^{page 113 note 2} Anal. Post. Ch. 2.

^{page 113 note 3} This characteristic is not actually stated in Ch. 2, in the enumeratiion of the characteristics of the ⋯ρχα⋯ of science. But it is implied by by 71b 13 and stated in Ch. 6; and I have therefore included it.

^{page 114 note 1} Cf. Ross, , Aristotle, p. 43Google Scholar. Dr. Ross (ibid. p. 44) notices the similarity between Aristotle's and Euclid's account of first principles: but does not work it or its implications out in any detail.

^{page 115 note 1} According to Aristotle the geometer must assume the existence of points and lines (76b 5): Euclid's Postulates 1 to 3 may in eflect be said to do this, declaring the possibility of drawing a but straight line between any two points, of producing a straight line indefinitely, and of describing a circle, ‘the only “lines” beside straight lines used in the elements’ (Heath, E. 146). Postulates 4 and 5 are also closely connected with constructions (Heath, , G.M. P. 375Google Scholar, q.v.): but v. below sect. 7.

^{page 116 note 1} Heath, E. p. 119 does not seem to keep these two senses distinct: at any rate he gives no indication that it is with a subsidiary sense only of hypothesis that Aristotle is dealing in this passage.

He remarks also (p. 119) that 76b 32, ἔστιναἴτημα τ⋯ ὐπεναντ⋯ον τοὐ μανθ⋯νοντος τῇ δοξῇ, ἤ ⋯ ἄντις ⋯ποδεικτ⋯ν ὂν λαμβ⋯νῃ κα⋯ χρ⋯ται μ⋯ δε⋯ξας, ‘gives a wider meaning to “postulate” which would cover “hypothesis” as well.’ If the reading given is correct, it is still only the subsidiary sense of hypothesis that would be covered. I prefer to leave out the ἤ with the Oxford Translation, thus making the sentence a definition postulate simply.

^{page 116 note 2} There seems to be a still further sense of hypothesis defined in 76b 39–77a 3: ‘assumptions which serve to bring the truth of the conclusion home to the student but whose truth is not required by the proof; e.g., the geometer's assumption that the line he draws is a foot long or that it is straight.’ (Ross, , Aristotle, p. 44.)Google Scholar

^{page 116 note 3} Cf. αἰτεῖν=to beg the question. αἴτημα scarcely occurs often enought in Aristotle to be a technical term. The Index Aristotelicus gives five references apart from this passage: 97a 21, where it again has the meaning illegitimate assumption: 86a 34, and 418b 26, where it seems neutral, meaning simply assumption: 1433b 17 ff. where a rhetorical postulate (referred to also at 1428a 8) is defined—a different sense entirely from the logical.

^{page 118 note 1} Used as a text-book by the Academy (Heath, l.c.).

^{page 118 note 2} Cf. Procl, . Eucl. I, p. 66Google Scholar, quoted Heath, , G.M. 320Google Scholar.

^{page 120 note 1} ‘αἴσθησις … is the most general term for immediate perception whether sensuous or intellectual’ (Burnet, , Ethics, Introd. p. xxxviii)Google Scholar.

^{page 120 note 2} I agree with Grant that it is to the intuitive perception of νο⋯ς that Aristotle, is here referring (Ethics, p. 453Google Scholar: note ad loc), rather than with Stewart, who says he refers to sense perception as the basis of ⋯παγωγ⋯ (Notes on N.E. Vol. I, p. 112).

^{page 120 note 3} Cf. Plato's ἄψασθαι.

^{page 120 note 4} Cf. ‘It is by perception or intuition that the first principles of mathematics, for instance, are apprehended’ (Burnet, , Ethics, Introd. p. xxxvii)Google Scholar.

^{page 121 note 1} Cf. Burnet, , Ethics, p. 39Google Scholar, note on ⋯θισμῷ 1098b 4: Stewart, Notes on the N.E. Vol I, pp. 112–3: Grant, , Ethics, Vol. I, p. 453Google Scholar.

^{page 122 note 1} The ‘particulars’ involved in this induction are species, e.g., man, horse and mule in the example Aristotle gives: v. Ross, , Aristotle, p. 39Google Scholar.

^{page 123 note 1} Cf. Burnet, : Ethics, Introd. §§ 24Google Scholar and 25 for the dialectical method in ethics.