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καὶ τὸ ἀλυπότερον καὶ τὸ μεθ᾽ ἡδονῆς] Top. Γ 2, 117 a 23, καὶ ταὐτὰ μεθ᾽ ἡδονῆς μᾶλλον ἄνευ ἡδονῆς. καὶ ταὐτὰ μετ̓ ἀλυπίας μᾶλλον μετὰ λύπης. The desirability of anything even which is desirable in itself or on other grounds, as things useful, is increased by the addition of any pleasure that accompanies such things; so the ἐνέργειαι are completed and perfected by the accompanying ἡδονή in each case, Eth. N. X 3, 4, 5. And likewise the absence of pain, as compared with its presence, may be regarded as a positive good. The topic in the Rhetoric combines the two, positive pleasure and negative relief from pain; these together being ‘more than one’ are superior to either of the two separately. καί is therefore ‘together with’; and ὥστε ὑπάρχει κ.τ.λ. ‘and so (in the case supposed) we have (there are there, ὑπάρχει) the positive pleasure and the absence of pain, which may both be regarded as a good’.

καὶ δυοῖν...τὸ ὅλον ποιεῖ] A + B is greater than A + C, therefore B is greater than C. Top. Γ 5, 119 a 22, ἔτι ἐκ τῆς προσθέσεως, εἰ τῷ αὐτῷ προστιθέμενον τὸ ὅλον μᾶλλον ποιεῖ τοιοῦτο, εἰ τῷ ἧττον τοιούτῳ προστιθέμενον τὸ ὅλον μᾶλλον ποιεῖ τοιοῦτο. In the second of these two cases, if the addition of a quantity to the less of two other quantities makes the sum total of the two greater than the sum total arising from the addition of another different quantity to the other, we may infer that the former of the two added quantities is greater than or preferable to the latter. 4 is less than 6: if the addition of 8 to 4 produces a total 12, which is greater than the total resulting from the addition of an unknown quantity x, to 6, and therefore less than 12, we may infer (by calculation) that x is less than 8.

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