NOTE ON THE PLURALITY OF WORLDS AND THE FIVE REGULAR SOLIDS

The opinion that our World, or universe, is not the only one in the Whole, is attributed, in general terms, to many of the early Greek philosophers, notably to Anaximander. The exact meaning of a ‘Cosmos’, in this connexion, is perhaps not easy to fix. Aristotle is clear that the circle of the fixed stars is one and constant, but the author of the Stoical treatise on the Cosmos, found among his works, takes stars to be a part of the (one) Cosmos. An earth, such as ours with her atmosphere and moon, is essential, and a sun, or access to sunlight, and perhaps some planets. In the Dream of Scipio our solar system, with the earth in its centre, is described with great distinctness as a unit in space. The planets are always regarded as luminous points, stars somewhat out of place (see p. [268]), possessing no definite magnitude or solid substance.

In theory the number of Cosmi might be infinite, but a shrinking from the vague ‘Infinity’, in later times associated with the Epicureans, led Plato, for instance, to restrict the number to a possible five. That he based this number upon that of the five regular solids may seem fanciful, but the solid angles and forms observed in crystals might reasonably suggest the hypothesis that the ultimate constituents of the crust of the earth would be found in the most perfect solid structures known to theory. In theory there is much that is attractive in these five solids. To one coming fresh from a study of Plane Polygonal Figures, which exist in infinite number, and, when regular, approximate more and more closely to the Plane Circle, it comes as a surprise to find that, in the next higher degree, the number of solid bodies so approximating to the Sphere is five only. Again, it seems almost a paradox that, of these five, the nearest approximation to the Sphere is attained, not by the body with twenty fine faces, but by that which shews only twelve, and those comparatively blunted and unshapely (pentagons). It was perhaps from such considerations that the Dodecahedron was held of special importance by the Pythagoreans. Plato’s study of the several faces of these solids, as available for construction or reconstruction of a world, leaves nothing to be desired, assuming that a solid body can be built out of plane figures, an assumption which appears to belong to the same habit of thought as that which makes the point the square of unity, and the lineal measure corresponding to the number two the first rectangle. As the pentagon defies the analysis available for the equilateral triangle or for the square, the Dodecahedron remains over, a model or pattern of a stitch-work world, as viewed from outside (Phaedo 110 B and Timaeus 55 C; see also Burnet’s Early Greek Philosophy, p. 341 foll.). It may not be amiss to be reminded that Kepler, mathematician as well as astronomer, spent many toilsome years in the endeavour to arrange the members of our solar system upon a plan based on the five solids. ‘If Kepler went out “to seek his father’s asses”, he found a kingdom, for it was in the course of these speculations, and through them, that he discovered not only his own “Third Law”, but also the truth, overlooked by Copernicus, that the orbit of each planet lies in a plane which passes through the centre of the sun.’ (Dreyer, Planetary Systems, p. 410.)

The discussion of the plurality of worlds, in the modern sense, begins with the very attractive work of Fontenelle, brought out, in its original form, in 1686, a year before Newton’s Principia, being a series of conversations between the Author and a witty and accomplished Marquise, as to the habitability of the several members of the solar system. The argument which followed is distinguished by many great names, those of Newton himself, Bentley, Huyghens, the Herschels, Dr. Chalmers, till it was brought to a head in the middle of the nineteenth century by Dr. Whewell and Sir David Brewster, writing respectively against and for the hypothesis. The subject was then one (as readers of Anthony Trollope will remember) upon which any one might be called upon to take a side in a London drawing-room. In more recent times interest has been concentrated upon Mars, who now possesses the distinction of having two satellites. We are only concerned to invite the reader to compare the religious argument addressed to the Stoics by Plutarch (p. 142 foll.) with the religious argument drawn by Dr. Chalmers and Sir David Brewster from the enrichment of the providential scheme for man upon our earth which would follow the conception of other earths tenanted by other beings perhaps of a higher order.

