ καὶ ἐπίπεδον
ἐπιπέδῳ τὸν αὐτὸν τρόπον. Γραμμὴ δὲ δύναται γραμμῇ
συντίθεσθαι κατὰ γραμμὴν ἐπιτιθεμένη ἀλλ' οὐ προστιθεμένη.
Ἀλλὰ μὴν εἴ γε καὶ κατὰ πλάτος ἐνδέχεται συντίθεσθαι,
30 ἔσται τι σῶμα ὃ οὔτε στοιχεῖον οὔτε ἐκ στοιχείων, συντιθέμενον
ἐκ τῶν οὕτω συντιθεμένων ἐπιπέδων. Ἔτι εἰ μὲν
πλήθει βαρύτερα τὰ σώματα τῶν ἐπιπέδων, ὥσπερ ἐν τῷ
1A thing which, judged absolutely, is small may none the less be larger than other things. Whatever, then, is heavy and also heavier than something else, must exceed this by something which is heavy. A heavy thing therefore is always divisible. But it is common ground that a 5point is indivisible. Again, suppose that what is heavy or weight is a dense body, and what is light rare. Dense differs from rare in containing more matter in the same cubic area. A point, then, if it may be heavy or light, may be dense or rare. But the dense is divisible while a point is indivisible. And if what is heavy must be either hard or 10soft, an impossible consequence is easy to draw. For a thing is soft if its surface can be pressed in, hard if it cannot; and if it can be pressed in it is divisible.
Moreover, no weight can consist of parts not possessing weight. For how, except by the merest fiction, can they specify the number and character of the parts which will produce weight? 15And, further, when one weight is greater than another, the difference is a third weight; from which it will follow that every indivisible part possesses weight. For suppose that a body of four points possesses weight. A body composed of more than four points will superior in weight to it, a thing which has weight. But the difference between 20weight and weight must be a weight, as the difference between white and whiter is white. Here the difference which makes the superior weight heavier is the single point which remains when the common number, four, is subtracted. A single point, therefore, has weight.
Further, to assume, on the one hand, that the planes can only be put in linear 25contact would be ridiculous. For just as there are two ways of putting lines together, namely, end to and side by side, so there must be two ways of putting planes together. Lines can be put together so that contact is linear by laying one along the other, though not by putting them end to end. But if, similarly, in putting the lanes together, 30superficial contact is allowed as an alternative to linear, that method will give them bodies which are not any element nor composed of elements.
Moreover, no weight can consist of parts not possessing weight. For how, except by the merest fiction, can they specify the number and character of the parts which will produce weight? 15And, further, when one weight is greater than another, the difference is a third weight; from which it will follow that every indivisible part possesses weight. For suppose that a body of four points possesses weight. A body composed of more than four points will superior in weight to it, a thing which has weight. But the difference between 20weight and weight must be a weight, as the difference between white and whiter is white. Here the difference which makes the superior weight heavier is the single point which remains when the common number, four, is subtracted. A single point, therefore, has weight.
Further, to assume, on the one hand, that the planes can only be put in linear 25contact would be ridiculous. For just as there are two ways of putting lines together, namely, end to and side by side, so there must be two ways of putting planes together. Lines can be put together so that contact is linear by laying one along the other, though not by putting them end to end. But if, similarly, in putting the lanes together, 30superficial contact is allowed as an alternative to linear, that method will give them bodies which are not any element nor composed of elements.
300a
1 Τιμαίῳ διώρισται, δῆλον ὡς ἕξει καὶ ἡ γραμμὴ καὶ ἡ
στιγμὴ βάρος· ἀνάλογον γὰρ πρὸς ἄλληλα ἔχουσιν, ὥσπερ
καὶ πρότερον εἰρήκαμεν. Εἰ δὲ μὴ τοῦτον διαφέρει τὸν τρόπον
ἀλλὰ τῷ τὴν μὲν γῆν εἶναι βαρὺ τὸ δὲ πῦρ κοῦφον, ἔσται
5 καὶ τῶν ἐπιπέδων τὸ μὲν κοῦφον τὸ δὲ βαρύ. Καὶ τῶν γραμμῶν
δὴ καὶ τῶν στιγμῶν ὡσαύτως· τὸ γὰρ τῆς γῆς ἐπίπεδον
ἔσται βαρύτερον ἢ τὸ τοῦ πυρός. Ὅλως δὲ συμβαίνει ἢ
μηδέν ποτ' εἶναι μέγεθος, ἢ δύνασθαί γε ἀναιρεθῆναι, εἴπερ
ὁμοίως ἔχει στιγμὴ μὲν πρὸς γραμμήν, γραμμὴ δὲ πρὸς
10 ἐπίπεδον, τοῦτο δὲ πρὸς σῶμα· πάντα γὰρ εἰς ἄλληλα
ἀναλυόμενα εἰς τὰ πρῶτα ἀναλυθήσεται· ὥστ' ἐνδέχοιτ' ἂν
στιγμὰς μόνον εἶναι, σῶμα δὲ μηθέν. Πρὸς δὲ τούτοις καὶ εἰ
ὁ χρόνος ὁμοίως ἔχει, ἀναιροῖτ' ἄν ποτε ἢ ἐνδέχοιτ' ἂν ἀναιρεθῆναι·
τὸ γὰρ νῦν τὸ ἄτομον οἷον στιγμὴ γραμμῆς ἐστιν. Τὸ
15 δ' αὐτὸ συμβαίνει καὶ τοῖς ἐξ ἀριθμῶν συντιθεῖσι τὸν οὐρανόν·
ἔνιοι γὰρ τὴν φύσιν ἐξ ἀριθμῶν συνιστᾶσιν, ὥσπερ τῶν
Πυθαγορείων τινές· τὰ μὲν γὰρ φυσικὰ σώματα φαίνεται
βάρος ἔχοντα καὶ κουφότητα, τὰς δὲ μονάδας οὔτε σώματα
ποιεῖν οἷόν τε συντιθεμένας οὔτε βάρος ἔχειν.
1Again, if it is the number of planes in a body that makes one heavier than another, as the Timaeus explains, clearly the line and the point will have weight. For the three cases are, as we said before, analogous. But if the reason of differences of weight is not this, but rather the heaviness of earth and the 5lightness of fire, then some of the planes will be light and others heavy (which involves a similar distinction in the lines and the points); the earthplane, I mean, will be heavier than the fire-plane. In general, the result is either that there is no magnitude at all, or that all magnitude could be done away with. For a point is to a line as a line is to a plane and as a plane is to a 10body. Now the various forms in passing into one another will each be resolved into its ultimate constituents. It might happen therefore that nothing existed except points, and that there was no body at all. A further consideration is that if time is similarly constituted, there would be, or might be, a time at which it was done away with. For the indivisible now is like a point in a line. 15The same consequences follow from composing the heaven of numbers, as some of the Pythagoreans do who make all nature out of numbers. For natural bodies are manifestly endowed with weight and lightness, but an assemblage of units can neither be composed to form a body nor possess weight.
Book 3,Chapter 2 (300a20–302a9)
20 Ὅτι δ' ἀναγκαῖον ὑπάρχειν κίνησιν τοῖς ἁπλοῖς σώμασι
φύσει τινὰ πᾶσιν, ἐκ τῶνδε δῆλον. Ἐπεὶ γὰρ κινούμενα
φαίνεται, κινεῖσθαί γε ἀναγκαῖον βίᾳ, εἰ μὴ οἰκείαν ἔχει
κίνησιν· τὸ δὲ βίᾳ καὶ παρὰ φύσιν ταὐτόν. Ἀλλὰ μὴν εἰ
παρὰ φύσιν ἐστί τις κίνησις, ἀνάγκη εἶναι καὶ κατὰ φύσιν,
25 παρ' ἣν αὕτη· καὶ εἰ πολλαὶ αἱ παρὰ φύσιν, τὴν κατὰ
φύσιν μίαν· κατὰ φύσιν μὲν γὰρ ἁπλῶς, παρὰ φύσιν δ'
ἔχει πολλὰς ἕκαστον. Ἔτι δὲ καὶ ἐκ τῆς ἠρεμίας δῆλον·
καὶ γὰρ ἠρεμεῖν ἀναγκαῖον ἢ βίᾳ ἢ κατὰ φύσιν· βίᾳ δὲ
μένει οὗ καὶ φέρεται βίᾳ, καὶ κατὰ φύσιν οὗ κατὰ φύσιν.
30 Ἐπεὶ οὖν φαίνεταί τι μένον ἐπὶ τοῦ μέσου, εἰ μὲν κατὰ φύσιν,
δῆλον ὅτι καὶ ἡ φορὰ ἡ ἐνταῦθα κατὰ φύσιν αὐτῷ·
εἰ δὲ βίᾳ, τί τὸ φέρεσθαι κωλῦον; Εἰ μὲν ἠρεμοῦν, τὸν αὐτὸν
κυκλήσομεν λόγον· ἀνάγκη γὰρ ἢ κατὰ φύσιν εἶναι τὸ
The necessity that each of the simple bodies should have a natural movement may be shown as follows. 20They manifestly move, and if they have no proper movement they must move by constraint: and the constrained is the same as the unnatural. Now an unnatural movement presupposes a natural movement which it contravenes, and which, however many the unnatural movements, is always one. For naturally a thing moves in one way, while its unnatural movements are manifold. The same may be shown, 25from the fact of rest. Rest, also, must either be constrained or natural, constrained in a place to which movement was constrained, natural in a place movement to which was natural. Now manifestly there is a body which is at rest at the centre. If then this rest is natural to it, clearly motion to this place is natural to it. If, on the other hand, its rest is constrained, what is 30hindering its motion? Something, which is at rest: but if so, we shall simply repeat the same argument; and either we shall come to an ultimate something to which rest where it is or we shall have an infinite process, which is impossible.
300b
1 πρῶτον ἠρεμοῦν ἢ εἰς ἄπειρον ἰέναι, ὅπερ ἀδύνατον· εἰ δὲ
κινούμενον τὸ κωλῦον φέρεσθαι, καθάπερ φησὶν Ἐμπεδοκλῆς
τὴν γῆν ὑπὸ τῆς δίνης ἠρεμεῖν, ποῦ ἂν ἐφέρετο, ἐπειδὴ
εἰς ἄπειρον ἀδύνατον; Οὐθὲν γὰρ γίγνεται ἀδύνατον, τὸ
5 δ' ἄπειρον διελθεῖν ἀδύνατον. Ὥστ' ἀνάγκη στῆναί που τὸ φερόμενον,
κἀκεῖ μὴ βίᾳ μένειν ἀλλὰ κατὰ φύσιν. Εἰ δ' ἐστὶν
ἠρεμία κατὰ φύσιν, ἔστι καὶ κίνησις κατὰ φύσιν, ἡ εἰς τοῦτον
τὸν τόπον φορά. Διὸ καὶ Λευκίππῳ καὶ Δημοκρίτῳ,
τοῖς λέγουσιν ἀεὶ κινεῖσθαι τὰ πρῶτα σώματα ἐν τῷ κενῷ
10 καὶ τῷ ἀπείρῳ, λεκτέον τίνα κίνησιν καὶ τίς ἡ κατὰ φύσιν
αὐτῶν κίνησις. Εἰ γὰρ ἄλλο ὑπ' ἄλλου κινεῖται βίᾳ τῶν
στοιχείων, ἀλλὰ καὶ κατὰ φύσιν ἀνάγκη τινὰ εἶναι κίνησιν
ἑκάστου, παρ' ἣν ἡ βίαιός ἐστιν· καὶ δεῖ τὴν πρώτην κινοῦσαν
μὴ βίᾳ κινεῖν, ἀλλὰ κατὰ φύσιν· εἰς ἄπειρον γὰρ εἶσιν,
15 εἰ μή τι ἔσται κατὰ φύσιν κινοῦν πρῶτον, ἀλλ' ἀεὶ τὸ πρότερον
βίᾳ κινούμενον κινήσει. Τὸ αὐτὸ δὲ τοῦτο συμβαίνειν
ἀναγκαῖον κἂν εἰ καθάπερ ἐν τῷ Τιμαίῳ γέγραπται, πρὶν
γενέσθαι τὸν κόσμον ἐκινεῖτο τὰ στοιχεῖα ἀτάκτως. Ἀνάγκη
γὰρ ἢ βίαιον εἶναι τὴν κίνησιν ἢ κατὰ φύσιν. Εἰ δὲ κατὰ
20 φύσιν ἐκινεῖτο, ἀνάγκη κόσμον εἶναι, ἐάν τις βούληται θεωρεῖν
ἐπιστήσας· τό τε γὰρ πρῶτον κινοῦν ἀνάγκη κινεῖν ἑαυτὸ
κινούμενον κατὰ φύσιν, καὶ τὰ κινούμενα μὴ βίᾳ, ἐν τοῖς
οἰκείοις ἠρεμοῦντα τόποις, ποιεῖν ἥνπερ ἔχουσι νῦν τάξιν, τὰ
μὲν βάρος ἔχοντα ἐπὶ τὸ μέσον, τὰ δὲ κουφότητα ἔχοντα ἀπὸ
25 τοῦ μέσου· ταύτην δ' ὁ κόσμος ἔχει τὴν διάταξιν. Ἔτι δὲ
τοσοῦτον ἐπανέροιτ' ἄν τις, πότερον οὐχ οἷόν τ' ἦν
κινούμενα ἀτάκτως καὶ μίγνυσθαι τοιαύτας μίξεις ἔνια, ἐξ
ὧν συνίσταται τὰ κατὰ φύσιν συνιστάμενα σώματα, λέγω
δ' οἷον ὀστᾶ καὶ σάρκας, καθάπερ Ἐμπεδοκλῆς φησὶ γίνεσθαι
30 ἐπὶ τῆς φιλότητος· λέγει γὰρ ὡς
Τοῖς δ' ἄπειρα ἐν ἀπείρῳ τὰ κινούμενα
ποιοῦσιν, εἰ μὲν ἓν τὸ κινοῦν, ἀνάγκη μίαν φέρεσθαι
φοράν, ὥστ' οὐκ ἀτάκτως κινηθήσεται, εἰ δ' ἄπειρα τὰ κινοῦντα,
1The hindrance to its movement, then, we will suppose, is a moving thing-as Empedocles says that it is the vortex which keeps the earth still-: but in that case we ask, where would it have moved to but for the vortex? It could not move infinitely; for to traverse an infinite is impossible, and impossibilities 5do not happen. So the moving thing must stop somewhere, and there rest not by constraint but naturally. But a natural rest proves a natural movement to the place of rest. Hence Leucippus and Democritus, who say that the primary bodies are in perpetual movement in the void or infinite, may be asked to explain the manner of their motion and the kind of movement which is natural 10to them. For if the various elements are constrained by one another to move as they do, each must still have a natural movement which the constrained contravenes, and the prime mover must cause motion not by constraint but naturally. If there is no ultimate natural cause of movement and each preceding term in the series is always moved by constraint, we shall have an infinite process. 15The same difficulty is involved even if it is supposed, as we read in the Timaeus, that before the ordered world was made the elements moved without order. Their movement must have been due either to constraint or to their nature. And if their movement was natural, a moment's consideration shows that there was already an ordered world. For the prime mover must cause motion in 20virtue of its own natural movement, and the other bodies, moving without constraint, as they came to rest in their proper places, would fall into the order in which they now stand, the heavy bodies moving towards the centre and the light bodies away from it. But that is the order of their distribution in our world. There is a further question, too, which might be asked. Is it possible 25or impossible that bodies in unordered movement should combine in some cases into combinations like those of which bodies of nature's composing are composed, such, I mean, as bones and flesh? Yet this is what Empedocles asserts to have occurred under Love. 'Many a head', says he, 'came to birth without a neck.' The answer to the view that there are infinite bodies moving in an 30infinite is that, if the cause of movement is single, they must move with a single motion, and therefore not without order; and if, on the other hand, the causes are of infinite variety, their motions too must be infinitely varied.
