[1]: This fourth guest cannot be identified. Some have supposed that Plato himself is intended.
[2]: i.e., the Republic, of which the political part (books ii.-v.) is here briefly recapitulated.
[3]: See Rep. 369 E ff., 374 E ff.
[4]: Cf. Rep. 375 B ff.
[5]: Cf. Rep. 376 D ff.
[6]: Cf. Ref. 416 D ff.
[7]: Cf. Rep. 451 C ff.
[8]: Cf Rep. 457 ff.,461 D.
[9]: Cf. Rep. 458 ff.
[10]: Cf. Rep. 415 B.C., 459 D ff.
[11]: For poetry as an imitative art Cf. Rep. 392 D, 579 E ff.
[12]: Cf. Laws638 B. The laws of Epizephyrian Locri were ascribed to Zaleucus (circa 650 B.C.).
[13]: i.e., the Lesser Panathenaea, held early in June, just after the Bendideia.
[14]: The Apaturia was a feast held in October in honor of Dionysus. On the third day of the feast the children born during the year were registered (hence the name Cureotis: κοῦροι=youths).
[15]: Amasis (Aahmes) was king of Egypt 569-525 B.C., and a phil-Hellene; Cf. Hdt. ii. 162 ff.
[16]: Neith is identified by Plutarch with Isis; Cf. Hdt. ii. 28.
[17]: Cf. Laws676 ff.
[18]: For the legend pf Phaethon see Ovid,Met. i. 751 ff.
[19]: Cf. Laws677 B.
[20]: i.e., from the elements earth and fire, cf. 31 B. For the legend of Erechtheus, son of Ge and Hephaestus, and king of Athens (Hom.Il. ii. 547), see Eurip.Ion.
[21]: Egypt being reckoned part of Asia.
[22]: i.e., the Straits of Gibraltar.
[23]: i.e., Africa.
[24]: i.e., the Mediterranean Sea, contrasted with the Atlantic Ocean.
[25]: Cf. 28 A.
[26]: Cf. 55 C ff. The Atomists held that there is an infinite number of worlds.
[27]: Cf. 92 C.
[28]: Dealing first with square numbers, the proportion here indicated is—a2 : ab :: ab :: b2; conversely, b2 : ab :: ab :: a2; alternately, ab : a2 :: b2 : ab.
[29]: Two mean terms are required for a continuous proportion of solid (or cubic) numbers, e.g. a3 :a2b :: a2b : ab2 :: ab2 : b3.
[30]: For the seven motions see 43 B; and for the (rotary) motion of reason Cf. Laws898 A. Cf. also 37 A ff., 42 C, 47 D, 77 B.
[31]: For the priority of Soul Cf. Laws892 A, B, 896 C ff.; and for the right of the elder to rule Cf. Laws714 E.
[32]: The choice of these three as constituents of the Soul is explained by the use of the same terms in the Sophist (244-245) to denote certain Greatest Kinds or main categories. As Professor Paul Shorey has aptly observed (Amer. Journ. Philol. ix. p. 298), It is necessary that the Soul should recognize everywhere . . . the same, the other and essence, those three μέγιστα γένηof the . . .Sophist. Hence on the Greek principle that like is known by like, Plato makes real substances out of these three abstractions and puts them as plastic material into the hands of the Demiurgus for the formation of the Soul.
[33]: These seven numbers may be arranged in two branches, in order to show the two series of which Timaeus immediately goes on the speak:1 (the 1st), 2 (the 2nd), 4 (the 4th), 8 (the 6th); 3 (the 3rd), 9 (the 5th), 27 (the 7th). The former branch contains the double intervals, i.e., the powers of 2; the latter one the triple intervals, i.e., the powers of 3.
[34]: Lit. the double intervals and the triple intervals. See the preceding note.
[35]: The harmonic Mean.
[36]: He now tilts the inner band, so that it makes an oblique angle with the outer, which is set at the horizontal; from which we see that the Revolution of the Same represents the celestial Equator, moving horizontally to the right (from East to West), and the Revolution of the Other represents the Ecliptic, which moves in a contrary direction to the Equator (from West to East), and at an angle to it. The Ecliptic He divides into seven, to represent the seven planets
[37]: Viz. 2, 3, 4, 8, 9, 27.