But it is natural that any such speculation should begin with the moon, and in fact we find the question of her habitability discussed by Theon and by Lamprias (pp. 293-9). With the later treatises on this subject, beginning with Lucian’s witty flight of fancy, we are not concerned. But an exception must be made for the very able works of Savinien de Cyrano, known to us as Cyrano de Bergerac, whose Histoire comique des États et Empires de la Lune appeared, probably, in 1650, and was followed by a similar work about the sun. Cyrano appears to be familiar with Plutarch: thus he meets in the moon the ‘daemon of Socrates’, who has also been the tutelary spirit of Epaminondas, of Cato of Utica, and of Brutus. The idea (due in the first place to Heraclitus) of being fed on smells, is worked out with much vivacity. But with so original and daring a writer, it is not quite easy to settle how much is due to any hint from others and how much to himself. A modern reader will not need to be reminded that Cyrano was not a person of whom it was wise to give an outspoken opinion in his lifetime. But I had wished to speak with nothing but respect of a man of real learning and genius, who, from whatever cause, did not bring to perfection any work worthy of himself.

See, on the general subject, an Essay by the late Professor Henry J. S. Smith in Oxford Essays, 1855.

INDEX
OF PERSONS AND PLACES MENTIONED BY PLUTARCH IN THESE DIALOGUES

¶ In this Index the Greek spelling of ei (Lat. ī) has been usually retained.

All dates are B. C. unless otherwise stated.

The dates are often approximate and conventional.

Other numerals refer to pages of this volume.

For the speakers in each Dialogue see that Dialogue passim and the Introductions.

(The ‘Three Pythian Dialogues’ are quoted under that designation See p. [52].)

Printed in England at the Oxford University Press

Footnotes

[1]. ‘Tout abregé sur un bon livre est un sot abregé.’—Montaigne, iii. 8.

[2]. Xylander reads οὐδέν, but οὐ before πολλά seems simpler, and makes better logic.

[3]. See, e. g., p. [266].

[4]. On this point, and on Plutarch’s life generally, see the buoyant and chivalrous pages of the late Mr. George Wyndham’s introduction to North’s Lives in the Tudor Translations.

[5]. See pp. [54], [253]. I have searched such numbers of the Dissertations as appear to have reached this country from Vienna since 1910, without coming upon the continuation of Dr. Adler’s argument. It will be of great interest when it comes to hand, but could not adequately be discussed here.

[6]. ‘Où je puyse comme les Danaïdes, remplissant et versant sans cesse.’—i. 25.

[7]. The Symposiacs were specially favourite reading of Archbishop Trench, whose bright little volume of Lectures is perhaps the best introduction for English readers to the Moralia.

[8]. The same argument might perhaps be applied to the Lives, even as far as that of Dion, but there is no elaborate dedication there.

[9]. Dr. Mahaffy has acutely pointed out that the tract De Tranquillitate animi must have been written before the accession of Titus in A. D. 79, because it contains a remark (467 E) that no Roman Emperor had yet been succeeded by his son. It is this sort of evidence of a date which we seek, but do not find, in the Symposiacs.

[10]. Some of Plutarch’s characters exemplify the ‘sternness of the judgements of youth’, as the younger Diogenianus.—See p. [94].

[11]. See Vol. I, p. 25.

[12]. See his Preface in Vol. I, p. xlii.

[13]. M. Chenevière’s study mentioned on p. [53] is very helpful but not easily accessible.

[14]. See p. [14]; see also Apollonius of Perga, by Sir Thomas Heath, F.R.S., Introd., p. xxi.

[15]. ‘Forte’ is always used where we expect ‘fortasse’, and ‘nisi’ often for ‘si non’.

[16]. Adrien Turnĕbus (i. q. Toranebus?) was a native of Les Andelys (Eure), near Rouen, and the name is said to be of local origin. Montaigne, who knew him personally, always writes Turnebus; the later form Turnèbe seems to be due to false analogy.

[17]. I may now name Mr. Walter Sumner Gibson, M.A. of Balliol College, formerly an assistant-master at Charterhouse, who died on the 20th January, 1918, having in recent years acted as a Reader to the Clarendon Press.

[18]. ii. 4.

[19]. 1514-93.

[20]. See, however, an article by Mr. R. F. Macnaghten in the Classical Review of September 1914 (vol. 28, p. 185 foll.).

[21]. Isthm. 1, 2.

[22]. So C. F. Hermann (ap. Ed. Teub.) for δυσί τῶν ἱερῶν.

[23]. Here several words of the text have been lost.

[24]. Many words have been lost (three separate lacunae).

[25]. Reading διεκώλυεν for διακούων.

[26]. Supplying προσδοκῶν, as Ed. Teub.

[27]. Many words are here lost, to the general effect of those in the brackets.