301a
1 καὶ τὰς φορὰς ἀναγκαῖον ἀπείρους εἶναι· εἰ γὰρ
πεπερασμέναι, τάξις τις ἔσται· οὐ γὰρ τῷ μὴ φέρεσθαι εἰς
τὸ αὐτὸ ἡ ἀταξία συμβαίνει· οὐδὲ γὰρ νῦν εἰς τὸ αὐτὸ φέρεται
πάντα, ἀλλὰ τὰ συγγενῆ μόνον. Ἔτι τὸ ἀτάκτως
5 οὐθέν ἐστιν ἕτερον ἢ τὸ παρὰ φύσιν· ἡ γὰρ τάξις ἡ οἰκεία
τῶν αἰσθητῶν φύσις ἐστίν. Ἀλλὰ μὴν καὶ τοῦτο ἄτοπον καὶ
ἀδύνατον, τὸ ἄπειρον ἄτακτον ἔχειν κίνησιν· ἔστι γὰρ φύσις
ἐκείνη τῶν πραγμάτων οἵαν ἔχει τὰ πλείω καὶ τὸν
πλείω χρόνον· συμβαίνει οὖν αὐτοῖς τοὐναντίον τὴν μὲν ἀταξίαν
10 εἶναι κατὰ φύσιν, τὴν δὲ τάξιν καὶ τὸν κόσμον παρὰ
φύσιν· καίτοι οὐδὲν ὡς ἔτυχε γίγνεται τῶν κατὰ φύσιν. Ἔοικε
δὲ τοῦτό γε αὐτὸ καλῶς Ἀναξαγόρας λαβεῖν· ἐξ ἀκινήτων
γὰρ ἄρχεται κοσμοποιεῖν. Πειρῶνται δὲ καὶ οἱ ἄλλοι συγκρίνοντές
πως πάλιν κινεῖν καὶ διακρίνειν. Ἐκ διεστώτων δὲ καὶ
15 κινουμένων οὐκ εὔλογον ποιεῖν τὴν γένεσιν. Διὸ καὶ Ἐμπεδοκλῆς
παραλείπει τὴν ἐπὶ τῆς φιλότητος· οὐ γὰρ ἂν ἠδύνατο
συστῆσαι τὸν οὐρανὸν ἐκ κεχωρισμένων μὲν κατασκευάζων,
σύγκρισιν δὲ ποιῶν διὰ τὴν φιλότητα· ἐκ διακεκριμένων γὰρ
συνέστηκεν ὁ κόσμος τῶν στοιχείων· ὥστ' ἀναγκαῖον γίνεσθαι
20 ἐξ ἑνὸς καὶ συγκεκριμένου. Ὅτι μὲν οὖν ἐστι φυσική τις κίνησις
ἑκάστου τῶν σωμάτων, ἣν οὐ βίᾳ κινοῦνται οὐδὲ παρὰ
φύσιν, φανερὸν ἐκ τούτων. Ὅτι δ' ἔχειν ἔνια ἀναγκαῖον ῥοπὴν
βάρους καὶ κουφότητος, ἐκ τῶνδε δῆλον. Κινεῖσθαι μὲν
γάρ φαμεν ἀναγκαῖον εἶναι· εἰ δὲ μὴ ἕξει φύσει ῥοπὴν τὸ
25 κινούμενον, ἀδύνατον κινεῖσθαι ἢ πρὸς τὸ μέσον ἢ ἀπὸ τοῦ
μέσου. Ἔστω γὰρ τὸ μὲν ἐφ' οὗ Α ἀβαρές, τὸ δ' ἐφ' οὗ Β
βάρος ἔχον, ἐνηνέχθω δὲ τὸ ἀβαρὲς τὴν ΓΔ, τὸ δὲ Β ἐν
τῷ ἴσῳ χρόνῳ τὴν ΓΕ· μείζω γὰρ οἰσθήσεται τὸ βάρος
ἔχον. Ἐὰν δὴ διαιρεθῇ τὸ σῶμα τὸ ἔχον βάρος ὡς ἡ ΓΕ
30 πρὸς τὴν ΓΔ (δυνατὸν γὰρ οὕτως ἔχειν πρός τι τῶν ἐν αὐτῷ
μορίων), εἰ τὸ ὅλον φέρεται τὴν ὅλην τὴν ΓΕ, τὸ μόριον
ἀνάγκη ἐν τῷ αὐτῷ χρόνῳ τὴν ΓΔ φέρεσθαι, ὥστε
ἴσον οἰσθήσεται τὸ ἀβαρὲς καὶ τὸ βάρος ἔχον· ὅπερ ἀδύνατον.
1For a finite number of causes would produce a kind of order, since absence of order is not proved by diversity of direction in motions: indeed, in the world we know, not all bodies, but only bodies of the same kind, have a common goal of movement. Again, disorderly movement means 5in reality unnatural movement, since the order proper to perceptible things is their nature. And there is also absurdity and impossibility in the notion that the disorderly movement is infinitely continued. For the nature of things is the nature which most of them possess for most of the time. Thus their view brings them into the contrary position 10that disorder is natural, and order or system unnatural. But no natural fact can originate in chance. This is a point which Anaxagoras seems to have thoroughly grasped; for he starts his cosmogony from unmoved things. The others, it is true, make things collect together somehow before they try to produce motion and separation. But there is no sense 15in starting generation from an original state in which bodies are separated and in movement. Hence Empedocles begins after the process ruled by Love: for he could not have constructed the heaven by building it up out of bodies in separation, making them to combine by the power of Love, since our world has its constituent elements in separation, and 20therefore presupposes a previous state of unity and combination.
These arguments make it plain that every body has its natural movement, which is not constrained or contrary to its nature. We go on to show that there are certain bodies whose necessary impetus is that of weight and lightness. Of necessity, we assert, they must move, and a moved thing 25which has no natural impetus cannot move either towards or away from the centre. Suppose a body A without weight, and a body B endowed with weight. Suppose the weightless body to move the distance CD, while B in the same time moves the distance Ce, which will be greater since the heavy thing must move further. Let the heavy body then be divided in 30the proportion CE: CD (for there is no reason why a part of B should not stand in this relation to the whole). Now if the whole moves the whole distance CE, the part must in the same time move the distance CD.
These arguments make it plain that every body has its natural movement, which is not constrained or contrary to its nature. We go on to show that there are certain bodies whose necessary impetus is that of weight and lightness. Of necessity, we assert, they must move, and a moved thing 25which has no natural impetus cannot move either towards or away from the centre. Suppose a body A without weight, and a body B endowed with weight. Suppose the weightless body to move the distance CD, while B in the same time moves the distance Ce, which will be greater since the heavy thing must move further. Let the heavy body then be divided in 30the proportion CE: CD (for there is no reason why a part of B should not stand in this relation to the whole). Now if the whole moves the whole distance CE, the part must in the same time move the distance CD.
301b
1 Ὁ δ' αὐτὸς λόγος καὶ ἐπὶ κουφότητος. Ἔτι δ' εἰ ἔσται
τι σῶμα κινούμενον μήτε κουφότητα μήτε βάρος ἔχον, ἀνάγκη
τοῦτο βίᾳ κινεῖσθαι, βίᾳ δὲ κινούμενον ἄπειρον ποιεῖ τὴν κίνησιν.
Ἐπεὶ γὰρ δύναμίς τις ἡ κινοῦσα, τὸ δ' ἔλαττον καὶ
5 τὸ κουφότερον ὑπὸ τῆς αὐτῆς δυνάμεως πλεῖον κινηθήσεται,
κεκινήσθω τὸ μὲν ἐφ' ᾧ τὸ Α, τὸ ἀβαρές, τὴν ΓΕ, τὸ δ'
ἐφ' ᾧ τὸ Β, τὸ βάρος ἔχον, ἐν τῷ ἴσῳ χρόνῳ τὴν ΓΔ.
Διαιρεθέντος δὴ τοῦ βάρος ἔχοντος σώματος ὡς ἡ ΓΕ πρὸς
τὴν ΓΔ, συμβήσεται τὸ ἀφαιρούμενον ἀπὸ τοῦ βάρος ἔχοντος
10 σώματος τὴν ΓΕ φέρεσθαι ἐν τῷ ἴσῳ χρόνῳ, ἐπείπερ
τὸ ὅλον ἐφέρετο τὴν ΓΔ. Τὸ γὰρ τάχος ἕξει τὸ τοῦ ἐλάττονος
πρὸς τὸ τοῦ μείζονος ὡς τὸ μεῖζον σῶμα πρὸς τὸ ἔλαττον.
Ἴσον ἄρα τὸ ἀβαρὲς οἰσθήσεται σῶμα καὶ τὸ βάρος
ἔχον ἐν τῷ αὐτῷ χρόνῳ. Τοῦτο δ' ἀδύνατον. Ὥστ' ἐπεὶ παντὸς
15 τοῦ προτεθέντος μεῖζον κινηθήσεται διάστημα τὸ ἀβαρές,
ἄπειρον ἂν φέροιτο. Φανερὸν οὖν ὅτι ἀνάγκη σῶμα πᾶν
βάρος ἔχειν ἢ κουφότητα διωρισμένον. Ἐπεὶ δὲ φύσις μέν
ἐστιν ἡ ἐν αὐτῷ ὑπάρχουσα κινήσεως ἀρχή, δύναμις δ' ἡ ἐν
ἄλλῳ ἢ ᾗ ἄλλο, κίνησις δὲ ἡ μὲν κατὰ φύσιν ἡ δὲ βίᾳ
20 πᾶσα, τὴν μὲν κατὰ φύσιν, οἷον τῷ λίθῳ τὴν κάτω, θάττω
ποιήσει τὸ κατὰ δύναμιν, τὴν δὲ παρὰ φύσιν ὅλως
αὐτή. Πρὸς ἀμφότερα δὲ ὥσπερ ὀργάνῳ χρῆται τῷ ἀέρι
(πέφυκε γὰρ οὗτος καὶ κοῦφος εἶναι καὶ βαρύς)· τὴν μὲν οὖν
ἄνω ποιήσει φορὰν ᾗ κοῦφος, ὅταν ὠσθῇ καὶ λάβῃ τὴν
25 ἀρχὴν ἀπὸ τῆς δυνάμεως, τὴν δὲ κάτω πάλιν ᾗ βαρύς·
ὥσπερ γὰρ ἐναφάψασα παραδίδωσιν ἑκατέρῳ. Διὸ καὶ οὐ
παρακολουθοῦντος τοῦ κινήσαντος φέρεται τὸ βίᾳ κινηθέν. Εἰ
γὰρ μὴ τοιοῦτόν τι σῶμα ὑπῆρχεν, οὐκ ἂν ἦν βίᾳ κίνησις.