[38]: Viz. 2, 4, 8 double; 3, 9, 27 triple.
[39]: The three are Sun, Venus, Mercury; the four Moon, Mars, Jupiter, Saturn.
[40]: Note the play on ἄγαλμα thing of joy or statue and ἠγάσθη rejoiced.
[41]: i.e.it is incorrect to use the term is (ἐστί) both as a mere copula and in the sense of exists.
[42]: Cf. 36 D.
[43]: i.e.a tendency as to direction.
[44]: i.e., a tendency as to direction.
[45]: i.e., a planet moving along the Ecliptic from W. to E. is at the same time drawn from E. to W. (in the plane of the Equator) by the regular motion of the sphere of the fixed stars (the circle of the same which moves at a higher velocity than that of the other).
[46]: i.e.Saturn appears to be nearest to the sphere of the fixed stars in point of velocity. Cf. Laws822 A ff.
[47]: An allusion to the name planets, i.e. wanderers; Cf. 38 c.
[48]: i.e., the Great World-Year, which is completed when all the planets return simultaneously to their original starting points. Its length was variously computed: Plato seems to have put it at 36,000 years (Cf. Rep. 546 B ff.).
[49]: i.e., the stars.
[50]: i.e., the fixed stars, and their sphere which moves with the daily rotation of the spherical Cosmos (the motion proper to intelligence, Cf. 36 C,Cratyl. 411 D).
[51]: i.e., the intelligent outermost sphere of the same (cf. the derivation of φρόνησιςfrom φοράin Cratyl. 411 D).
[52]: There is a play here on the word κόσμος, as meaning (1) adornment, (2) universe.
[53]: i.e. (1) the rotation of the star on its own axis; (2) the diurnal revolution of the sphere of fixed stars.
[54]: Cf. 34 A, 43 B.
[55]: The Word εἴλλεσθαι(or ἴλλεσθαι) is taken by some to imply oscillation or rotation (Cf. Aristot.De caeloii. 293 b 30); but it seems best to suppose that Plato is here regarding the Earth as stationary. Her potential motion (we may assume) is equal and opposite to that of the Universe, of which she is the center, and by thus neutralizing it she remains at rest.
[56]: i.e.such instruments as a celestial globe or planetarium.
[57]: This is, obviously, ironical; Cf. Cratyl. 402 B,Phileb. 66 C.
[58]: i.e.the Stars; the others are the deities of popular belief (such as Homer depicts).
[59]: An intensive form of expression, like the Biblical King of kings and Lord of lords.
[60]: Viz. the inhabitants of air, of water, and of earth.
[61]: Cf. Laws899 A.
[62]: i.e. star.
[63]: Cf. 90 E.
[64]: i.e. omitting the seventh motion (rotation), Cf. 34 A.
[65]: i.e., αἴσθησις (sensation) is here derived from ἀίσσω (dart, rush).
[66]: Cf. 35 B.
[67]: Cf. 37 A.
[68]: Cf. 86 E;Phaedo81 C, 83 D.
[69]: i.e.ignorance; Cf. 86 B ff.,Laws863 C ff.
[70]: Cf. 86 B ff.
[71]: Cf. 29 C, D.
[72]: Cf. 73 C, 81 D.
[73]: There is a play here on the words ἥμερον (mild)... ἡμέρας (day); Cf. Cratyl. 418 C.
[74]: Vision is explained on the principle that like is known by like: a fire-stream issuing from the eye meets a fire-stream coming from the object of vision ( Cf. the view of Empedocles).
[75]: e.g.when a man looks at his own face reflected in a mirror. Cf. Soph.266 C.
[76]: i.e., concave (and hemi-cylindrical).
[77]: These causes are secondary, as contrasted with the primary or First Cause (which is also the final Cause), the Good; Cf. 29 E, 68 E,Phaedo99 B.
[78]: e.g. Anaxagoras and the Atomists.
[79]: Cf. 37 D ff.
[80]: Cf. Phileb. 16 C ff.