[28]. i. e. each of the four sides of each of the six faces. The Greek word for ‘side’ and ‘face’ is the same.

[29]. This problem (mentioned by Plutarch also in the E at Delphi, see p. [63]) was in fact solved by Menaechmus, a pupil of Eudoxus, through Conic Sections, and also by Archytas, whose method is much more elaborate. See Preface, p. [xiv].

[30]. Il. 10, 279; Od. 13, 300-1.

[31]. Il. 20, 95.

[32]. συμπιέσας for the MSS. reading συμπείσας (Reiske).

[33]. πταρμὸς ἤ (Ed. Teub.), for ἐφαρμόσει, is attractive, but it seems better not to anticipate the word.

[34]. ἐπὶ ῥειτοῖς is K. O. Müller’s reading for ἐπὶ ρητις της of the MSS. See Wordsworth’s Athens and Attica, p. 9.

[35]. Fr. 284 (the well-known fragment of the Autolycus about Athletes) l. 22.

[36]. Cp. Od. 1, 170, &c.

[37]. Od. 1, 27.

[38]. See Life of Nicias, c. 3.

[39]. Aeschylus, Prometheus, 545.

[40]. Cp. Bacchylides, Fr. 37 (Life of Numa, c. 4): ‘Broad is the road’, i. e. ‘there is room for divergent opinions.’

[41]. Compare Life of Coriolanus, c. 32, p. 229, with this difficult passage.

[42]. Of the participle so translated only the termination remains. Reiske’s μεταλλευόντων well completes this fine image.

[43]. This word is not in the Greek text.

[44]. See note on the Myths of Plutarch, p. [315].

[45]. Lucian (Musc. Encom. c. 7) tells the same story of Hermodorus. Plutarch has probably made a slip, as elsewhere, in names. See p. [99].

[46]. Il. 7, 44-5.

[47]. l. 53.

[48]. i. e. in the Wooden Horse, Od. 11, 526-32.

[49]. Perhaps rather ‘the Laconizing party’, as the Teubner editor suggests.

[50]. 8,000 feet above the sea. The Phaedriades rose to about 800 feet.

[51]. Fr. 960.

[52]. i.e. at draughts, with a play on words.

[53]. Fr. 71.

[54]. Il. 17, 29.

[55]. See p. [14].

[56]. Il. 1, 70.

[57]. So Emperius, whose reading is that of the Paris MS. E. (See Paton in loco.)

[58]. Fr. 22.

[59]. A reference to the complaint with which the first attempts of Aeschylus and others to give literary form to the popular hymns in honour of Dionysus were greeted.

[60]. i.e. ‘not many’.

[61]. See p. [76].

[62]. Fr. 392.

[63]. Terms used by Heraclitus (Fr. 24), adapted by the Stoics for the periodic conflagration and renewal of the universe.

[64]. Timaeus, 31 A and 55 E foll.

[65]. De Caelo, 1, 8-9, 276 a 18.

[66]. Il. 15, 190.

[67]. See Iph. Aul. 865 and Herc. Fur. 1221.

[68]. P. 409 A.

[69]. Pp. 255-6.

[70]. P. 23 D and p. 66 C.

[71]. Cp. Pindar’s:

All vocal to the hearing of the wise,

All voiceless to the herd.Ol. 2, 152-3.

[72]. From Simonides, a favourite phrase with Plutarch.

[73]. Fr. 41.

[74]. Fr. 25.

[75]. See on this remarkable passage E. Norden, Agnostos Theos, p. 231 f., and the view of H. Diels, communicated to him. I have followed Norden in reading εἶ, ἤ (he suggests with hesitation προσεπιθειάζειν) (and so Paton and Diels). Diels thinks that οἱ παλαιοί may cover later philosophers such as Xenophanes.

[76]. Il. 4, 141.

[77]. Il. 15, 362.

[78]. Pindar (probably from a Threnos).

[79]. Il. 9, 158.

[80]. Fr. 149.

[81]. Suppl. 975.

[82]. Fr. 50.

[83]. Fr. 728, probably from the Thamyras.

[84]. Again quoted by Plutarch, p. 777 C.

[85]. Od. 7, 107.

[86]. Fr. 7.

[87]. In a lost ‘Hymn’, Fr. 32.

[88]. See H. Richards in Classical Review, vol. 29, p. 233.

[89]. Reading Ἑλλήνων as Ed. Teub. fr. Stegmann.