Καὶ τὴν κατὰ φύσιν δ' ἑκάστου κίνησιν συνεπουρίζει
30 τὸν αὐτὸν τρόπον. Ὅτι μὲν οὖν ἅπαν ἢ κοῦφον ἢ βαρύ, καὶ
πῶς αἱ παρὰ φύσιν κινήσεις ἔχουσι ἐν τούτοις, φανερόν. Ὅτι
δ' οὔτε πάντων ἐστὶ γένεσις οὔθ' ἁπλῶς οὐθενός, δῆλον ἐκ τῶν
προειρημένων· ἀδύνατον γὰρ παντὸς σώματος εἶναι γένεσιν,
1A weightless body, therefore, and one which has weight will move the same distance, which is impossible. And the same argument would fit the case of lightness. Again, a body which is in motion but has neither weight nor lightness, must be moved by constraint, and must continue its constrained movement 5infinitely. For there will be a force which moves it, and the smaller and lighter a body is the further will a given force move it. Now let A, the weightless body, be moved the distance Ce, and B, which has weight, be moved in the same time the distance Cd. Dividing the heavy body in the proportion CE:CD, we subtract from the heavy body a part which will in the same time move 10the distance CE, since the whole moved CD: for the relative speeds of the two bodies will be in inverse ratio to their respective sizes. Thus the weightless body will move the same distance as the heavy in the same time. But this is impossible. Hence, since the motion of the weightless body will cover a greater distance than any that is suggested, it will continue infinitely. 15It is therefore obvious that every body must have a definite weight or lightness. But since 'nature' means a source of movement within the thing itself, while a force is a source of movement in something other than it or in itself qua other, and since movement is always due either to nature or to constraint, movement which is natural, as downward movement is to a stone, will 20be merely accelerated by an external force, while an unnatural movement will be due to the force alone. In either case the air is as it were instrumental to the force. For air is both light and heavy, and thus qua light produces upward motion, being propelled and set in motion by the force, and qua heavy produces a downward motion. In either case the force transmits the movement 25to the body by first, as it were, impregnating the air. That is why a body moved by constraint continues to move when that which gave the impulse ceases to accompany it. Otherwise, i.e. if the air were not endowed with this function, constrained movement would be impossible. And the natural movement of a body may be helped on in the same way. This discussion suffices to 30show (1) that all bodies are either light or heavy, and (2) how unnatural movement takes place.
From what has been said earlier it is plain that there cannot be generation either of everything or in an absolute sense of anything.
From what has been said earlier it is plain that there cannot be generation either of everything or in an absolute sense of anything.
302a
1 εἰ μὴ καὶ κενὸν εἶναί τι δυνατὸν κεχωρισμένον· ἐν ᾧ γὰρ
ἔσται τόπῳ τὸ νῦν γιγνόμενον εἰ ἐγίγνετο, ἐν τούτῳ πρότερον
τὸ κενὸν ἀναγκαῖον εἶναι σώματος μηθενὸς ὄντος. Ἄλλο μὲν
γὰρ ἐξ ἄλλου σῶμα γίγνεσθαι δυνατόν, οἷον ἐξ ἀέρος πῦρ,
5 ὅλως δ' ἐκ μηδενὸς ἄλλου προϋπάρχοντος μεγέθους ἀδύνατον·
μάλιστα γὰρ ἂν ἐκ δυνάμει τινὸς ὄντος σώματος ἐνεργείᾳ
γένοιτ' ἂν σῶμα. Ἀλλ' εἰ τὸ δυνάμει ὂν σῶμα μηθέν
ἐστιν ἄλλο σῶμα ἐνεργείᾳ πρότερον, κενὸν ἔσται κεχωριςμένον.
1It is impossible that everything should be generated, unless an extra-corporeal void is possible. For, assuming generation, the place which is to be occupied by that which is coming to be, must have been previously occupied by void in which no body was. Now it is quite possible 5for one body to be generated out of another, air for instance out of fire, but in the absence of any pre-existing mass generation is impossible. That which is potentially a certain kind of body may, it is true, become such in actuality, But if the potential body was not already in actuality some other kind of body, the existence of an extra-corporeal 10void must be admitted.
Book 3,Chapter 3 (302a10–302b9)
10 Λοιπὸν δ' εἰπεῖν τίνων τέ ἐστι γένεσις [σωμάτων], καὶ
διὰ τί ἐστιν. Ἐπεὶ οὖν ἐν ἅπασιν ἡ γνῶσις διὰ τῶν πρώτων,
πρῶτα δὲ τῶν ἐνυπαρχόντων τὰ στοιχεῖα, σκεπτέον ποῖα
τῶν τοιούτων σωμάτων ἐστὶ στοιχεῖα, καὶ διὰ τί ἐστιν, ἔπειτα
μετὰ ταῦτα πόσα καὶ ποῖ' ἄττα. Τοῦτο δ' ἔσται φανερὸν
15 ὑποθεμένοις τίς ἐστιν ἡ τοῦ στοιχείου φύσις. Ἔστω δὴ στοιχεῖον
τῶν σωμάτων, εἰς ὃ τἆλλα σώματα διαιρεῖται, ἐνυπάρχον
δυνάμει ἢ ἐνεργείᾳ (τοῦτο γὰρ ποτέρως, ἔτι ἀμφισβητήσιμον),
αὐτὸ δ' ἐστὶν ἀδιαίρετον εἰς ἕτερα τῷ εἴδει· τοιοῦτον γάρ
τι τὸ στοιχεῖον ἅπαντες καὶ ἐν ἅπασι βούλονται λέγειν. Εἰ
20 δὴ τὸ εἰρημένον ἐστὶ στοιχεῖον, ἀνάγκη εἶναι ἄττα τοιαῦτα
τῶν σωμάτων. Ἐν μὲν γὰρ σαρκὶ καὶ ξύλῳ καὶ ἑκάστῳ τῶν
τοιούτων ἔνεστι δυνάμει πῦρ καὶ γῆ· φανερὰ γὰρ ταῦτα ἐξ
ἐκείνων ἐκκρινόμενα. Ἐν δὲ πυρὶ σὰρξ ἢ ξύλον οὐκ ἐνυπάρχουσιν,
οὔτε κατὰ δύναμιν οὔτε κατ' ἐνέργειαν· ἐξεκρίνετο γὰρ
25 ἄν. Ὁμοίως δ' οὐδ' εἰ ἕν τι μόνον εἴη τοιοῦτον, οὐδ' ἐν ἐκείνῳ·
οὐ γὰρ εἰ ἔσται σὰρξ ἢ ὀστοῦν ἢ τῶν ἄλλων ὁτιοῦν, οὔπω φατέον
ἐνυπάρχειν δυνάμει, ἀλλὰ προσθεωρητέον τίς ὁ τρόπος
τῆς γενέσεως. Ἀναξαγόρας δ' ἐναντίως Ἐμπεδοκλεῖ λέγει
περὶ τῶν στοιχείων. Ὁ μὲν γὰρ πῦρ καὶ γῆν καὶ τὰ σύστοιχα
30 τούτοις στοιχεῖά φησιν εἶναι τῶν σωμάτων καὶ συγκεῖσθαι
πάντ' ἐκ τούτων, Ἀναξαγόρας δὲ τοὐναντίον· τὰ γὰρ ὁμοιομερῆ
στοιχεῖα (λέγω δ' οἷον σάρκα καὶ ὀστοῦν καὶ τῶν τοιούτων
It remains to say what bodies are subject to generation, and why. Since in every case knowledge depends on what is primary, and the elements are the primary constituents of bodies, we must ask which of such bodies are elements, and why; and after that what is their number and character. The answer will be plain if we first 15explain what kind of substance an element is. An element, we take it, is a body into which other bodies may be analysed, present in them potentially or in actuality (which of these, is still disputable), and not itself divisible into bodies different in form. That, or something like it, is what all men in every case mean by element. Now if what we 20have described is an element, clearly there must be such bodies. For flesh and wood and all other similar bodies contain potentially fire and earth, since one sees these elements exuded from them; and, on the other hand, neither in potentiality nor in actuality does fire contain flesh or wood, or it would exude them. Similarly, even if there were 25only one elementary body, it would not contain them. For though it will be either flesh or bone or something else, that does not at once show that it contained these in potentiality: the further question remains, in what manner it becomes them. Now Anaxagoras opposes Empedocles' view of the elements. Empedocles says that fire and earth and the related 30bodies are elementary bodies of which all things are composed; but this Anaxagoras denies. His elements are the homoeomerous things, viz.
302b
1 ἕκαστον), ἀέρα δὲ καὶ πῦρ μίγματα τούτων καὶ τῶν
ἄλλων σπερμάτων πάντων· εἶναι γὰρ ἑκάτερον αὐτῶν ἐξ ἀοράτων
τῶν ὁμοιομερῶν πάντων ἠθροισμένον. Διὸ καὶ γίγνεσθαι
πάντ' ἐκ τούτων· τὸ γὰρ πῦρ καὶ τὸν αἰθέρα προσαγορεύει
5 ταὐτό. Ἐπεὶ δ' ἐστὶ παντὸς φυσικοῦ σώματος κίνησις οἰκεία,
τῶν δὲ κινήσεων αἱ μὲν ἁπλαῖ αἱ δὲ μικταί, καὶ αἱ μὲν
μικταὶ τῶν μικτῶν, αἱ δὲ ἁπλαῖ τῶν ἁπλῶν εἰσι, φανερὸν
ὅτι ἔσται ἄττα σώματα ἁπλᾶ. Εἰσὶ γὰρ καὶ κινήσεις ἁπλαῖ.
Ὥστε δῆλον καὶ ὅτι ἐστὶ στοιχεῖα καὶ διὰ τί ἐστιν.
1flesh, bone, and the like. Earth and fire are mixtures, composed of them and all the other seeds, each consisting of a collection of all the homoeomerous bodies, separately invisible; and that explains why from these two bodies all others are generated. (To 5him fire and aither are the same thing.) But since every natural body has it proper movement, and movements are either simple or mixed, mixed in mixed bodies and simple in simple, there must obviously be simple bodies; for there are simple movements. It is plain, then, that there are elements, and why.
Book 3,Chapter 4 (302b10–303b8)
10 Πότερον δὲ πεπερασμένα ἢ ἄπειρα, καὶ εἰ πεπεραςμένα,
πόσα τὸν ἀριθμόν, ἑπόμενον ἂν εἴη σκοπεῖν. Πρῶτον
μὲν οὖν ὅτι οὐκ ἔστιν ἄπειρα, καθάπερ οἴονταί τινες, θεωρητέον,
καὶ πρῶτον τοὺς πάντα τὰ ὁμοιομερῆ στοιχεῖα ποιοῦντας,
καθάπερ καὶ Ἀναξαγόρας. Οὐθεὶς γὰρ τῶν οὕτως ἀξιούντων
15 ὀρθῶς λαμβάνει τὸ στοιχεῖον· ὁρῶμεν γὰρ πολλὰ καὶ τῶν
μικτῶν σωμάτων εἰς ὁμοιομερῆ διαιρούμενα, λέγω δ' οἷον
σάρκα καὶ ὀστοῦν καὶ ξύλον καὶ λίθον. Ὥστ' εἴπερ τὸ σύνθετον
οὐκ ἔστι στοιχεῖον, οὐχ ἅπαν ἔσται τὸ ὁμοιομερὲς στοιχεῖον,
ἀλλὰ τὸ ἀδιαίρετον εἰς ἕτερα τῷ εἴδει, καθάπερ εἴρηται
20 πρότερον. Ἔτι δ' οὐδ' οὕτως λαμβάνοντας τὸ στοιχεῖον ἀνάγκη
ποιεῖν ἄπειρα· πάντα γὰρ ταὐτὰ ἀποδοθήσεται καὶ πεπερασμένων
ὄντων, ἐάν τις λάβῃ· τὸ αὐτὸ γὰρ ποιήσει, κἂν
δύο ἢ τρία μόνον ᾖ τοιαῦτα, καθάπερ ἐγχειρεῖ καὶ Ἐμπεδοκλῆς.
Ἐπεὶ γὰρ καὶ ὣς αὐτοῖς συμβαίνει μὴ πάντα ποιεῖν
25 ἐξ ὁμοιομερῶν (πρόσωπον γὰρ οὐκ ἐκ προσώπων ποιοῦσιν,
οὐδ' ἄλλο τῶν κατὰ φύσιν ἐσχηματισμένων οὐθέν), φανερὸν
ὅτι πολλῷ βέλτιον πεπερασμένας ποιεῖν τὰς ἀρχάς, καὶ ταύτας
ὡς ἐλαχίστας πάντων γε τῶν αὐτῶν μελλόντων δείκνυσθαι,
καθάπερ ἀξιοῦσι καὶ οἱ ἐν τοῖς μαθήμασιν· ἀεὶ γὰρ πεπερασμένας
30 λαμβάνουσιν ἀρχὰς ἢ τῷ εἴδει ἢ τῷ ποσῷ. Ἔτι
εἰ σῶμα σώματος ἕτερον λέγεται κατὰ τὰς οἰκείας διαφοράς,
αἱ δὲ τῶν σωμάτων διαφοραὶ πεπερασμέναι (διαφέρουσι
The next question 10to consider is whether the elements are finite or infinite in number, and, if finite, what their number is. Let us first show reason or denying that their number is infinite, as some suppose. We begin with the view of Anaxagoras that all the homoeomerous bodies are elements. Any one who adopts this view misapprehends 15the meaning of element. Observation shows that even mixed bodies are often divisible into homoeomerous parts; examples are flesh, bone, wood, and stone. Since then the composite cannot be an element, not every homoeomerous body can be an element; only, as we said before, that which is not divisible into bodies different 20in form. But even taking 'element' as they do, they need not assert an infinity of elements, since the hypothesis of a finite number will give identical results. Indeed even two or three such bodies serve the purpose as well, as Empedocles' attempt shows. Again, even on their view it turns out that all things are not 25composed of homocomerous bodies. They do not pretend that a face is composed of faces, or that any other natural conformation is composed of parts like itself. Obviously then it would be better to assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving what has to be 30proved. This is the common demand of mathematicians, who always assume as principles things finite either in kind or in number.
