Aristotle, Mechanical Problems

LCL 307: 332-333

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Aristotle

847 b καὶ ταῦτα μετὰ βάρους πλείονος· ὃ γὰρ ἄνευ μοχλοῦ κινεῖν οὐ δύναταί τις, τοῦτο ταὐτὸ βάρος, 15προσλαβὼν ἔτι τὸ τοῦ μοχλοῦ βάρος, κινεῖ θᾶττον.

Πάντων δὲ τῶν τοιούτων ἔχει τῆς αἰτίας τὴν ἀρχὴν ὁ κύκλος. καὶ τοῦτο εὐλόγως συμβέβηκεν· ἐκ μὲν γὰρ θαυμασιωτέρου συμβαίνειν τι θαυμαστὸν οὐδὲν ἄτοπον, θαυμασιώτατον δὲ τὸ τἀναντία γίνεσθαι μετ᾿ ἀλλήλων. ὁ δὲ κύκλος συνέστηκεν 20ἐκ τοιούτων· εὐθὺς γὰρ ἐκ κινουμένου τε γεγένηται καὶ μένοντος, ὧν ἡ φύσις ἐστὶν ὑπεναντία ἀλλήλοις. ὥστ᾿ ἐνταῦθα ἔστιν ἐπιβλέψασιν ἧττον θαυμάζειν τὰς συμβαινούσας ὑπεναντιώσεις περὶ αὐτόν. πρῶτον μὲν γὰρ τῇ περιεχούσῃ γραμμῇ τὸν κύκλον, πλάτος οὐθὲν ἐχούσῃ, τἀναντία πως προσεμφαίνεται, 25τὸ κοῖλον καὶ τὸ κυρτόν. ταῦτα δὲ διέστηκεν ἀλλήλων ὃν τρόπον τὸ μέγα καὶ τὸ μικρόν· ἐκείνων τε γὰρ μέσον τὸ ἴσον καὶ τούτων τὸ εὐθύ. διὸ μεταβάλλοντα εἰς ἄλληλα τὰ μὲν ἀναγκαῖον 848 aἴσα γενέσθαι πρότερον ἢ τῶν ἄκρων ὁποτερονοῦν, τὴν δὲ γραμμὴν εὐθεῖαν, ὅταν ἐκ κυρτῆς εἰς κοῖλον ἢ πάλιν ἐκ ταύτης γίνηται κυρτὴ καὶ περιφερής. ἓν μὲν οὖν τοῦτο τῶν ἀτόπων ὑπάρχει περὶ τὸν κύκλον, δεύτερον δὲ ὅτι ἅμα κινεῖται τὰς ἐναντίας 5κινήσεις· ἅμα γὰρ εἰς τὸν ἔμπροσθεν κινεῖται τόπον καὶ τὸν ὄπισθεν. ἥ τε γράφουσα γραμμὴ τὸν κύκλον ὡσαύτως ἔχει· ἐξ οὗ γὰρ ἄρχεται τόπου τὸ πέρας αὐτῆς, εἰς τὸν αὐτὸν τοῦτον τόπον ἔρχεται πάλιν· συνεχῶς γὰρ κινουμένης αὐτῆς τὸ ἔσχατον πάλιν ἀπῆλθε πρῶτον, ὥστε καὶ φανερὸν ὅτι μετέβαλεν 10ἐντεῦθεν.

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Mechanical Problems

force, and that, too, when a greater weight is involved. For the very same weight, which a man cannot move without a lever, he quickly moves by applying the weight of the lever.

Now the original cause of all such phenomena is the The peculiarities of the circle. circle; and this is natural, for it is in no way strange that something remarkable should result from something more remarkable, and the most remarkable fact is the combination of opposites with each other. The circle is made up of such opposites, for to begin with it is composed both of the moving and of the stationary,a which are by nature opposite to each other. So when one reflects on this, it becomes less remarkable that opposites should exist in it. First of all, in the circumference of the circle which has no breadth, an opposition of the kind appears, the concave and the convex. These differ from each other in the same way as the great and small; for the mean between these latter is the equal, and between the former is the straight line. Therefore, as in the former case, if they were to change into each other they must become equal before they could pass to either of the extremes, so also the line must become straight either when it changes from convex to concave, or by the reverse process becomes a convex curve. This, then, is one peculiarity of the circle, and a second is that it moves simultaneously in opposite directions; for it moves simultaneously forwards and backwards, and the radius which describes it behaves in the same way; for from whatever point it begins, it returns again to the same point; and as it moves continuously the last point again becomes the first in such a way that it is evidently changed from its first position.

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DOI: 10.4159/DLCL.aristotle-mechanical_problems.1936