[90]. Rhet. 3, 11.

[91]. Puteoli.

[92]. πετρῶν καταφλεγομένων (J. H. W. Strijd in Class. Rev. vol. 28, p. 218).

[93]. Quoted by Menander, Fr. 243 (Meineke).

[94]. Quoted also in the Life of Agesilaus, c. 3, p. 597.

[95]. Palaea Kaumene, a volcanic island ejected in 196 B. C. See Tozer’s Islands of the Aegean, p. 97 foll.

[96]. Od. 3, 1.

[97]. Tim. 90.

[98]. See p. [283].

[99]. Xen. Sympos. c. 2.

[100]. Reading χώρας for δωρεᾶς with Emperius (ap. Ed. Teub.).

[101]. See Herod. 1, 51.

[102]. Fr. 44.

[103]. Here the text is defective.

[104]. Here the text is defective.

[105]. I, 118.

[106]. MSS. have ‘Pausanias’.

[107]. These words are supplied from the text of Thucydides, 5, 10.

[108]. The word ἀναγκαῖον is suggested by the Teubner Editor.

[109]. Fr. 11.

[110]. Od. 2, 372.

[111]. Il. 2, 169 foll.

[112]. Il. 4, 86 foll.

[113]. Il. 5, beg.

[114]. The MSS. have ‘Pandarus’, but ‘Pindar’ is a likely correction. Yet Plutarch cannot have supposed Pindar to have written this iambic line. It is quoted by Aristophanes, Peace, 699, in connexion with the stinginess of Sophocles or Simonides, and the scholiast quotes from Pindar a censure of that vice in a poet: so some confusion is possible.

[115]. Oeconom. 7, 4 foll.

[116]. In the Stheneboea.

[117]. Isthm. 2, 3.

[118]. Fr. 16 (Nauck).

[119]. Isthm. 1, 69.

[120]. Fr. 707.

[121]. So Cobet (for Cinesons).

[122]. Phoen. 958.

[123]. See Herod. 4, 155 foll. and Pind. Pyth. 4. There is something amiss with Plutarch’s text here.

[124]. See his Life, c. 29.

[125]. Od. 2, 190.

[126]. See additional note on p. [312].

[127]. Fragm. adespota, 90.

[128]. Whose account is, for convenience, somewhat recast and amplified. The fact is understated. ‘There cannot be more than five solids, each of which has all its faces with the same number of sides, and all its solid angles formed with the same number of plane angles.’ Todhunter, Spherical Trigonometry, c. 151.

[129]. Il. 10, 173, and Leaf’s note.

[130]. Od. 3, 367-8.

[131]. Il. 10, 394. See p. [265].

[132]. Herodotus, 8, 133-5. I have followed W.’s reconstruction.

[133]. See Life of Aristides, c. 19.

[134]. W. and D. 199.

[135]. See p. [231].

[136]. Fr. 149: see above, p. [77].

[137]. Herod. 9, 28 (and see ib. c. 21).

[138]. Fr. 729. Cp. O. C. 607.

[139]. The words ‘and here—heroes’ have been supplied from a quotation in Eusebius, Praep. Evan. 5, 4.

[140]. From a fragment, Gaisford, Poetae Minores, ii, p. 489 (cp. Ausonius, Id. 18; and Sir T. Browne, Vulgar Errors, 3, 9).

[141]. Fr. 165.

[142]. As Ausonius, loc. cit.

[143]. Fr. 87.

[144]. 1 + 2 × 1 + 3 × 1 + 22 + 32 + 23 + 33 = 54.

[145]. See Timaeus, 35.

[146]. Il. 20, 8-9.

[147]. See Heraclitus, Fr. 34.

[148]. Inserting, with Mezirius, ἢ δεκάκις before τεσσάρων.

[149]. The meaning is simply that 40 × 35 = 9720, and ‘triangle-wise’ seems irrelevant.

[150]. Fr. 961 (from the Phaethon).

[151]. Sympos. 202 F.

[152]. W. and D. 125. Cp. Plato, Crat. 397.

[153]. 2, 171.

[154]. Pindar, Fr. 208 (cp. Sympos. 7, 5, 4).

[155]. Suppl. 214.

[156]. Fr. 730.

[157]. See additional note, p. [312].

[158]. Cp. Life of Timoleon, c. 1.

[159]. Cp. Herod. 2, 145.