303a
1 γὰρ τοῖς αἰσθητοῖς, ταῦτα δὲ πεπέρανται· δεῖ δὲ
τοῦτο δειχθῆναι), φανερὸν ὅτι καὶ τὰ στοιχεῖα ἀνάγκη πεπερασμένα
εἶναι. Ἀλλὰ μὴν οὐδ' ὡς ἕτεροί τινες λέγουσιν,
οἷον Λεύκιππός τε καὶ Δημόκριτος ὁ Ἀβδηρίτης, εὔλογα τὰ
5 συμβαίνοντα· φασὶ γὰρ εἶναι τὰ πρῶτα μεγέθη πλήθει μὲν
ἄπειρα, μεγέθει δὲ ἀδιαίρετα, καὶ οὔτ' ἐξ ἑνὸς πολλὰ γίγνεσθαι
οὔτε ἐκ πολλῶν ἕν, ἀλλὰ τῇ τούτων συμπλοκῇ καὶ
περιπαλάξει πάντα γεννᾶσθαι. Τρόπον γάρ τινα καὶ οὗτοι
πάντα τὰ ὄντα ποιοῦσιν ἀριθμοὺς καὶ ἐξ ἀριθμῶν· καὶ γὰρ εἰ
10 μὴ σαφῶς δηλοῦσιν, ὅμως τοῦτο βούλονται λέγειν. Καὶ πρὸς
τούτοις, ἐπεὶ διαφέρει τὰ σώματα σχήμασιν, ἄπειρα δὲ τὰ
σχήματα, ἄπειρα καὶ τὰ ἁπλᾶ σώματά φασιν εἶναι. Ποῖον
δὲ καὶ τί ἑκάστου τὸ σχῆμα τῶν στοιχείων, οὐθὲν ἐπιδιώρισαν,
ἀλλὰ μόνον τῷ πυρὶ τὴν σφαῖραν ἀπέδωκαν· ἀέρα δὲ καὶ
15 ὕδωρ καὶ τἆλλα μεγέθει καὶ μικρότητι διεῖλον, ὡς οὖσαν
αὐτῶν τὴν φύσιν οἷον πανσπερμίαν πάντων τῶν στοιχείων.
Πρῶτον μὲν οὖν ταὐτὸν καὶ τούτοις ἁμάρτημα τὸ μὴ πεπερασμένας
λαβεῖν τὰς ἀρχάς, ἐξὸν ἅπαντα ταὐτὰ λέγειν.
Ἔτι δ' εἰ μὴ ἄπειροι τῶν σχημάτων αἱ διαφοραί, δῆλον ὅτι
20 οὐκ ἔσται τὰ στοιχεῖα ἄπειρα. Πρὸς δὲ τούτοις ἀνάγκη μάχεσθαι
ταῖς μαθηματικαῖς ἐπιστήμαις ἄτομα σώματα λέγοντας,
καὶ πολλὰ τῶν ἐνδόξων καὶ τῶν φαινομένων κατὰ τὴν
αἴσθησιν ἀναιρεῖν, περὶ ὧν εἴρηται πρότερον ἐν τοῖς περὶ χρόνου
καὶ κινήσεως. Ἅμα δὲ καὶ ἐναντία λέγειν αὐτοὺς αὑτοῖς
25 ἀνάγκη· ἀδύνατον γὰρ ἀτόμων ὄντων τῶν στοιχείων μεγέθει
καὶ μικρότητι διαφέρειν ἀέρα καὶ γῆν καὶ ὕδωρ· οὐ γὰρ
οἷόν τ' ἐξ ἀλλήλων γίγνεσθαι· ὑπολείψει γὰρ ἀεὶ τὰ μέγιστα
σώματα ἐκκρινόμενα, φασὶ δ' οὕτω γίγνεσθαι ὕδωρ
καὶ ἀέρα καὶ γῆν ἐξ ἀλλήλων. Ἔτι οὐδὲ κατὰ τὴν τούτων
30 ὑπόληψιν δόξειεν ἂν ἄπειρα γίγνεσθαι τὰ στοιχεῖα, εἴπερ
τὰ μὲν σώματα διαφέρει σχήμασι, τὰ δὲ σχήματα πάντα
σύγκειται ἐκ πυραμίδων, τὰ μὲν εὐθύγραμμα ἐξ εὐθυγράμμων,
1Again, if body is distinguished from body by the appropriate qualitative difference, and there is a limit to the number of differences (for the difference lies in qualities apprehended by sense, which are in fact finite in number, though this requires proof), then manifestly there is necessarily a 5limit to the number of elements.
There is, further, another view-that of Leucippus and Democritus of Abdera-the implications of which are also unacceptable. The primary masses, according to them, are infinite in number and indivisible in mass: one cannot turn into many nor many into one; and all things are generated by their combination and involution. Now this view in a 10sense makes things out to be numbers or composed of numbers. The exposition is not clear, but this is its real meaning. And further, they say that since the atomic bodies differ in shape, and there is an infinity of shapes, there is an infinity of simple bodies. But they have never explained in detail the shapes of the various elements, except so far to allot the sphere to 15fire. Air, water, and the rest they distinguished by the relative size of the atom, assuming that the atomic substance was a sort of master-seed for each and every element. Now, in the first place, they make the mistake already noticed. The principles which they assume are not limited in number, though such limitation would necessitate no other alteration in their theory. 20Further, if the differences of bodies are not infinite, plainly the elements will not be an infinity. Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data of sense perception. But of these things we have already spoken in our discussion of time and movement. 25They are also bound to contradict themselves. For if the elements are atomic, air, earth, and water cannot be differentiated by the relative sizes of their atoms, since then they could not be generated out of one another. The extrusion of the largest atoms is a process that will in time exhaust the supply; and it is by such a process that they account for the generation 30of water, air, and earth from one another. Again, even on their own presuppositions it does not seem as if the clements would be infinite in number.
There is, further, another view-that of Leucippus and Democritus of Abdera-the implications of which are also unacceptable. The primary masses, according to them, are infinite in number and indivisible in mass: one cannot turn into many nor many into one; and all things are generated by their combination and involution. Now this view in a 10sense makes things out to be numbers or composed of numbers. The exposition is not clear, but this is its real meaning. And further, they say that since the atomic bodies differ in shape, and there is an infinity of shapes, there is an infinity of simple bodies. But they have never explained in detail the shapes of the various elements, except so far to allot the sphere to 15fire. Air, water, and the rest they distinguished by the relative size of the atom, assuming that the atomic substance was a sort of master-seed for each and every element. Now, in the first place, they make the mistake already noticed. The principles which they assume are not limited in number, though such limitation would necessitate no other alteration in their theory. 20Further, if the differences of bodies are not infinite, plainly the elements will not be an infinity. Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data of sense perception. But of these things we have already spoken in our discussion of time and movement. 25They are also bound to contradict themselves. For if the elements are atomic, air, earth, and water cannot be differentiated by the relative sizes of their atoms, since then they could not be generated out of one another. The extrusion of the largest atoms is a process that will in time exhaust the supply; and it is by such a process that they account for the generation 30of water, air, and earth from one another. Again, even on their own presuppositions it does not seem as if the clements would be infinite in number.
303b
1 ἡ δὲ σφαῖρα ἐξ ὀκτὼ μορίων. Ἀνάγκη γὰρ εἶναί
τινας ἀρχὰς τῶν σχημάτων. Ὥστε εἴτε μία εἴτε δύο εἴτε
πλείους, καὶ τὰ ἁπλᾶ σώματα τοσαῦτα ἔσται τὸ πλῆθος.
Ἔτι δ' εἰ ἑκάστῳ μὲν τῶν στοιχείων ἐστί τις οἰκεία κίνησις,
5 καὶ ἡ τοῦ ἁπλοῦ σώματος ἁπλῆ, μή εἰσι δ' αἱ ἁπλαῖ κινήσεις
ἄπειροι διὰ τὸ μήτε τὰς ἁπλᾶς φορὰς πλείους εἶναι δυοῖν
μήτε τοὺς τόπους ἀπείρους, οὐκ ἂν εἴη οὐδ' οὕτως ἄπειρα τὰ
στοιχεῖα.
1The atoms differ in figure, and all figures are composed of pyramids, rectilinear the case of rectilinear figures, while the sphere has eight pyramidal parts. The figures must have their principles, and, whether these are one or two or more, the simple bodies must be the same in number as 5they. Again, if every element has its proper movement, and a simple body has a simple movement, and the number of simple movements is not infinite, because the simple motions are only two and the number of places is not infinite, on these grounds also we should have to deny that the number of elements is infinite.
Book 3,Chapter 5 (303b9–304b22)
Ἐπεὶ δ' ἀνάγκη πεπεράνθαι τὰ στοιχεῖα, λοιπὸν σκέψασθαι
10 πότερον πλείω ἔσται ἢ ἕν. Ἔνιοι γὰρ ἓν μόνον ὑποτίθενται,
καὶ τοῦτο οἱ μὲν ὕδωρ, οἱ δ' ἀέρα, οἱ δὲ πῦρ, οἱ
δ' ὕδατος μὲν λεπτότερον, ἀέρος δὲ πυκνότερον, ὃ περιέχειν
φασὶ πάντας τοὺς οὐρανοὺς ἄπειρον ὄν. Ὅσοι μὲν οὖν τὸ ἓν
τοῦτο ποιοῦσιν ὕδωρ ἢ ἀέρα ἢ ὕδατος μὲν λεπτότερον, ἀέρος δὲ
15 πυκνότερον, εἶτ' ἐκ τούτου μανότητι καὶ πυκνότητι τἆλλα
γεννῶσιν, οὗτοι λανθάνουσιν αὐτοὶ αὑτοὺς ἄλλο τι πρότερον τοῦ
στοιχείου ποιοῦντες· ἔστι γὰρ ἡ μὲν ἐκ τῶν στοιχείων γένεσις
σύνθεσις, ὥς φασιν, ἡ δ' εἰς τὰ στοιχεῖα διάλυσις, ὥστ'
ἀνάγκη πρότερον εἶναι τῇ φύσει τὸ λεπτομερέστερον. Ἐπεὶ οὖν
20 φασὶ πάντων τῶν σωμάτων τὸ πῦρ λεπτότατον εἶναι, πρῶτον
ἂν εἴη τῇ φύσει τὸ πῦρ· διαφέρει δ' οὐθέν, ἀνάγκη γὰρ
ἕν τι τῶν ἄλλων εἶναι πρῶτον, καὶ μὴ τὸ μέσον. Ἔτι δὲ τὸ
μὲν πυκνότητι καὶ μανότητι τἆλλα γεννᾶν οὐθὲν διαφέρει ἢ
λεπτότητι καὶ παχύτητι· τὸ μὲν γὰρ λεπτὸν μανόν, τὸ δὲ
25 παχὺ βούλονται εἶναι πυκνόν. Πάλιν δὲ τὸ λεπτότητι καὶ
παχύτητι ταὐτὸν καὶ τὸ μεγέθει καὶ μικρότητι· λεπτὸν
μὲν γὰρ τὸ μικρομερές, παχὺ δὲ τὸ μεγαλομερές· τὸ γὰρ
ἐπεκτεινόμενον ἐπὶ πολὺ λεπτόν, τοιοῦτον δὲ τὸ ἐκ μικρῶν
μερῶν συνεστός, ὥστ' αὐτοῖς συμβαίνει μεγέθει καὶ μικρότητι
30 διαιρεῖν τὴν τῶν ἄλλων οὐσίαν. Οὕτω δὲ διοριζομένοις ἅπαντα
συμβήσεται λέγειν πρός τι, καὶ οὐκ ἔσται ἁπλῶς τὸ μὲν
πῦρ τὸ δ' ὕδωρ τὸ δ' ἀήρ, ἀλλὰ τὸ αὐτὸ πρὸς μὲν τόδε
Since the number of the elements must be limited, it 10remains to inquire whether there is more than one element. Some assume one only, which is according to some water, to others air, to others fire, to others again something finer than water and denser than air, an infinite body-so they say-bracing all the heavens.
Now those who decide for a single element, which is either water or air or a body finer than water and 15denser than air, and proceed to generate other things out of it by use of the attributes density and rarity, all alike fail to observe the fact that they are depriving the element of its priority. Generation out of the elements is, as they say, synthesis, and generation into the elements is analysis, so that the body with the finer parts must have priority in the 20order of nature. But they say that fire is of all bodies the finest. Hence fire will be first in the natural order. And whether the finest body is fire or not makes no difference; anyhow it must be one of the other bodies that is primary and not that which is intermediate. Again, density and rarity, as instruments of generation, are equivalent to fineness and 25coarseness, since the fine is rare, and coarse in their use means dense. But fineness and coarseness, again, are equivalent to greatness and smallness, since a thing with small parts is fine and a thing with large parts coarse. For that which spreads itself out widely is fine, and a thing composed of small parts is so spread out. In the end, then, they distinguish the 30various other substances from the element by the greatness and smallness of their parts. This method of distinction makes all judgement relative.