[81]: An echo of Eurip.Phoenissae1762 ἀλλὰ γὰρ τί ταῦτα θρηνῶ καὶ μάτην ὀδύρομαι;
[82]: For the importance of music in education Cf. Rep.401 D,Laws666 D ff.; also Tim.80 B.
[83]: i.e., the sphere of mechanical causation, physical and physiological processes and results.
[84]: στοιχεῖα, here applied to physical elements, was the regular term for letters of the alphabet; Cf. Theaet. 203 B ff.,Rep.402 A ff.
[85]: i.e., a method which aims only at probability or likelihood: to attain to first principles we should need to employ the dialectic method.
[86]: Cf. 27 C.
[87]: Cf. 28 A.
[88]: Cf. 53 C.
[89]: i.e., the rectangular isosceles triangle and the rectangular scalene; all other triangles can be built up from these two (e.g. see 54 E N.).
[90]: i.e., the half of an equilateral triangle; e.g. if the triangle ABC is bisected by the line AD, we have two such triangles in ADB and ADC.
[91]: i.e., in the triangle ADB (see last note) AB = 2Bsquared, and (AB)squared = (BD)squared + (AD)squared; therefore 4(BD)squared = (BD)squared + (AD)squared, and so 3(BD)squared = (AD)squared.
[92]: As in the figure the equilateral triangle ABC is divided into 6 triangles of unequal sides by joining the vertical points A, B, C to the points of bisection of the opposite sides, viz. D, E, F. Then the hypotenuse in each such triangle is double the shortest side (e.g. AO = 2FO). And FAO = 1/3 right angle; while FOA = 2/3 right angle. The three plane edges are thus of 60 degrees each = 180 degrees = the most obtuse plane angle; so that the solid angle is one degree less, i.e., 179 degrees.
[93]: i.e., the tetrahedron or pyramid (molecule of fire).
[94]: i.e., the octahedron (molecule of air).
[95]: i.e., the icosahedron (molecule of water).
[96]: i.e., the cube, composed of 6x4 rectangular isosceles triangles (molecule of earth).
[97]: i.e., the dodecahedron. How God used it up is obscure: the reference may be to the 12 signs of the Zodiac.
[98]: There is a play here on the two senses of ἄπειρος, unlimited and unskilled; Cf. Phileb. 17 E. The doctrine of an infinite number of worlds was held by the Atomists.
[99]: The affinity of like to like was an axiom in early Greek thought; Cf. Lysis215 C ff.,Sympos. 186 A ff.
[100]: The elements are conceived as having their proper abodes in concentric strata of space, one above another—earth in the center, water next, then air, and fire at the circumference of the World-Sphere.
[101]: Cf. 53 C ff.: the varying shapes and sizes of the primary triangles account for the inequality.
[102]: i.e., exerts a centripetal force. For this compression cf. Emped. Frag. 185 Τιτὰν ἠδʼ αἰθὴρ σφίγγων περὶ κύκλον ἅπαντα.
[103]: i.e., metals are classes as water, cf. 59 B ff.
[104]: Perhaps haematite or platinum.
[105]: Cf. 29 B, D, 48 C, etc.
[106]: Alluding to a fanciful derivation of ὑγρόνfrom ὑπὲρ γῆν ῥέον.
[107]: Perhaps a kind of fig-juice.
[108]: i.e., potash or saltpeter.
[109]: Cf. Hom.Il. ix. 214 πάσσε δʼ ἁλὸς θείοιο.
[110]: i.e., θερμόν (quasi κερμόν) is derived from κερματίζω (minced up or mint).
[111]: The reference here is, probably to Democritus (Aristotle also speaks of τὸ ἄνω φύσει, Phys. 208 b 14).
[112]: i.e., above and below are purely relative terms.
[113]: i.e., the attraction takes different directions, therefore up and down are relative terms.
[114]: Cf. 54 B ff., 57 D, E.
[115]: Cf. Rep. 583 C ff.,Phileb. 31 D ff.
[116]: Cf. 45 B.
[117]: Cf. 64 E.
[118]: The function of the nerves is here assigned to the veins.
[119]: Cf. 80 A.