[160]. See p. [54].

[161]. Reading οὐ πολλά (‘nihil secum trahit impossibile’. Xylander). See Preface, p. [vi].

[162]. Timaeus, 55.

[163]. As Aristotle, De Caelo, I, 8, 276 a 18.

[164]. Od. 21, 397.

[165]. Il. 15, 189.

[166]. Tim. 31 A, 55 C.

[167]. Reading, with Madvig (partly anticipated by Emperius) ... ὃ μὴ κοινῶς ποιὸν ἢ ἰδίως ἐστίν· ὁ δὲ κόσμος οὐ λέγεται κοινῶς εἶναι ποιός· ἰδίως τοίνυν ...

[168]. See e. g. De Caelo, 1, 6, 275 b 29, and Burnet, Early Greek Philosophy, p. 397 note; see also p. 270 foll.

[169]. Inserting κάτω, with Meziriac.

[170]. Il. 13, 1 foll.

[171]. See p. [115].

[172]. Tim. 55 E, foll.

[173]. There is a play on the words for ‘fire’, ‘Pyramid’.

[174]. Soph. 249 B.

[175]. Is. et Osir. c. 12.

[176]. De Caelo, 2, 4, 286 b 10.

[177]. Tim. 55 C.

[178]. Tim. 57 C.

[179]. Tim. 52 E.

[180]. Fr. 925.

[181]. See p. [70].

[182]. W. and D. 124.

[183]. W. and D. 122.

[184]. μᾶλλον δὲ ὄντα. Cp. Plato, Philebus, 33, διὰ μνήμης πᾶν ἔστι τὸ γεγονός.

[185]. See Thuc. 1, 12.

[186]. Fr. 963.

[187]. Bacchae, 297-8.

[188]. Fr. 75.

[189]. The text is corrupt, but probably contained ὁμίχλην. Cp. Plato, Sympos. 736 A.

[190]. Theogon. 117.

[191]. Fr. 371.

[192]. Meteor. 1, 3, 340 b 29.

[193]. Cyclops, I. 332-3 (Shelley’s tr.).

[194]. Phaedo, 97 C.

[195]. 1, 25, where the work is ascribed to Glaucus.

[196]. Od. 9, 393.

[197]. Rep. 6, 18, 507 C.

[198]. Cp. Plato, Laws, 716 E.

[199]. See p. [313].

[200]. On the proverb ‘Post Lesbium Cantorem’.

[201]. i. e. in the battle of Amphipolis. See Thuc. 5, 10 and Plut. Life of Nicias, c. 9.

[202]. Orestes, 420.

[203]. 3, 38.

[204]. See Pausanias, 4, 17.

[205]. Fr. 969.

[206]. The author of this famous line is unknown.

[207]. Fr. 57.

[208]. Minos, 319 C.

[209]. No specific passage can be identified with the words in the text. For the sequel cp. Timaeus, 30 A.

[210]. Cp. Rep. 6, 508 A.

[211]. See p. [181] n. 1.

[212]. This line is a continuation of the quotation from Melanthius above.

[213]. Cp. Aesch. Cho. 313, &c.

[214]. Quoted several times as from Pindar (see Fr. 77), but perhaps rather Simonides.

[215]. Il. 15, 641.

[216]. Cp. Aristot. Poet. c. 9.

[217]. W. and D. 266, 265.

[218]. Laws, 5, 728 C.

[219]. i.e. under Roman law. See Smith’s Dict. Ant., s.v. Crux.

[220]. Rep. 406 B.

[221]. See H. Richards in Class. Rev. vol. 29, p. 235, and, for the quotation, the Life of Lucullus, c. 1.

[222]. Fr. 42, and see Jebb’s Introd. to the Electra of Sophocles.

[223]. See Life of Aristides, c. 6. also Dion Chrys. Orat. 64.

[224]. See Life of Cimon, c. 6.

[225]. Again quoted, De Curiosit. 520 A.

[226]. Eur. Ino, Fr. 403.

[227]. Fr. 970.

[228]. See Herod. 2, 134.

[229]. i. e. Polyphemus. See Od. 9, 375 foll.

[230]. See Herod. 66, 74, and Pausan. 4, 252, and 8, 18.

[231]. From an unknown poet; Euphorion and Arctinus are suggested.

[232]. Fr. 123.

[233]. Hence a proverb applied to what was second-rate.