Now those who decide for a single element, which is either water or air or a body finer than water and 15denser than air, and proceed to generate other things out of it by use of the attributes density and rarity, all alike fail to observe the fact that they are depriving the element of its priority. Generation out of the elements is, as they say, synthesis, and generation into the elements is analysis, so that the body with the finer parts must have priority in the 20order of nature. But they say that fire is of all bodies the finest. Hence fire will be first in the natural order. And whether the finest body is fire or not makes no difference; anyhow it must be one of the other bodies that is primary and not that which is intermediate. Again, density and rarity, as instruments of generation, are equivalent to fineness and 25coarseness, since the fine is rare, and coarse in their use means dense. But fineness and coarseness, again, are equivalent to greatness and smallness, since a thing with small parts is fine and a thing with large parts coarse. For that which spreads itself out widely is fine, and a thing composed of small parts is so spread out. In the end, then, they distinguish the 30various other substances from the element by the greatness and smallness of their parts. This method of distinction makes all judgement relative.
304a
1 πῦρ, πρὸς δέ τι ἄλλο ἀήρ, ὅπερ συμβαίνει καὶ τοῖς πλείω
μὲν τὰ στοιχεῖα λέγουσι, μεγέθει δὲ καὶ μικρότητι διαφέρειν
φάσκουσιν· ἐπεὶ γὰρ τῷ ποσῷ διώρισται ἕκαστον, ἔσται
τις λόγος πρὸς ἄλληλα τῶν μεγεθῶν, ὥστε τὰ τοῦτον ἔχοντα
5 τὸν λόγον πρὸς ἄλληλα ἀνάγκη τὸ μὲν ἀέρα εἶναι τὸ δὲ
πῦρ τὸ δὲ γῆν τὸ δ' ὕδωρ, διὰ τὸ ἐνυπάρχειν ἐν τοῖς μείζοσι
τοὺς τῶν ἐλαττόνων λόγους. Ὅσοι δὲ πῦρ ὑποτίθενται τὸ
στοιχεῖον, τοῦτο μὲν διαφεύγουσιν, ἄλλα δ' αὐτοῖς ἀναγκαῖον
ἄλογα συμβαίνειν. Οἱ μὲν γὰρ αὐτῶν σχῆμα περιάπτουσι
10 τῷ πυρί, καθάπερ οἱ τὴν πυραμίδα ποιοῦντες, καὶ
τούτων οἱ μὲν ἁπλουστέρως λέγοντες ὅτι τῶν μὲν σχημάτων
τμητικώτατον ἡ πυραμίς, τῶν δὲ σωμάτων τὸ πῦρ, οἱ δὲ
κομψοτέρως τῷ λόγῳ προσάγοντες ὅτι τὰ μὲν σώματα
πάντα σύγκειται ἐκ τοῦ λεπτομερεστάτου, τὰ δὲ σχήματα
15 τὰ στερεὰ ἐκ πυραμίδων, ὥστ' ἐπεὶ τῶν μὲν σωμάτων
τὸ πῦρ λεπτότατον, τῶν δὲ σχημάτων ἡ πυραμὶς μικρομερέστατον
καὶ πρῶτον, τὸ δὲ πρῶτον σχῆμα τοῦ πρώτου
σώματος, πυραμὶς ἂν εἴη τὸ πῦρ. Οἱ δὲ περὶ μὲν σχήματος
οὐδὲν ἀποφαίνονται, λεπτομερέστατον δὲ μόνον ποιοῦσιν,
20 ἔπειτ' ἐκ τούτου συντιθεμένου φασὶ γίγνεσθαι τἆλλα
καθάπερ ἂν εἰ συμφυσωμένου ψήγματος. Ἀμφοτέροις δὲ
ταὐτὰ συμβαίνει δυσχερῆ· εἰ μὲν γὰρ ἄτομον τὸ πρῶτον
σῶμα ποιοῦσι, πάλιν ἥξουσιν οἱ πρότερον εἰρημένοι λόγοι
πρὸς ταύτην τὴν ὑπόθεσιν. Ἔτι οὐκ ἐνδέχεται τοῦτο λέγειν
25 φυσικῶς βουλομένοις θεωρεῖν. Εἰ γὰρ ἅπαν σῶμα σώματι
συμβλητὸν κατὰ τὸ ποσόν, ἔχει δ' ἀνάλογον τὰ μεγέθη
τά τε τῶν ὁμοιομερῶν πρὸς ἄλληλα καὶ τὰ τῶν στοιχείων
(οἷον τὰ τοῦ παντὸς ὕδατος πρὸς τὸν ἅπαντα ἀέρα καὶ τοῦ
στοιχείου πρὸς τὸ στοιχεῖον, ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων),
30 ὁ δ' ἀὴρ πλείων τοῦ ὕδατος καὶ ὅλως τὸ λεπτομερέστερον
τοῦ παχυμερεστέρου, φανερὸν ὅτι καὶ τὸ στοιχεῖον ἔλαττον
ἔσται τὸ τοῦ ὕδατος ἢ τὸ τοῦ ἀέρος. Εἰ οὖν τὸ ἔλαττον μέγεθος
ἐνυπάρχει τῷ μείζονι, διαιρετὸν ἂν εἴη τὸ τοῦ ἀέρος
1There will be no absolute distinction between fire, water, and air, but one and the same body will be relatively to this fire, relatively to something else air. The same difficulty is involved equally in the view elements and distinguishes them by their greatness and smallness. The principle of 5distinction between bodies being quantity, the various sizes will be in a definite ratio, and whatever bodies are in this ratio to one another must be air, fire, earth, and water respectively. For the ratios of smaller bodies may be repeated among greater bodies.
Those who start from fire as the single element, while avoiding this difficulty, involve themselves in many 10others. Some of them give fire a particular shape, like those who make it a pyramid, and this on one of two grounds. The reason given may be-more crudely-that the pyramid is the most piercing of figures as fire is of bodies, or-more ingeniously-the position may be supported by the following argument. As all bodies are composed of that which has the finest parts, so all solid 15figures are composed of pryamids: but the finest body is fire, while among figures the pyramid is primary and has the smallest parts; and the primary body must have the primary figure: therefore fire will be a pyramid. Others, again, express no opinion on the subject of its figure, but simply regard it as the of the finest parts, which in combination will form other 20bodies, as the fusing of gold-dust produces solid gold. Both of these views involve the same difficulties. For (1) if, on the one hand, they make the primary body an atom, the view will be open to the objections already advanced against the atomic theory. And further the theory is inconsistent with a regard for the facts of nature. For if all bodies are quantitatively 25commensurable, and the relative size of the various homoeomerous masses and of their several elements are in the same ratio, so that the total mass of water, for instance, is related to the total mass of air as the elements of each are to one another, and so on, and if there is more air than water and, generally, more of the finer body than of the coarser, obviously the element 30of water will be smaller than that of air. But the lesser quantity is contained in the greater. Therefore the air element is divisible. And the same could be shown of fire and of all bodies whose parts are relatively fine.
Those who start from fire as the single element, while avoiding this difficulty, involve themselves in many 10others. Some of them give fire a particular shape, like those who make it a pyramid, and this on one of two grounds. The reason given may be-more crudely-that the pyramid is the most piercing of figures as fire is of bodies, or-more ingeniously-the position may be supported by the following argument. As all bodies are composed of that which has the finest parts, so all solid 15figures are composed of pryamids: but the finest body is fire, while among figures the pyramid is primary and has the smallest parts; and the primary body must have the primary figure: therefore fire will be a pyramid. Others, again, express no opinion on the subject of its figure, but simply regard it as the of the finest parts, which in combination will form other 20bodies, as the fusing of gold-dust produces solid gold. Both of these views involve the same difficulties. For (1) if, on the one hand, they make the primary body an atom, the view will be open to the objections already advanced against the atomic theory. And further the theory is inconsistent with a regard for the facts of nature. For if all bodies are quantitatively 25commensurable, and the relative size of the various homoeomerous masses and of their several elements are in the same ratio, so that the total mass of water, for instance, is related to the total mass of air as the elements of each are to one another, and so on, and if there is more air than water and, generally, more of the finer body than of the coarser, obviously the element 30of water will be smaller than that of air. But the lesser quantity is contained in the greater. Therefore the air element is divisible. And the same could be shown of fire and of all bodies whose parts are relatively fine.
304b
1 στοιχεῖον. Ὡσαύτως δὲ καὶ τὸ τοῦ πυρὸς καὶ ὅλως τῶν λεπτομερεστέρων.
Εἰ δὲ διαιρετόν, τοῖς μὲν σχηματίζουσι τὸ
πῦρ συμβήσεται μὴ εἶναι τὸ τοῦ πυρὸς μέρος πῦρ διὰ τὸ
μὴ συγκεῖσθαι τὴν πυραμίδα ἐκ πυραμίδων, ἔτι δὲ μὴ
5 πᾶν σῶμα εἶναι ἢ στοιχεῖον ἢ ἐκ στοιχείων (τὸ γὰρ μέρος
τοῦ πυρὸς οὔτε πῦρ οὔθ' ἕτερον στοιχεῖον οὐδέν)· τοῖς δὲ τῷ
μεγέθει διορίζουσι πρότερόν τι τοῦ στοιχείου στοιχεῖον εἶναι,
καὶ τοῦτ' εἰς ἄπειρον βαδίζειν, εἴπερ ἅπαν σῶμα διαιρετὸν καὶ
τὸ μικρομερέστατον στοιχεῖον. Ἔτι δὲ καὶ τούτοις συμβαίνει
10 λέγειν ὡς ταὐτὸν πρὸς μὲν τόδε πῦρ ἐστι, πρὸς ἄλλο δ'
ἀήρ, καὶ πάλιν ὕδωρ καὶ γῆ. Κοινὸν δὲ πᾶσιν ἁμάρτημα
τοῖς ἓν τὸ στοιχεῖον ὑποτιθεμένοις τὸ μίαν μόνην κίνησιν ποιεῖν
φυσικήν, καὶ πάντων τὴν αὐτήν. Ὁρῶμεν γὰρ πᾶν τὸ
φυσικὸν σῶμα κινήσεως ἔχον ἀρχήν. Εἰ οὖν ἅπαντα τὰ σώματα
15 ἕν τί ἐστι, πάντων ἂν εἴη μία κίνησις· καὶ ταύτην
ἀναγκαῖον ὥσῳπερ ἂν πλείω γίγνηται, κινεῖσθαι μᾶλλον,
ὥσπερ καὶ τὸ πῦρ ὅσῳ ἂν πλεῖον γίγνηται, φέρεται θᾶττον
ἄνω τὴν αὑτοῦ φοράν. Συμβαίνει δὲ πολλὰ κάτω φέρεσθαι
θᾶττον. Ὥστε διά τε ταῦτα καὶ πρὸς τούτοις ἐπεὶ διώρισται
20 πρότερον ὅτι πλείους αἱ φυσικαὶ κινήσεις, δῆλον ὅτι
ἀδύνατον ἓν εἶναι τὸ στοιχεῖον. Ἐπειδὴ δὲ οὔτε ἄπειρα οὔτε ἕν,
ἀνάγκη πλείω εἶναι καὶ πεπερασμένα.
1(2) If, on the other hand, the primary body is divisible, then (a) those who give fire a special shape will have to say that a part of fire is not fire, because a pyramid is not composed of pyramids, and also that not every body is either an element or composed of elements, since a part of fire will 5be neither fire nor any other element. And (b) those whose ground of distinction is size will have to recognize an element prior to the element, a regress which continues infinitely, since every body is divisible and that which has the smallest parts is the element. Further, they too will have to say that the same body is relatively to this fire and relatively to that air, 10to others again water and earth.
The common error of all views which assume a single element is that they allow only one natural movement, which is the same for every body. For it is a matter of observation that a natural body possesses a principle of movement. If then all bodies are one, all will have one movement. With this motion the greater their quantity the more 15they will move, just as fire, in proportion as its quantity is greater, moves faster with the upward motion which belongs to it. But the fact is that increase of quantity makes many things move the faster downward. For these reasons, then, as well as from the distinction already established of a plurality of natural movements, it is impossible that there should be only one 20element. But if the elements are not an infinity and not reducible to one, they must be several and finite in number.
The common error of all views which assume a single element is that they allow only one natural movement, which is the same for every body. For it is a matter of observation that a natural body possesses a principle of movement. If then all bodies are one, all will have one movement. With this motion the greater their quantity the more 15they will move, just as fire, in proportion as its quantity is greater, moves faster with the upward motion which belongs to it. But the fact is that increase of quantity makes many things move the faster downward. For these reasons, then, as well as from the distinction already established of a plurality of natural movements, it is impossible that there should be only one 20element. But if the elements are not an infinity and not reducible to one, they must be several and finite in number.
Book 3,Chapter 6 (304b23–305a32)
Ἐπισκεπτέον δὲ πρῶτον πότερον ἀΐδιά ἐστιν ἢ γινόμενα
φθείρεται· τούτου γὰρ δειχθέντος φανερὸν ἔσται καὶ
25 πόσ' ἄττα καὶ ποῖά ἐστιν. Ἀΐδια μὲν οὖν εἶναι ἀδύνατον·
ὁρῶμεν γὰρ καὶ πῦρ καὶ ὕδωρ καὶ ἕκαστον τῶν ἁπλῶν σωμάτων
διαλυόμενον. Ἀνάγκη δὲ ἢ ἄπειρον εἶναι ἢ ἵστασθαι
τὴν διάλυσιν. Εἰ μὲν οὖν ἄπειρος, ἔσται καὶ ὁ χρόνος ὁ τῆς
διαλύσεως ἄπειρος, καὶ πάλιν ὁ τῆς συνθέσεως· ἕκαστον
30 γὰρ ἐν ἄλλῳ χρόνῳ διαλύεται καὶ συντίθεται τῶν μορίων.
