§4.2#12 Τῶν δὴ πρότερον ἐλθόντων ἐπὶ τὴν περὶ τούτων σκέψιν σχεδὸν οἱ πλεῖστοι περὶ τῶν οὕτω βαρέων καὶ κούφων εἰρήκασι μόνον, ὅσων ἀμφοτέρων ἐχόντων βάρος θάτερόν ἐστι κουφότερον.
2 Now, of those who previously entered upon the inquiry into these things, nearly the majority have spoken only of such heavy and light things of which, both possessing weight, one of them is lighter.
οὕτω δὲ διελθόντες οἴονται διωρίσθαι καὶ περὶ τοῦ ἀπλῶς κούφου καὶ βαρέος·
And having distinguished them in this way, they think they have defined also the absolutely light and heavy.
ὁ δὲ λόγος αὐτοῖς οὐκ ἐφαρμόττει.
But their account does not apply to them.
δῆλον δʼ ἔσται τοῦτο μᾶλλον προελθοῦσιν.
This will be clearer as we proceed.
λέγουσι γὰρ τὸ κουφότερον καὶ βαρύτερον οἱ μὲν ὥσπερ ἐν τῷ Τικαίῳ τυγχάνει γεγραμμένον, βαρύτερον μὲν τὸ ἐκ πλειόνων τῶν αὐτῶν συνεστός, κουφότερον δὲ τὸ ἐξ ἐλαττόνων, ὥσπερ μολίβδου μόλιβδος ὁ πλείων βαρύτερος καὶ χαλκοῦ χαλκός.
For some speak of the lighter and heavier as it happens to be written in the Timaeus: that the heavier is that which is composed of more of the same constituents, and the lighter is that composed of fewer, just as a larger quantity of lead is heavier than a smaller, and a larger quantity of bronze is heavier than a smaller.
ὁμοίως δὲ καὶ τῶν ἄλλων τῶν ὁμοειδῶν ἕκαστον· ἐν ὑπεροχῇ γὰρ τῶν ἴσων μορίων βαρύτερον ἕκαστόν ἐστιν.
And likewise with each of the other things of the same kind; for each is heavier by the excess of equal parts.
τὸν αὐτὸν δὲ τρόπον καὶ ξύλου μόλιβδόν φασιν· ἔκ τινων γὰρ τῶν αὐτῶν εἶναι πάντα τὰ σώματα καὶ μιᾶς ὕλης, ἀλλʼ οὐ δοκεῖν.
In the same way, they also say that lead is heavier than wood; for they say that all bodies are made of certain identical things and of one matter, though they do not appear to be.
οὕτω δὴ διωρισμένων οὐκ εἴρηται περὶ τοῦ ἁπλῶς πούφου καὶ βαρέος·
But if they are defined in this way, nothing has been said about the absolutely light and heavy.
νῦν γὰρ τὸ μὲν πῦρ ἀεὶ ποῦφον καὶ ἄνω φέρεται, ἡ δὲ γῇ καὶ τὰ γεηρὰ πάντα κάτω καὶ πρὸς τὸ μέσον.
For as it is, fire is always light and is carried upward, while earth and all earthy things are carried downward and toward the center.
ὥστʼ οὐ διʼ ὀλιγότητα τῶν τριγώνων ἐξ ὧν συνεστάναι φασὶν ἕκαστον αὐτῶν, τὸ πῦρ ἄνω φέρεσθαι πέφυκεν· τό τε γὰρ πλεῖον ἧττον ἂν ἐφέρετο καὶ βαρύτερον ἂν ἦν ἐκ πλειόνων ὄν τριγώνων.
Hence, it is not because of the small number of triangles from which they say each of them is composed that fire is naturally carried upward; for the larger quantity of fire would be carried upward less, and would be heavier, being composed of more triangles.
νῦν δὲ φαίνεται τοὐναντίον· ὅσῳ γὰρ ἂν ᾖ πλεῖον, κουφότερόν ἐστι καὶ ἄνω φέρεται θᾶττον.
But in fact the contrary is observed; for the more there is, the lighter it is and the faster it is carried upward.
καὶ ἄνωθεν δὲ κάτω τὸ ὀλίγον οἰσθήσεται θάττον πῦρ, τὸ δὲ πολὺ βραδύτερον.
And from above downward, a small quantity of fire will be carried faster, and a large quantity more slowly.
πρὸς δὲ τούτοις, ἐπεὶ τὸ μὲν ἐλάσσω ἔχον τὰ ὁμογενῆ κουφότερον εἶναί φασι, τὸ δὲ πλείω βαρύτερον, ἀέρα δὲ καὶ ὕδωρ καὶ πῦρ ἐκ τῶν αὐτῶν εἶναι τριγώνων, ἀλλὰ διαφέρειν ὀλιγότητι καὶ πλήθει, διὸ τὸ μὲν αὐτῶν εἶναι κουφότερον τὸ δὲ βαρύτερον, ἔσται τι πλῆθος ἀέρος ὁ βαρύτερον ὕδατος ἔσται.
In addition to these points, since they say that what has fewer homogeneous parts is lighter, and what has more is heavier, and that air and water and fire are composed of the same triangles, but differ in fewness and multitude, which is why one of them is lighter and another heavier, there will be some quantity of air which will be heavier than water.
συμβαίνει δὲ πᾶν τοὐναντίον· ἀεί τε γὰρ ὁ πλείων ἀὴρ ἄνω φέρεται μᾶλλον, καὶ ὅλως ὁτιοῦν μέρος ἀέρος ἄνω φέρεται ἐκ τοῦ ὕδατος.
But the very opposite happens; for a larger quantity of air is always carried upward more, and in general any part of air whatever is carried upward out of water.