[234]. Arist. H. A. 9, 3, 610 b 29.

[235]. See Thuc. 2, 48; also Plague and Pestilence in Literature and Art, by Raymond Crawfurd, M.D., chap. 2 and Appendix.

[236]. Cp. Plato, Laws, 4, 715 A.

[237]. Fr. 41.

[238]. Il. 6, 146.

[239]. Fr. 211.

[240]. W. and D. 735-6.

[241]. Eur. Fr. 970.

[242]. I have transposed the verbs as suggested in Wyttenbach’s Commentary.

[243]. Cp. Dante, Purg. 3, 19 foll. The idea is Pythagorean (see Quaest. Graec. 40, p. 300).

[244]. Cp. Plato, Gorg. 524 D.

[245]. See H. Richards in Class. Rev., vol. 29, p. 236.

[246]. Cp. p. 215, n. 1.

[247]. Cp. p. 89.

[248]. Probably a Sibylline verse. See Suetonius, Life of Vespasian.

[249]. Reading ἅτε δή with C. F. Hermann.

[250]. Cp. Aristot. Hist. Anim. 2, 14, 505 b 13, and 10, 37, 621 a 6.

[251]. Where it is ascribed to Themistius. It was reclaimed for Plutarch by Wyttenbach in the Preface to his edition of the De Sera Numinum Vindicta—Leiden 1772.

[252]. In the Dialogue (Ne suaviter quidem, c. 26) in which the Epicureans are attacked, the ‘hope of eternal existence’ or ‘desire to be’, is spoken of as the ‘oldest and greatest of loves’.

[253]. θάνατος—ἀναθεῖν εἰς θεόν.

[254]. γένεσις—γῆ, νεῦσις. Cp. p. 210, l. 6.

[255]. γενέθλιον—γένεσις ἄθλων.

[256]. Reading ἂν δὲ ἔρῃ, καὶ σώματος for ἂν δὲ ἔρημαι σώματος. See the Lex.-Plat. s.v. ἔρομαι.

[257]. e.g. Od. 1, 423.

[258]. τελευτᾶν—τελεῖσθαι.

[259]. Od. 12, 432 foll.

[260]. W. and D. 42.

[261]. Fr. 122.

[262]. Polybius (6, 56) points to ‘Deisidaimonia’ as the force which has held the Roman Commonwealth together, and kept the Romans honest.

[263]. See Nauck, p. 910 (Hercules speaks).

[264]. δεῖμα—δέω: τάρβος—ταράσσω.

[265]. Cf. Aristot. Eth. Nic. 3, 7.

[266]. Eur. Or. 211-12.

[267]. Nauck, p. 910, Fragm. 375 (probably from Aeschylus).

[268]. Eur. Tro. 759.

[269]. Meineke 4, p. 670.

[270]. Fr. 95.

[271]. Nauck, Fragm. adespota, 376.

[272]. Dem. de Cor., s. 97.

[273]. A difficult passage. I follow W.’s suggested restoration.

[274]. Tim. 47 C, &c.

[275]. Pyth. 1, 25.

[276]. Or perhaps ‘that which knows no wrath’.

[277]. Fr. 143, quoted twice elsewhere by Plutarch.

[278]. Pythag. Carm. Aur. 42.

[279]. See Life of T. Q. Flamin. c. 20.

[280]. Life of Nicias, c. 23. Thuc. 7, 50, 86.

[281]. i.e. as the moon plunges into the shadow of the earth. See p. [269].

[282]. Archilochus, Fr. 54, Bergk.

[283]. Nauck, Fragm. adespota, 377.

[284]. W. and D. 465 foll.

[285]. Il. 7, 193 foll.

[286]. Il. 2, 382, 414.

[287]. 1 Maccab. 2, 32 foll.

[288]. Soph. O. T. 4.

[289]. See p. [123].

[290]. In the main from Wyttenbach’s reconstruction of this desperate passage.

[291]. Il. 24, 604.

[292]. Il. 24, 212.

[293]. Cp. Menander, Fragm. of Demiurgus, Meineke 4, p. 102.

[294]. Soph. Ant. 291.

[295]. Il. 22, 20.

[296]. Plat. Tim. 40 E.

[297]. See Strabo, 4, c. 4.

[298]. Cp. p. 183.

[299]. Herod. 7, 114.

[300]. Crat. 403 A, 404 B.