Ὥστε συμβήσεται ἔξω τοῦ ἀπείρου χρόνου ἄλλον εἶναι ἄπειρον,
ὅταν ὅ τε τῆς συνθέσεως ἄπειρος ᾖ καὶ ἔτι πρότερος τούτου
ὁ τῆς διαλύσεως. Ὥστε τοῦ ἀπείρου ἔξω γίγνεται ἄπειρον·
First we must inquire whether the elements are eternal or subject to generation and destruction; for when this question has been answered their number and character will be manifest. In the first place, they cannot be eternal. It is a matter of observation 25that fire, water, and every simple body undergo a process of analysis, which must either continue infinitely or stop somewhere. (1) Suppose it infinite. Then the time occupied by the process will be infinite, and also that occupied by the reverse process of synthesis. For the processes of analysis and synthesis succeed one another in the various parts. It will follow that 30there are two infinite times which are mutually exclusive, the time occupied by the synthesis, which is infinite, being preceded by the period of analysis. There are thus two mutually exclusive infinites, which is impossible.
305a
1 ὅπερ ἀδύνατον. Εἰ δὲ στήσεταί που ἡ διάλυσις, ἤτοι ἄτομον
ἔσται τὸ σῶμα ἐν ᾧ ἵσταται, ἢ διαιρετὸν μὲν οὐ μέντοι
διαιρεθησόμενον οὐδέποτε, καθάπερ ἔοικεν Ἐμπεδοκλῆς βούλεσθαι
λέγειν. Ἄτομον μὲν οὖν οὐκ ἔσται διὰ τοὺς πρότερον εἰρημένους
5 λόγους· ἀλλὰ μὴν οὐδὲ διαιρετὸν μὲν οὐδέποτε δὲ διαλυθησόμενον.
Τὸ γὰρ ἔλαττον σῶμα τοῦ μείζονος εὐφθαρτότερόν
ἐστιν. Εἴπερ οὖν καὶ τὸ πολὺ φθείρεται κατὰ ταύτην
τὴν φθοράν, ὥστε διαλύεσθαι εἰς ἐλάττω, ἔτι μᾶλλον
τοῦτο πάσχειν εὔλογον τὸ ἔλαττον. Δύο δὲ τρόπους ὁρῶμεν
10 φθειρόμενον τὸ πῦρ· ὑπό τε γὰρ τοῦ ἐναντίου φθείρεται σβεννύμενον,
καὶ αὐτὸ ὑφ' αὑτοῦ μαραινόμενον. Τοῦτο δὲ πάσχει
τὸ ἔλαττον ὑπὸ τοῦ πλείονος, καὶ θᾶττον, ὅσῳ ἂν ᾖ ἔλαττον.
Ὥστ' ἀνάγκη φθαρτὰ καὶ γενητὰ εἶναι τὰ στοιχεῖα τῶν
σωμάτων. Ἐπεὶ δ' ἐστὶ γενητά, ἤτοι ἐξ ἀσωμάτου ἢ ἐκ σώματος
15 ἔσται ἡ γένεσις, καὶ εἰ ἐκ σώματος, ἤτοι ἐξ ἄλλου
ἢ ἐξ ἀλλήλων. Ὁ μὲν οὖν ἐξ ἀσωμάτου γεννῶν λόγος ποιεῖ κεχωρισμένον
κενόν. Πᾶν γὰρ τὸ γινόμενον <ἔν τινι γίγνεται καὶ>
ἤτοι ἀσώματον ἔσται ἐν ᾧ ἡ γένεσις, ἢ ἕξει σῶμα· καὶ εἰ
μὲν ἕξει σῶμα, δύο ἅμα ἔσται σώματα ἐν τῷ αὐτῷ, τό
20 τε γιγνόμενον καὶ τὸ προϋπάρχον· εἰ δ' ἀσώματον, ἀνάγκη
κενὸν εἶναι ἀφωρισμένον· τοῦτο δ' ὅτι ἀδύνατον, δέδεικται
πρότερον. Ἀλλὰ μὴν οὐδ' ἐκ σώματός τινος ἐγχωρεῖ γίνεσθαι
τὰ στοιχεῖα· συμβήσεται γὰρ ἄλλο σῶμα πρότερον
εἶναι τῶν στοιχείων. Τοῦτο δ' εἰ μὲν ἕξει βάρος ἢ κουφότητα,
25 τῶν στοιχείων ἔσται τι, μηδεμίαν δ' ἔχον ῥοπὴν ἀκίνητον ἔσται
καὶ μαθηματικόν· τοιοῦτον δὲ ὂν οὐκ ἔσται ἐν τόπῳ. Ἐν ᾧ γὰρ
ἠρεμεῖ, ἐν τούτῳ καὶ κινεῖσθαι δυνατόν. Καὶ εἰ μὲν βίᾳ, παρὰ
φύσιν, εἰ δὲ μὴ βίᾳ, κατὰ φύσιν. Εἰ μὲν οὖν ἔσται ἐν τόπῳ
καί που, ἔσται τι τῶν στοιχείων· εἰ δὲ μὴ ἐν τόπῳ, οὐδὲν ἐξ
30 αὐτοῦ ἔσται· τὸ γὰρ γινόμενον, καὶ ἐξ οὗ γίγνεται, ἀνάγκη
ἅμα εἶναι. Ἐπεὶ δ' οὔτε ἐξ ἀσωμάτου γίγνεσθαι δυνατὸν
οὔτ' ἐξ ἄλλου σώματος, λείπεται ἐξ ἀλλήλων γίγνεσθαι.
1(2) Suppose, on the other hand, that the analysis stops somewhere. Then the body at which it stops will be either atomic or, as Empedocles seems to have intended, a divisible body which will yet never be divided. The foregoing arguments show that it cannot be an atom; but neither can it be a divisible body which analysis 5will never reach. For a smaller body is more easily destroyed than a larger; and a destructive process which succeeds in destroying, that is, in resolving into smaller bodies, a body of some size, cannot reasonably be expected to fail with the smaller body. Now in fire we observe a destruction of two kinds: it is destroyed by its contrary when it is quenched, and by itself when it dies out. But the effect 10is produced by a greater quantity upon a lesser, and the more quickly the smaller it is. The elements of bodies must therefore be subject to destruction and generation.
Since they are generated, they must be generated either from something incorporeal or from a body, and if from a body, either from one another or from something else. The theory which generates them from something incorporeal requires 15an extra-corporeal void. For everything that comes to be comes to be in something, and that in which the generation takes place must either be incorporeal or possess body; and if it has body, there will be two bodies in the same place at the same time, viz. that which is coming to be and that which was previously there, while if it is incorporeal, there must be an extra-corporeal void. But we have 20already shown that this is impossible. But, on the other hand, it is equally impossible that the elements should be generated from some kind of body. That would involve a body distinct from the elements and prior to them. But if this body possesses weight or lightness, it will be one of the elements; and if it has no tendency to movement, it will be an immovable or mathematical entity, and therefore not 25in a place at all. A place in which a thing is at rest is a place in which it might move, either by constraint, i.e. unnaturally, or in the absence of constraint, i.e. naturally. If, then, it is in a place and somewhere, it will be one of the elements; and if it is not in a place, nothing can come from it, since that which comes into being and that out of which it comes must needs be together. The elements 30therefore cannot be generated from something incorporeal nor from a body which is not an element, and the only remaining alternative is that they are generated from one another.
Since they are generated, they must be generated either from something incorporeal or from a body, and if from a body, either from one another or from something else. The theory which generates them from something incorporeal requires 15an extra-corporeal void. For everything that comes to be comes to be in something, and that in which the generation takes place must either be incorporeal or possess body; and if it has body, there will be two bodies in the same place at the same time, viz. that which is coming to be and that which was previously there, while if it is incorporeal, there must be an extra-corporeal void. But we have 20already shown that this is impossible. But, on the other hand, it is equally impossible that the elements should be generated from some kind of body. That would involve a body distinct from the elements and prior to them. But if this body possesses weight or lightness, it will be one of the elements; and if it has no tendency to movement, it will be an immovable or mathematical entity, and therefore not 25in a place at all. A place in which a thing is at rest is a place in which it might move, either by constraint, i.e. unnaturally, or in the absence of constraint, i.e. naturally. If, then, it is in a place and somewhere, it will be one of the elements; and if it is not in a place, nothing can come from it, since that which comes into being and that out of which it comes must needs be together. The elements 30therefore cannot be generated from something incorporeal nor from a body which is not an element, and the only remaining alternative is that they are generated from one another.
Book 3,Chapter 7 (305a33–306b2)
Πάλιν οὖν ἐπισκεπτέον τίς ὁ τρόπος τῆς ἐξ ἀλλήλων
γενέσεως, πότερον ὡς Ἐμπεδοκλῆς λέγει καὶ Δημόκριτος,
35 ἢ ὡς οἱ εἰς τὰ ἐπίπεδα διαλύοντες, ἢ ἔστιν ἄλλος τις τρόπος
We must, therefore, turn to the question, what is the manner of their generation from one another? Is it as Empedocles and Democritus say, or as those who resolve bodies into planes say, or is there yet another possibility?
305b
1 παρὰ τούτους. Οἱ μὲν οὖν περὶ Ἐμπεδοκλέα καὶ Δημόκριτον
λανθάνουσιν αὐτοὶ αὑτοὺς οὐ γένεσιν ἐξ ἀλλήλων ποιοῦντες,
ἀλλὰ φαινομένην γένεσιν· ἐνυπάρχον γὰρ ἕκαστον ἐκκρίνεσθαί
φασιν, ὥσπερ ἐξ ἀγγείου τῆς γενέσεως οὔσης, ἀλλ'
5 οὐκ ἔκ τινος ὕλης, οὐδὲ γίγνεσθαι μεταβάλλοντος. Ἔπειτα
κἂν οὕτως οὐδὲν ἧττον ἄλογα τὰ συμβαίνοντα. Τὸ γὰρ αὐτὸ
μέγεθος οὐ δοκεῖ συμπιληθὲν γίνεσθαι βαρύτερον. Ἀνάγκη δὲ
τοῦτο λέγειν τοῖς φάσκουσιν ἐκκρίνεσθαι τὸ ὕδωρ ἐκ τοῦ ἀέρος
ἐνυπάρχον· ὅταν γὰρ ὕδωρ ἐξ ἀέρος γένηται, βαρύτερόν
10 ἐστιν. Ἔτι δὲ τῶν μεμιγμένων σωμάτων οὐκ ἀνάγκη χωρισθὲν
θάτερον ἀεὶ πλείω τόπον ἐπέχειν· ὅταν δ' ἐξ ὕδατος ἀὴρ
γένηται, πλείω καταλαμβάνει τόπον· τὸ γὰρ λεπτομερέστερον
ἐν πλείονι τόπῳ γίγνεται. Φανερὸν δὲ τοῦτό γε καὶ ἐν
τῇ μεταβάσει· διατμιζομένου γὰρ καὶ πνευματουμένου τοῦ
15 ὑγροῦ ῥήγνυται τὰ περιέχοντα τοὺς ὄγκους ἀγγεῖα διὰ τὴν
στενοχωρίαν. Ὥστ' εἰ μὲν ὅλως μή ἐστι κενὸν μηδ' ἐπεκτείνεται
τὰ σώματα, καθάπερ φασὶν οἱ ταῦτα λέγοντες, φανερὸν
τὸ ἀδύνατον· εἰ δ' ἔστι κενὸν καὶ ἐπέκτασις, ἄλογον
τὸ ἐξ ἀνάγκης ἀεὶ πλείω τόπον ἐπιλαμβάνειν τὸ χωριζόμενον.
20 Ἀνάγκη δὲ καὶ ὑπολείπειν τὴν ἐξ ἀλλήλων γένεσιν,
εἴπερ ἐν τῷ πεπερασμένῳ μεγέθει μὴ ἐνυπάρχει ἄπειρα
πεπερασμένα. Ὅταν γὰρ ἐκ γῆς ὕδωρ γένηται, ἀφῄρηταί
τι τῆς γῆς, εἴπερ ἐκκρίσει ἡ γένεσις· καὶ πάλιν
ὅταν ἐκ τῆς ὑπολειπομένης, ὡσαύτως. Εἰ μὲν οὖν ἀεὶ τοῦτ'
25 ἔσται, συμβήσεται ἐν τῷ πεπερασμένῳ ἄπειρα ἐνυπάρχειν·
ἐπεὶ δὲ τοῦτ' ἀδύνατον, οὐκ ἂν ἀεὶ γίγνοιτο ἐξ ἀλλήλων. Ὅτι
μὲν οὖν οὐκ ἔστι τῇ ἐκκρίσει ἡ εἰς ἄλληλα μετάβασις, εἴρηται.
Λείπεται δ' εἰς ἄλληλα μεταβάλλοντα γίγνεσθαι.