εἱ μὲν οὖν τοῦτον τὸν τρόπον περὶ κούφου καὶ βαρέος διώρισαν·
Some, then, defined the light and heavy in this way.
τοῖς δʼ οὖχ ἱκανὸν ἔδοξεν οὕτω διελεῖν, ἀλλὰ καίπερ ὄντες ἀρχαιότεροι τῆς νῶν ἡλικίας καινοτέρως ἐνόησαν περὶ τῶν νῦν λεχθέντων.
But to others, it did not seem sufficient to distinguish them in this way; instead, although they were older than our present generation, they thought about the things just mentioned in a more novel way.
φαίνεται γὰρ ἔνια τὸν ὄγκον μὲν ἐλάττω τῶν σωμάτων, ὄντα δὲ βαρύτερα.
For some bodies are observed to be smaller in volume but heavier.
δῆλον οὖν ὡς οὐχ ἱκανὸν τὸ φάσκειν ἐξ ἴσων συγκεῖσθαι τῶν πρώτων τὰ ἰσοβαρῆ· ἴσα γὰρ ἂν ἦν τὸν ὄγκον.
Hence, it is clear that it is not sufficient to claim that things of equal weight are composed of equal first elements; for they would then be equal in volume.
τὰ δὲ πρῶτα καὶ ἄτομα τοῖς μὲν ἐπίπεδα λέγουσιν ἐξ ὧν συνέστηκε τὰ βάρος ἔχοντα τῶν σωμάτων, ἄτοπον τὸ φάναι·
Now, for those who say that the first and indivisible parts, from which bodies possessing weight are composed, are planes, it is absurd to say this; but for those who say they are solids, it is more possible to say that the larger of them is heavier.
τοῖς δὲ στερεὰ μᾶλλον ἐνδέχεται λέγειν τὸ μεῖζον εἶναι βαρύτερον αὐτῶν, τῶν δὲ συνθέτων, ἐπειδήπερ οὐ φαίνεται τοῦτον ἔχειν ἕκαστον τὸν τρόπον, ἀλλὰ πολλὰ βαρύτερα ὁρῶμεν ἐλάττω τὸν ὄγκον ὄντα, καθάπερ ἐρίου χαλκόν, ἕτερον τὸ αἴτιον οἴονταί τε καὶ λέγουσιν ἔνιοι·
However, regarding composite things, since each does not appear to be this way, but we see many things that are heavier while being smaller in volume, as copper is in comparison with wool, some think and state that the cause is different.
τὸ γὰρ κενὸν ἐμπεριλαμβανόμενον κουφίζειν τὰ σώματά φασι καὶ ποιεῖν ἔστιν ὅτε τὰ μείζω κουφότερα·
For they say that the void enclosed within lightens the bodies and sometimes makes the larger ones lighter, because they contain more void.
πλεῖον γὰρ ἔχειν κενόν. διὰ τοῦτο γὰρ καὶ τὸν ὄγκον εἶναι μείζω συγκείμενα πολλάκις ἐξ ἴσων στερεῶν ἢ καὶ ἐλαττόνων, ὅλως δὲ καὶ παντὸς αἴτιον εἶναι τοῦ κουφοτέρου τὸ πλεῖον ἐνυπάρχειν κενόν.
For this reason, indeed, they are also larger in volume, often though composed of equal or even fewer solids, and in general, the cause of everything being lighter is the presence of more void within.
λέγουσι μὲν οὖν τοῦτον τὸν τρόπον, ἀνάγκη δὲ προσθεῖναι τοῖς οὕτω διορίζουσι μὴ μόνον τὸ κενὸν ἔχειν πλεῖον, ἄν ᾖ κουφότερον, ἀλλὰ καὶ τὸ στερεὸν ἔλαττον·
Now they speak in this way, but it is necessary for those who define things in this way to add that if a thing is lighter, it must not only have more void, but also less solid.
εἰ γὰρ ὑπερέξει τῆς τοιαύτης ἀναλογίας, οὐκ ἔσται κουφότερον.
For if it exceeds such a proportion, it will not be lighter.
διὰ γὰρ τοῦτο καὶ τὸ πῦρ εἶναί φασι κουφότατον, ὅτι πλεῖστον ἔχει κενόν.
For this is also why they say that fire is the lightest, because it contains the most void.
συμβήσεται οὖν μικροῦ πυρὸς πολὺν χρυσὸν πλεῖον ἔχοντα τὸ κενὸν εἶναι κουφότερον, εἰ μὴ καὶ στερεὸν ἕξει πολλαπλάσιον· ὥστε τοῦτο λεκτέον.
It will follow, then, that a large quantity of gold, containing more void than a small quantity of fire, would be lighter, unless it also contains many times more solid; so this must be stated.
ἔνιοι μὲν οὖν τῶν μὴ φασκόντων εἶναι κενὸν οὐδὲν διώρισαν περὶ κούφου καὶ βαρέος, οἷον Ἀναξαγόρας καὶ Ἐμπεδοκλῆς· οἱ δὲ διορίσαντες μέν, οὐ φάσκοντες δὲ εἶναι κενόν, οὐδὲν εἶπον διὰ τί τὰ μὲν ἀπλῶς κοῦφα τὰ δὲ βαρέα τῶν σωμάτων, καὶ φέρεται τὰ μὲν ἀεὶ ἄνω τὰ δὲ κάτω.
Now some of those who deny the existence of a void defined nothing about the light and heavy, as for instance Anaxagoras and Empedocles; while those who did define them, though denying the existence of a void, gave no explanation of why some bodies are absolutely light and others heavy, and why some are always carried upward and others downward.