[301]. Cp. Arist. Rhet. 2, 23, 27, 1400 b 5, where the Eleatae are named.

[302]. In c. 22 Apollonides is made to state the angular diameter of the moon at 12 ‘fingers’, i. e. one degree.

[303]. See Note (1), p. [309].

[304]. See Note (2), p. [309].

[305]. Arist. Probl. 12, 3.

[306]. See Note (3), p. [309].

[307]. See Aristarchus, Magnitudes and Distances, Hypothesis 2.

[308]. See the Homeric Hymn to Hermes, 99-100, where the moon is the daughter of Pallas (‘the Pallantean orb sublime’, Shelley), cp. p. 294.

[309]. As Homer, Od. 23, 330; 24, 539; Hesiod, Theog. 515.

[310]. e. g. Il. 10, 394. Cp. Heraclides Ponticus, 15.

[311]. P. V. 349.

[312]. Fr. 88.

[313]. W. reads μένειν (E has κινεῖν), but renders by ‘cieri’.

[314]. Fr. 733.

[315]. See note (4), p. [310].

[316]. Professor Henry Jackson has pointed out that the words form a hexameter line. For the Greek word see p. [291]. Its introduction here is due to M. Bernardakis.

[317]. Reading τῇ γῇ, with Madvig.

[318]. See note (5), p. [310].

[319]. αἰρομένη MSS.

[320]. Prop. 7.

[321]. See note (6), p. [310].

[322]. Cf. Il. 9, 63.

[323]. Reading ὅλως (Emperius, ap. Ed. Teub.), for ὅμως.

[324]. See additional note, p. [312].

[325]. See e. g. Tim. 32 C.

[326]. Theog. 120, 195.

[327]. Pindar, Fr. 57: see p. [179].

[328]. Reading ἕξει, with Emperius.

[329]. See note (7), p. [310].

[330]. Reading ᾀἱδίου, with Emperius.

[331]. Ion Chius, Fr. 57 (Nauck).

[332]. Reading διίησιν, with Madvig.

[333]. I have followed the paraphrase of the Greek words suggested by Wyttenbach. For the physical facts see Ganot’s Physics, 516.

[334]. Timaeus, 46 A-C (Plato does not discuss plane folding mirrors).

[335]. Reading χωρεῖν for χωροῦντες.

[336]. Kepler has supplied such a diagram (in his translation, p. 131).

[337]. See p. [253].

[338]. Pindar, Fr. 107. Paean 9 (see Oxy. Pap. 1908, 841).

[339]. Od. 20, 352 and 357; 14, 162; 19, 307.

[340]. Reading τὸ ἕν for τόν.

[341]. Prop. 17.

[342]. De Caelo, 2, 13, 293 b 20.

[343]. See note (8), p. [310].

[344]. See note (9), p. [310].

[345]. Reading ἡ δὲ τῆς Σελήνης with Mr. W. R. Paton, see Class. Rev. vol. 26, p. 269.

[346]. Strictly speaking, both cases are of ‘overtaking’, but the results follow as stated.

[347]. Il. 9, 212.

[348]. See Plato, Phaedo, 110 B-C.

[349]. Od. 311.

[350]. Soph. (Lemnians), Fr. 348.

[351]. τραπέμπαλιν is due here to Meineke, ap. Ed. Teub., see p. 267.

[352]. Tim. 40 B.

[353]. See note (10), p. [311].

[354]. Aesch. Suppl. 937.

[355]. See p. [262] and note.

[356]. See n. (11), p. [311].

[357]. Il. 14, 246. The second line appears to have been added by Crates and is not in our texts.

[358]. Tim. 40 C.

[359]. Kepler would read ‘twelve’.

[360]. Fr. 48.

[361]. W. and D. 41.

[362]. Il. 20, 64.

[363]. Il. 8, 16.

[364]. Od. 7, 244.

[365]. See n. (13), p. [311].

[366]. Reading ἐπειδὰν παύσῃ, with Madvig.

[367]. See n. (14), p. [312].

[368]. Od. 9, 563.

[369]. i. e. the words τελεῖν, τελευτᾶν are allied, see p. [215].

[370]. Plato, Tim. 31 B and end.

[371]. Fr. 38.

[372]. Tim. 31 B.

[373]. Od. 11, 222.

[374]. Od. 11, 600.

[375]. From a note made in 1910, which cannot at present (1916) be verified.