Τοῦτο δὲ διχῶς· ἢ γὰρ τῇ μετασχηματίσει, καθάπερ ἐκ
30 τοῦ αὐτοῦ κηροῦ γίγνοιτ' ἂν σφαῖρα καὶ κύβος, ἢ τῇ διαλύσει
τῇ εἰς τὰ ἐπίπεδα, ὥσπερ ἔνιοί φασιν. Εἰ μὲν οὖν τῇ μετασχηματίσει
γίνεται, συμβαίνει ἐξ ἀνάγκης ἄτομα λέγειν
τὰ σώματα· διαιρετῶν γὰρ ὄντων οὐκ ἔσται τὸ τοῦ πυρὸς
μέρος πῦρ, οὐδὲ τὸ τῆς γῆς γῆ, διὰ τὸ μὴ εἶναι μήτε τὸ
35 τῆς πυραμίδος μέρος πάντως πυραμίδα μήτε τὸ τοῦ κύβου
1(1) What the followers of Empedocles do, though without observing it themselves, is to reduce the generation of elements out of one another to an illusion. They make it a process of excretion from a body of what was in it all the time-as though generation required a vessel rather than a material-so that it involves 5no change of anything. And even if this were accepted, there are other implications equally unsatisfactory. We do not expect a mass of matter to be made heavier by compression. But they will be bound to maintain this, if they say that water is a body present in air and excreted from air, since air becomes heavier when it turns into water. Again, when the mixed body is divided, they can show 10no reason why one of the constituents must by itself take up more room than the body did: but when water turns into air, the room occupied is increased. The fact is that the finer body takes up more room, as is obvious in any case of transformation. As the liquid is converted into vapour or air the vessel which contains it is often burst because it does not contain room enough. Now, if there is 15no void at all, and if, as those who take this view say, there is no expansion of bodies, the impossibility of this is manifest: and if there is void and expansion, there is no accounting for the fact that the body which results from division cfpies of necessity a greater space. It is inevitable, too, that generation of one out of another should come to a stop, since a finite quantum cannot 20contain an infinity of finite quanta. When earth produces water something is taken away from the earth, for the process is one of excretion. The same thing happens again when the residue produces water. But this can only go on for ever, if the finite body contains an infinity, which is impossible. Therefore the generation of elements out of one another will not always continue.
(2) We have now 25explained that the mutual transformations of the elements cannot take place by means of excretion. The remaining alternative is that they should be generated by changing into one another. And this in one of two ways, either by change of shape, as the same wax takes the shape both of a sphere and of a cube, or, as some assert, by resolution into planes. (a) Generation by change of shape would 30necessarily involve the assertion of atomic bodies. For if the particles were divisible there would be a part of fire which was not fire and a part of earth which was not earth, for the reason that not every part of a pyramid is a pyramid nor of a cube a cube. But if (b) the process is resolution into planes, the first difficulty is that the elements cannot all be generated out of one another.
(2) We have now 25explained that the mutual transformations of the elements cannot take place by means of excretion. The remaining alternative is that they should be generated by changing into one another. And this in one of two ways, either by change of shape, as the same wax takes the shape both of a sphere and of a cube, or, as some assert, by resolution into planes. (a) Generation by change of shape would 30necessarily involve the assertion of atomic bodies. For if the particles were divisible there would be a part of fire which was not fire and a part of earth which was not earth, for the reason that not every part of a pyramid is a pyramid nor of a cube a cube. But if (b) the process is resolution into planes, the first difficulty is that the elements cannot all be generated out of one another.
306a
1 κύβον. Εἰ δὲ τῇ τῶν ἐπιπέδων διαλύσει, πρῶτον μὲν ἄτοπον
τὸ μὴ πάντα γεννᾶν ἐξ ἀλλήλων, ὅπερ ἀνάγκη λέγειν αὐτοῖς,
καὶ λέγουσιν. Οὔτε γὰρ εὔλογον ἓν μόνον ἄμοιρον γενέσθαι
τῆς μεταβάσεως, οὔτε φαίνεται κατὰ τὴν αἴσθησιν,
5 ἀλλ' ὁμοίως πάντα μεταβάλλειν εἰς ἄλληλα. Συμβαίνει
δὲ περὶ τῶν φαινομένων λέγουσι μὴ ὁμολογούμενα λέγειν
τοῖς φαινομένοις. Τούτου δ' αἴτιον τὸ μὴ καλῶς λαβεῖν τὰς
πρώτας ἀρχάς, ἀλλὰ πάντα βούλεσθαι πρός τινας δόξας
ὡρισμένας ἀνάγειν. Δεῖ γὰρ ἴσως τῶν μὲν αἰσθητῶν αἰσθητάς,
10 τῶν δὲ ἀϊδίων ἀϊδίους, τῶν δὲ φθαρτῶν φθαρτὰς εἶναι
τὰς ἀρχάς, ὅλως δ' ὁμογενεῖς τοῖς ὑποκειμένοις. Οἱ δὲ διὰ
τὴν τούτων φιλίαν ταὐτὸ ποιεῖν ἐοίκασι τοῖς τὰς θέσεις ἐν
τοῖς λόγοις διαφυλάττουσιν· ἅπαν γὰρ ὑπομένουσι τὸ συμβαῖνον
ὡς ἀληθεῖς ἔχοντες ἀρχάς, ὥσπερ οὐκ ἐνίας δέον
15 κρίνειν ἐκ τῶν ἀποβαινόντων, καὶ μάλιστα ἐκ τοῦ τέλους.
Τέλος δὲ τῆς μὲν ποιητικῆς ἐπιστήμης τὸ ἔργον, τῆς δὲ φυσικῆς
τὸ φαινόμενον ἀεὶ κυρίως κατὰ τὴν αἴσθησιν. Συμβαίνει
δ' αὐτοῖς μάλιστα τὴν γῆν εἶναι στοιχεῖον, καὶ μόνην
ἄφθαρτον, εἴπερ τὸ ἀδιάλυτον ἄφθαρτόν τ' ἐστὶ καὶ στοιχεῖον·
20 ἡ γὰρ γῆ μόνη ἀδιάλυτος εἰς ἄλλο σῶμα. Ἀλλὰ
μὴν οὐδ' ἐν τοῖς διαλυομένοις ἡ τῶν τριγώνων παραιώρησις
εὔλογος. Συμβαίνει δὲ καὶ τοῦτο ἐν τῇ εἰς ἄλληλα μεταβάσει
διὰ τὸ ἐξ ἀνίσων τῷ πλήθει συνεστάναι τριγώνων. Ἔτι δ'
ἀνάγκη τοῖς ταῦτα λέγουσιν οὐκ ἐκ σώματος ποιεῖν γένεσιν·
25 ὅταν γὰρ ἐξ ἐπιπέδων γένηται, οὐκ ἐκ σώματος ἔσται γεγονός.
Πρὸς δὲ τούτοις ἀνάγκη μὴ πᾶν σῶμα λέγειν διαιρετόν,
ἀλλὰ μάχεσθαι ταῖς ἀκριβεστάταις ἐπιστήμαις· αἱ μὲν γὰρ
καὶ τὸ νοητὸν λαμβάνουσι διαιρετόν, αἱ μαθηματικαί, οἱ
δὲ οὐδὲ τὸ αἰσθητὸν ἅπαν συγχωροῦσι διὰ τὸ βούλεσθαι σῴζειν
30 τὴν ὑπόθεσιν. Ἀνάγκη γὰρ ὅσοι σχῆμα ποιοῦσιν ἑκάστου
τῶν στοιχείων καὶ τούτῳ διορίζουσι τὰς οὐσίας αὐτῶν, ἀδιαίρετα
ποιεῖν αὐτά· τῆς γὰρ πυραμίδος ἢ τῆς σφαίρας διαιρεθείσης
πως οὐκ ἔσται τὸ λειπόμενον σφαῖρα ἢ πυραμίς.
Ὥστε ἢ τὸ τοῦ πυρὸς μέρος οὐ πῦρ, ἀλλ' ἔσται τι πρότερον τοῦ
1This they are obliged to assert, and do assert. It is absurd, because it is unreasonable that one element alone should have no part in the transformations, and also contrary to the observed data of sense, according to which all alike change into one another. In fact their explanation of the observations 5is not consistent with the observations. And the reason is that their ultimate principles are wrongly assumed: they had certain predetermined views, and were resolved to bring everything into line with them. It seems that perceptible things require perceptible principles, eternal things eternal principles, corruptible things corruptible principles; and, in general, every 10subject matter principles homogeneous with itself. But they, owing to their love for their principles, fall into the attitude of men who undertake the defence of a position in argument. In the confidence that the principles are true they are ready to accept any consequence of their application. As though some principles did not require to be judged from their results, and particularly 15from their final issue! And that issue, which in the case of productive knowledge is the product, in the knowledge of nature is the unimpeachable evidence of the senses as to each fact.
The result of their view is that earth has the best right to the name element, and is alone indestructible; for that which is indissoluble is indestructible and elementary, and earth alone 20cannot be dissolved into any body but itself. Again, in the case of those elements which do suffer dissolution, the 'suspension' of the triangles is unsatisfactory. But this takes place whenever one is dissolved into another, because of the numerical inequality of the triangles which compose them. Further, those who hold these views must needs suppose that generation does not 25start from a body. For what is generated out of planes cannot be said to have been generated from a body. And they must also assert that not all bodies are divisible, coming thus into conflict with our most accurate sciences, namely the mathematical, which assume that even the intelligible is divisible, while they, in their anxiety to save their hypothesis, cannot even admit this 30of every perceptible thing. For any one who gives each element a shape of its own, and makes this the ground of distinction between the substances, has to attribute to them indivisibility; since division of a pyramid or a sphere must leave somewhere at least a residue which is not sphere or a pyramid.
The result of their view is that earth has the best right to the name element, and is alone indestructible; for that which is indissoluble is indestructible and elementary, and earth alone 20cannot be dissolved into any body but itself. Again, in the case of those elements which do suffer dissolution, the 'suspension' of the triangles is unsatisfactory. But this takes place whenever one is dissolved into another, because of the numerical inequality of the triangles which compose them. Further, those who hold these views must needs suppose that generation does not 25start from a body. For what is generated out of planes cannot be said to have been generated from a body. And they must also assert that not all bodies are divisible, coming thus into conflict with our most accurate sciences, namely the mathematical, which assume that even the intelligible is divisible, while they, in their anxiety to save their hypothesis, cannot even admit this 30of every perceptible thing. For any one who gives each element a shape of its own, and makes this the ground of distinction between the substances, has to attribute to them indivisibility; since division of a pyramid or a sphere must leave somewhere at least a residue which is not sphere or a pyramid.
306b
1 στοιχείου, διὰ τὸ πᾶν εἶναι ἢ στοιχεῖον ἢ ἐκστοιχείων·
ἢ οὐχ ἅπαν σῶμα διαιρετόν.
1Either, then, a part of fire is not fire, so that there is a body prior to the element-for every body is either an element or composed of elements-or not every body is divisible.
Book 3,Chapter 8 (306b3–307b24)
Ὅλως δὲ τὸ πειρᾶσθαι τὰ ἁπλᾶ σώματα σχηματίζειν
ἄλογόν ἐστι, πρῶτον μὲν ὅτι συμβήσεται μὴ ἀναπληροῦσθαι
5 τὸ ὅλον· ἐν μὲν γὰρ τοῖς ἐπιπέδοις τρία σχήματα
δοκεῖ συμπληροῦν τὸν τόπον, τρίγωνον καὶ τετράγωνον καὶ
ἑξάγωνον, ἐν δὲ τοῖς στερεοῖς δύο μόνον, πυραμὶς καὶ κύβος·
ἀνάγκη δὲ πλείω τούτων λαμβάνειν διὰ τὸ πλείω τὰ
στοιχεῖα ποιεῖν. Ἔπειτα φαίνεται πάντα μὲν τὰ ἁπλᾶ σώματα
10 σχηματιζόμενα τῷ περιέχοντι τόπῳ, μάλιστα δὲ τὸ
ὕδωρ καὶ ὁ ἀήρ. Διαμένειν μὲν οὖν τὸ τοῦ στοιχείου σχῆμα
ἀδύνατον· οὐ γὰρ ἂν ἥπτετο πανταχῇ τοῦ περιέχοντος τὸ
ὅλον. Ἀλλὰ μὴν εἰ μεταρρυθμισθήσεται, οὐκέτι ἔσται ὕδωρ,
εἴπερ τῷ σχήματι διέφερεν. Ὥστε φανερὸν ὅτι οὐκ ἔστιν ὡριςμένα
15 τὰ σχήματα αὐτῶν. Ἀλλ' ἔοικεν ἡ φύσις αὐτὴ τοῦτο
σημαίνειν ἡμῖν, ὃ καὶ κατὰ λόγον ἐστίν· ὥσπερ γὰρ ἐν
τοῖς ἄλλοις ἀειδὲς καὶ ἄμορφον δεῖ τὸ ὑποκείμενον εἶναι
(μάλιστα γὰρ ἂν οὕτω δύναιτο ῥυθμίζεσθαι, καθάπερ ἐν τῷ
Τιμαίῳ γέγραπται, τὸ πανδεχές), οὕτω καὶ τὰ στοιχεῖα δεῖ
20 νομίζειν ὥσπερ ὕλην εἶναι τοῖς συνθέτοις· διὸ καὶ δύναται
μεταβάλλειν εἰς ἄλληλα χωριζομένων τῶν κατὰ τὰ πάθη
διαφορῶν. Πρὸς δὲ τούτοις πῶς ἐνδέχεται γίγνεσθαι σάρκα
καὶ ὀστοῦν ἢ ὁτιοῦν τῶν συνεχῶν σωμάτων; οὔτε γὰρ ἐξ αὐτῶν
τῶν στοιχείων ἐγχωρεῖ διὰ τὸ μὴ γίγνεσθαι συνεχὲς ἐκ τῆς
25 συνθέσεως, οὔτ' ἐκ τῶν ἐπιπέδων συντιθεμένων· τὰ γὰρ στοιχεῖα
γεννᾶται τῇ συνθέσει καὶ οὐ τὰ ἐκ τῶν στοιχείων. Ὥστ'
ἐάν τις ἀκριβολογεῖσθαι βούληται καὶ μὴ ἐκ παρόδου τοὺς
λόγους ἀποδέχεσθαι τοὺς τοιούτους, ἀναιροῦντας ὄψεται τὴν
γένεσιν ἐκ τῶν ὄντων. Ἀλλὰ μὴν καὶ πρὸς τὰ πάθη τε καὶ
30 τὰς δυνάμεις καὶ τὰς κινήσεις ἀσύμφωνα τὰ σχήματα
τοῖς σώμασιν, εἰς ἃ μάλιστα βλέψαντες οὕτω διένειμαν.
