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1 See 929 B and note a on p. 48 supra.
2 This expression is intended to have the same sense as πρὸς ἴσας γίγνεσθαι γωνίας ἀνάκλασιν πᾶσαν (930 A infra), and both of them mean (pace Raingeard, p. 100, and Kepler in note 28 to his translation) ‘the angle of reflection is always equal to the angle of incidence.’ Cf. [Euclid], Catoptrica a´ (= Euclid, Opera Omnia, vii, p. 286. 21-22 [Heiberg]) with Olympiodorus, In Meteor. p. 212. 7 = Hero Alexandrinus, Opera, ii. 1, p. 368. 5 (Nix-Schmidt) and [Ptolemy], De Speculis, ii = Hero Alexandrinus, Opera, ii. 1, p. 320. 12-13 (Nix-Schmidt); and contrast the more precise formulation of Philoponus, In Meteor. p. 27. 34-35.
5 See note e on 929 F supra.
6 It has been suggested that οὔθ᾽ ὁμολογούμενον is a direct denial of ὡμολογημένον ἐστὶ παρὰ πᾶσιν at the beginning of Hero's demonstration (Schmidt in Hero Alexandrinus, Opera [ed. Nix-Schmidt], ii. 1, p. 314. However that may be, the law is assumed in Proposition XIX of Euclid's Optics, where it is said to have been stated in the Catoptrics (Euclid, Opera Omnia, vii, p. 30. 1-3 [Heiberg]); and a demonstration of it is ascribed to Archimedes (Scholia in Catoptrica, 7 = Euclid, Opera Omnia, vii, p. 348. 17-22 [Heiberg]; cf. Lejeune, Isis, xxxviii , pp. 51 ff.). It is assumed by Aristotle in Meteorology, iii. 3-5 and possibly also by Plato (cf. Cornford, Platos Cosmology, pp. 154 f. on Timaeus, 46 B); cf. also Lucretius, iv. 322-323 and [Aristotle], Problemata, 901 B 21-22 and 915 B 30-35. Proposition XIX of Euclids Optics, referred to above, is supposed to be part of the ‘Dioptrics’ of Euclid which Plutarch cites at Non Posse Suaviter Vivi, 1093 E (cf. Schmidt, op. cit. p. 304).
7 i.e. cylindrical, not spherical, convex mirrors; cf. Class. Phil. xlvi (1951), pp. 142-143 for the construction and meaning of this sentence.
8 For such mirrors cf. [Ptolemy], De Speculis, xii = Hero Alexandrinus, Opera, ii. 1, p. 342. 7 ff.
9 Plutarch means Timaeus, 46 B - C, where Plato, however, describes a concave, cylindrical mirror, not a folding plane mirror. Plutarch apparently mistook the words ἔνθεν καὶ ἔνθεν ὕψη λαβοῦσα, by which Plato describes the horizontal curvature of the mirror, to mean that the two planes of a folding mirror were raised to form an angle at the hinge which joined them.
10 See note e on 929 F supra.
11 i.e. the ‘theory’ that the angle of reflection is always equal to the angle of incidence.
12 With these words Plutarch means to refer to the effects of refraction; cf. De Placitis, 894 C = Aëtius, iii. 5. 5 (Dox. Graeci, p. 372. 21-26); Cleomedes, ii. 6. 124-125 (p. 224. 8-28 [Ziegler]); Alexander, In Meteor. p. 143. 7-10.
13 Cf. the argument given by Cleomedes, ii. 4. 103 (pp. 186. 14-188.7 [Ziegler]) and especially: ὅτι δ᾽ ἀπὸ παντὸς τοῦ κύκλου αὐτῆς φωτίζεται ἡ γῆ, γνώριμον. εὐθέως γὰρ ἅμα τῷ τὴν πρώτην ἴτυν ἀνασχεῖν ἐκ τοῦ ὁρίζοντος φωτίζει τὴν γῆν, τούτων τῶν μερῶν αὐτῆς περικλινῶν ὄντων καὶ πρός τὸν οὐρανόν, ἀλλ᾽οὐχί, μὰ Δία, πρὸς τὴν γῆν ὁρώντων. For ἡ ἐκκεκλιμένη cf. Hippocrates, Art. 38 (iv, p. 168. 18 [Littré]).