[120]: Cf. 45 C ff.
[121]: Cf. 65 E.
[122]: Cf. 45 C ff.
[123]: i.e., between the kinds of fire which produce blackness and brightness.
[124]: Cf. 46 D, 48 A.
[125]: i.e., 47 E.
[126]: Cf. 30 A, 42 D ff.
[127]: Cf. 44 E.
[128]: Cf. 64 E.
[129]: i.e., gall.
[130]: i.e., the right lobe, the viliary vesicle, and the vena porta; cf. Eurip.Electra827 ff.
[131]: Cf. Rep. 346 B,Laws772 D,Phaedo. 244 A ff.
[132]: Cf. Laws871 C, Eurip.Ion413 ff.
[133]: i.e., in the sacrificed victim; Cf. Rep. 364 C ff.
[134]: i.e., the spleen, which, in relation to the liver, is concave.
[135]: Cf. 68 D, 74 D.
[136]: Cf. 61 C.
[137]: Literally the lower belly, as distinct from the upper belly or thorax.
[138]: Cf. 53 C ff.
[139]: i.e., the rational (νοῦς), and spirited (θυμός), and appetitive (ἐπιθυμία) kinds or parts.
[140]: Cf. 44 D.
[141]: i.e., the vertebral column, cylindrical in shape.
[142]: i.e., the principle of plurality, cf. 35 B.
[143]: Cf. 70 D.
[144]: i.e., those of the head and spine.
[145]: Cf. 68 E f.
[146]: Cf. 90 E ff.
[147]: Cf. 70 D ff., 72 E ff.
[148]: i.e., the aorta and the vena cava. The distinction between veins and arteries was unknown in Plato’s time.
[149]: Cf. 56 A, 58 A ff.
[150]: A mythical figure, like Adam in Gen. 11. 19-20; Cf. Cratyl. 438-439.
[151]: Cf. 58 A.
[152]: Cf. 67 A ff.
[153]: εὐφροσύνη (quasi εὐφεροσύνη), derived from φέρω, φορά (motion); Cf. Cratyl. 419 D. The two kinds of sound, quicker and slower, are supposed to be blended by the time they reach the ear.
[154]: Cf. 47 C ff.
[155]: i.e., amber.
[156]: i.e., the loadstone or magnet; Cf. Ion533 D.
[157]: Cf. 77 A.
[158]: Cf. 68 B, C.
[159]: Cf. 53 D ff.
[160]: i.e., the radical structure of the primary triangles; cf. 53 D ff.
[161]: Cf. 41 D ff.
[162]: Cf. 74 D.
[163]: i.e., the synovial fluid.
[164]: Cf. 71 B.
[165]: Cf. 68 D.
[166]: Cf. 66 B.
[167]: Cf. 82 D.
[168]: i.e., epilepsy; Cf. Laws916 A.
[169]: Cf. 82 D.
[170]: Cf. 73 D, 81 D.
[171]: i.e., the fever recurs after an interval of two days.
[172]: Cf. Rep. 571 D,Soph. 228 A,Laws689 A ff.
[173]: Cf. 73 C, 91 C.
[174]: For this Socratic dictum Cf. Protag. 345 D ff.,Laws731 C ff.
[175]: Cf. 73 D ff.
[176]: Cf. 44 E, 69 C.
[177]: Cf. Laws728 E.
[178]: i.e., music in the wide sense of mental culture.
[179]: Cf. 49 A, 52 D.
[180]: Cf. 33 A.
[181]: Cf. Laws789 C.
[182]: Education is the theme of Rep. vii. and Lawsvii. and xii ad fin.
[183]: Cf. 69 D, 79 D, 87 A.
[184]: i.e., genius or guardian-angel; Cf. Laws732 C, 877 A.
[185]: Cf. Sympos. 212 A.
[186]: Literally, with a good daemon (a play on δαίμωνand εὐδαίμων).
[187]: Cf. 37 A ff.
[188]: Cf. 41 D ff.
[189]: Cf. 73 C, 86 C.
[190]: Cf. Rep. 529 A ff.
[191]: Cf. 69 E ff.
[192]: Cf. 30 C ff., 31 B.