Οἷον ἐπεὶ τὸ πῦρ εὐκίνητόν ἐστι καὶ θερμαντικὸν καὶ καυστικόν,
οἱ μὲν ἐποίησαν αὐτὸ σφαῖραν, οἱ δὲ πυραμίδα· ταῦτα
γὰρ εὐκινητότατα μὲν διὰ τὸ ἐλαχίστων ἅπτεσθαι καὶ ἥκιστα
In general, the attempt to give a shape to each of the simple bodies is unsound, for the reason, first, that they will not 5succeed in filling the whole. It is agreed that there are only three plane figures which can fill a space, the triangle, the square, and the hexagon, and only two solids, the pyramid and the cube. But the theory needs more than these because the elements which it recognizes are more in number. Secondly, it is manifest that the simple bodies are often given a shape by the place 10in which they are included, particularly water and air. In such a case the shape of the element cannot persist; for, if it did, the contained mass would not be in continuous contact with the containing body; while, if its shape is changed, it will cease to be water, since the distinctive quality is shape. Clearly, then, their shapes are not fixed. Indeed, nature itself seems 15to offer corroboration of this theoretical conclusion. Just as in other cases the substratum must be formless and unshapen-for thus the 'all-receptive', as we read in the Timaeus, will be best for modelling-so the elements should be conceived as a material for composite things; and that is why they can put off their qualitative distinctions and pass into one another. Further, 20how can they account for the generation of flesh and bone or any other continuous body? The elements alone cannot produce them because their collocation cannot produce a continuum. Nor can the composition of planes; for this produces the elements themselves, not bodies made up of them. Any one then who insists upon an exact statement of this kind of theory, instead of assenting 25after a passing glance at it, will see that it removes generation from the world.
Further, the very properties, powers, and motions, to which they paid particular attention in allotting shapes, show the shapes not to be in accord with the bodies. Because fire is mobile and productive of heat and combustion, some made it a sphere, others a pyramid. These shapes, they thought, 30were the most mobile because they offer the fewest points of contact and are the least stable of any; they were also the most apt to produce warmth and combustion, because the one is angular throughout while the other has the most acute angles, and the angles, they say, produce warmth and combustion.
Further, the very properties, powers, and motions, to which they paid particular attention in allotting shapes, show the shapes not to be in accord with the bodies. Because fire is mobile and productive of heat and combustion, some made it a sphere, others a pyramid. These shapes, they thought, 30were the most mobile because they offer the fewest points of contact and are the least stable of any; they were also the most apt to produce warmth and combustion, because the one is angular throughout while the other has the most acute angles, and the angles, they say, produce warmth and combustion.
307a
1 βεβηκέναι, θερμαντικώτατα δὲ καὶ καυστικώτατα,
διότι τὸ μὲν ὅλον ἐστὶ γωνία, τὸ δὲ ὀξυγωνιώτατον, καίει
δὲ καὶ θερμαίνει ταῖς γωνίαις, ὥς φασιν. Πρῶτον μὲν οὖν
κατὰ τὴν κίνησιν ἀμφότεροι διημαρτήκασιν· εἰ γὰρ καὶ
5 ἔστιν εὐκινητότατα ταῦτα τῶν σχημάτων, ἀλλ' οὐ τὴν τοῦ
πυρὸς κίνησιν εὐκίνητα· ἡ μὲν γὰρ τοῦ πυρὸς ἄνω καὶ κατ'
εὐθεῖαν, ταῦτα δ' εὐκίνητα κύκλῳ, τὴν καλουμένην κύλισιν.
Ἔπειτ' εἰ ἔστιν ἡ γῆ κύβος διὰ τὸ βεβηκέναι καὶ μένειν,
μένει δ' οὐχ οὗ ἔτυχεν ἀλλ' ἐν τῷ αὑτῆς τόπῳ, ἐκ δὲ
10 τοῦ ἀλλοτρίου φέρεται μὴ κωλυομένη, καὶ τὸ πῦρ δὲ καὶ
τὰ ἄλλα ὡσαύτως, δῆλον ὅτι καὶ τὸ πῦρ καὶ ἕκαστον τῶν
στοιχείων ἐν μὲν τῷ ἀλλοτρίῳ τόπῳ σφαῖρα ἔσται ἢ πυραμίς,
ἐν δὲ τῷ οἰκείῳ κύβος. Ἔτι δ' εἰ θερμαίνει καὶ καίει
τὸ πῦρ διὰ τὰς γωνίας, ἅπαντα ἔσται τὰ στοιχεῖα θερμαντικά,
15 μᾶλλον δ' ἴσως ἕτερον ἑτέρου· πάντα γὰρ ἔχει γωνίας,
οἷον τό τε ὀκτάεδρον καὶ τὸ δωδεκάεδρον. (Δημοκρίτῳ
δὲ καὶ ἡ σφαῖρα, ὡς γωνία τις οὖσα, τέμνει ὡς εὐκίνητον).
Ὥστε διοίσει τῷ μᾶλλον καὶ ἧττον. Τοῦτο δ' ὅτι ψεῦδος,
φανερόν. Ἅμα δὲ συμβήσεται καὶ τὰ μαθηματικὰ σώματα
20 καίειν καὶ θερμαίνειν· ἔχει γὰρ κἀκεῖνα γωνίας,
καὶ ἔνεισιν ἐν αὐτοῖς ἄτομοι καὶ σφαῖραι καὶ πυραμίδες,
ἄλλως τε καὶ εἰ ἔστιν ἄτομα μεγέθη, καθάπερ φασίν. Εἰ
γὰρ τὰ μὲν τὰ δὲ μή, λεκτέον τὴν διαφοράν, ἀλλ' οὐχ
ἁπλῶς οὕτω λεκτέον ὡς λέγουσιν. Ἔτι εἰ τὸ καιόμενον πυροῦται,
25 τὸ δὲ πῦρ ἐστι σφαῖρα ἢ πυραμίς, ἀνάγκη τὸ καιόμενον
γίγνεσθαι σφαίρας ἢ πυραμίδας. Τὸ μὲν οὖν τέμνειν
καὶ διαιρεῖν ἔστω κατὰ λόγον συμβαῖνον τῷ σχήματι·
τὸ δ' ἐξ ἀνάγκης τὴν πυραμίδα ποιεῖν πυραμίδας
ἢ τὴν σφαῖραν σφαίρας παντελῶς ἄλογον, καὶ ὅμοιον ὥςπερ
30 εἴ τις ἀξιοίη τὴν μάχαιραν εἰς μαχαίρας διαιρεῖν ἢ
τὸν πρίονα εἰς πρίονας. Ἔτι δὲ γελοῖον πρὸς τὸ διαιρεῖν μόνον
ἀποδοῦναι τὸ σχῆμα τῷ πυρί· δοκεῖ γὰρ μᾶλλον συγκρίνειν
καὶ συνορίζειν ἢ διακρίνειν. Διακρίνει μὲν γὰρ τὰ μὴ
1Now, in the first place, with regard to movement both are in error. These may be the figures best adapted to movement; they are not, however, well adapted to the movement of fire, which is an upward and rectilinear movement, but rather to that form of circular movement which 5we call rolling. Earth, again, they call a cube because it is stable and at rest. But it rests only in its own place, not anywhere; from any other it moves if nothing hinders, and fire and the other bodies do the same. The obvious inference, therefore, is that fire and each several element is in a foreign place a sphere or a pyramid, but in its 10own a cube. Again, if the possession of angles makes a body produce heat and combustion, every element produces heat, though one may do so more than another. For they all possess angles, the octahedron and dodecahedron as well as the pyramid; and Democritus makes even the sphere a kind of angle, which cuts things because of its mobility. The 15difference, then, will be one of degree: and this is plainly false. They must also accept the inference that the mathematical produce heat and combustion, since they too possess angles and contain atomic spheres and pyramids, especially if there are, as they allege, atomic figures. Anyhow if these functions belong to some of these things and not to 20others, they should explain the difference, instead of speaking in quite general terms as they do. Again, combustion of a body produces fire, and fire is a sphere or a pyramid. The body, then, is turned into spheres or pyramids. Let us grant that these figures may reasonably be supposed to cut and break up bodies as fire does; still it remains 25quite inexplicable that a pyramid must needs produce pyramids or a sphere spheres. One might as well postulate that a knife or a saw divides things into knives or saws. It is also ridiculous to think only of division when allotting fire its shape. Fire is generally thought of as combining and connecting rather than as separating. For though it 30separates bodies different in kind, it combines those which are the same; and the combining is essential to it, the functions of connecting and uniting being a mark of fire, while the separating is incidental.
307b
1 ὁμόφυλα, συγκρίνει δὲ τὰ ὁμόφυλα· καὶ ἡ μὲν σύγκρισις
καθ' αὑτό ἐστι (τὸ γὰρ συνορίζειν καὶ ἑνοῦν τοῦ πυρός),
ἡ δὲ διάκρισις κατὰ συμβεβηκός (συγκρῖνον γὰρ τὸ ὁμόφυλον
ἐξαιρεῖ τὸ ἀλλότριον). Ὥστ' ἢ πρὸς ἄμφω ἐχρῆν
5 ἀποδοῦναι ἢ μᾶλλον ἐπὶ τὸ συγκρίνειν. Πρὸς δὲ τούτοις,
ἐπεὶ τὸ θερμὸν καὶ τὸ ψυχρὸν ἐναντία τῇ δυνάμει, ἀδύνατον
ἀποδοῦναι τῷ ψυχρῷ σχῆμά τι· δεῖ γὰρ ἐναντίον
εἶναι τὸ ἀποδιδόμενον, οὐθὲν δ' ἐναντίον ἐστὶ σχῆμα σχήματι.
Διὸ καὶ πάντες ἀπολελοίπασι τοῦτο· καίτοι προσῆκεν ἢ
10 πάντα ἀφορίσαι σχήμασιν ἢ μηδέν. Ἔνιοι δὲ περὶ τῆς δυνάμεως
αὐτοῦ πειραθέντες εἰπεῖν ἐναντία λέγουσιν αὐτοὶ αὑτοῖς.
Φασὶ γὰρ εἶναι ψυχρὸν τὸ μεγαλομερὲς διὰ τὸ συνθλίβειν καὶ
μὴ διιέναι διὰ τῶν πόρων. Δῆλον τοίνυν ὅτι καὶ τὸ θερμὸν
ἂν εἴη τὸ διιόν· τοιοῦτον δ' ἀεὶ τὸ λεπτομερές. Ὥστε συμβαίνει
15 μικρότητι καὶ μεγέθει διαφέρειν τὸ θερμὸν καὶ τὸ
ψυχρόν, ἀλλ' οὐ τοῖς σχήμασιν. Ἔτι δ' εἰ ἄνισοι αἱ πυραμίδες,
αἱ μεγάλαι ἂν εἶεν οὐ πῦρ οὐδ' αἴτιον τὸ σχῆμα τοῦ
καίειν, ἀλλὰ τοὐναντίον. Ὅτι μὲν οὖν οὐ τοῖς σχήμασι διαφέρει
τὰ στοιχεῖα, φανερὸν ἐκ τῶν εἰρημένων· ἐπεὶ δὲ κυριώταται
20 διαφοραὶ τῶν σωμάτων αἵ τε κατὰ τὰ πάθη καὶ τὰ
ἔργα καὶ τὰς δυνάμεις (ἑκάστου γὰρ εἶναί φαμεν τῶν φύσει
καὶ ἔργα καὶ πάθη καὶ δυνάμεις), πρῶτον ἂν εἴη περὶ
τούτων λεκτέον, ὅπως θεωρήσαντες ταῦτα λάβωμεν τὰς ἑκάστου
πρὸς ἕκαστον διαφοράς.
1For the expulsion of the foreign body is an incident in the compacting of the homogeneous. In choosing the shape, then, they should have thought either of both functions or preferably of the combining function. In addition, since hot and cold are contrary powers, it is 5impossible to allot any shape to the cold. For the shape given must be the contrary of that given to the hot, but there is no contrariety between figures. That is why they have all left the cold out, though properly either all or none should have their distinguishing figures. Some of them, however, do attempt to explain this power, and 10they contradict themselves. A body of large particles, they say, is cold because instead of penetrating through the passages it crushes. Clearly, then, that which is hot is that which penetrates these passages, or in other words that which has fine particles. It results that hot and cold are distinguished not by the figure but by the size 15of the particles. Again, if the pyramids are unequal in size, the large ones will not be fire, and that figure will produce not combustion but its contrary.
From what has been said it is clear that the difference of the elements does not depend upon their shape. Now their most important differences are those of property, function, and 20power; for every natural body has, we maintain, its own functions, properties, and powers. Our first business, then, will be to speak of these, and that inquiry will enable us to explain the differences of each from each.
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From what has been said it is clear that the difference of the elements does not depend upon their shape. Now their most important differences are those of property, function, and 20power; for every natural body has, we maintain, its own functions, properties, and powers. Our first business, then, will be to speak of these, and that inquiry will enable us to explain the differences of each from each.
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