[1]: Theodorus was from Cyrene, not far from the oasis of Ammon.
[2]: i.e. one class is to be separated and then all the rest are to be marked as one other class—the familiar division into two parts.
[3]: The word diameter here denotes the diagonal of a square. The early Greek mathematicians worked out their arithmetical problems largely by geometrical methods (cf. Plat. Theaet. 147 D ff). The diagonal of the unit square (√2) was naturally of especial interest. It was called sometimes, as here simply ἡ διάμετρος, sometimes, as just below,ἡ διάμετρος ἡ δυνάμει δίπους, or, more briefly,ἡ διάμετρος δίπους. Given a square the side of which is the unit (i.e. one square foot), the length of the diagonal will be √2 and the square constructed with that diagonal as its side will contain two square feet. The length of the diagonal of this square will be √4=2 feet, and its area will be four square feet.
[4]: There is here a play upon words. Man, being a two-footed (δίπους) animal, is compared to the diagonal of the unit square (√2,διάμετρος δίπους).
[5]: i.e. the remaining species is four-footed. Our diameter is √2, and four is the area of the square constructed on the diagonal of the square which has √2 as its side. All this satirizes the tendency of contemporary thinkers to play with numbers.
[6]: The animal referred to is the pig. See P. Shorey, Classical Philology,1917, July, p. 308.
[7]: i.e. the swineherd, the pig belonging to γένει εὐχερεστάτῳ.
[8]: See Plat. Soph. 227B.
[9]: Hermes revenged upon the Pelopidae the death of his son Myrtilus by causing a lamb with golden fleece to be born among the flocks of Atreus. When his claim to the succession was disputed, Atreus promised to show this prodigy to prove that the gods were on his side. Thyestes persuaded Aerope, the wife of Atreus, to give him the lamb, and Atreus was in danger of losing his kingdom, had not Zeus, who favored his claim, made the sun and the Pleiades return from their setting towards their rising. This is the form of the story given in a scholium on Eur. Orest. 988, and Plato seems to have this form in mind, though variants existed. The lamb was a token (σημεῖον) of the favor of the gods, and the changed course of the sun and stars was a testimony (μαρτυρήσας) to the right of Atreus.
[10]: The tale of Atreus introduces the fanciful theory of the reversal of the revolution of the heavenly bodies, and this, especially in an age when the stars were believed to exercise a direct influence upon mankind and other creatures, naturally brings with it the reversal of all processes of growth. This leads to a new birth of mankind, and the Stranger then briefly describes the age of innocence, the fall of man and the barbarism that follows, and the partial restoration of man through divine interposition and the gift of the various arts of civilization. Plato does not offer this as a real explanation of the existing condition of the world, but it serves, like the myths introduced in other dialogues to present, in connection with accepted mythology, a theory which may account for some of the facts of life.
[11]: This may refer to philosophers (cf. Plat. Phaedo 82c) or, more probably, to those who, like Menelaus, were transferred to the abode of the blessed, or, like Heracles, became gods. Such individuals would be exempt from the consequences of any subsequent reversal of the World’s revolution.
[12]: The fellow-artisan of Hephaestus is Athena; seeds and plants are the gifts of Demeter and Dionysus.
[13]: i.e. the nature of example is to be explained below by means of an example. The example of the letters of the alphabet is employed also in the Plat. Theaet. 202 ff, but the Stranger cannot properly refer to that, as he was not present at the time. Or is this a dramatic slip on Plato’s part?
[14]: There is here a play on the words παρα-τιθέμενα δειχθῇ, δειχθέντα δέ, παρα-δείγματα Placed beside, they are shown and being shown, they become paradigms, i.e. objects of comparison, i.e. examples.
[15]: The weaver’s rod (for the Greeks appear to have used a rod, not a comb) was used to drive the threads of the woof close together, and also to keep the threads of the warp and woof distinct (cf. Plat. Crat. 388a). All the processes here described, familiar as they were to the ancients, have been done away with, or, at least, greatly modified, in Europe and America by the modern methods of industry.
[16]: i.e. the pull (ὁλκή)of the carder’s comb was less strong in the preparation of the threads of the woof than in that of the threads of the warp.
[17]: Plat. Soph. 235
[18]: i.e. relations to each other and relations to the standard of the mean.
[19]: See Plat. theaet. 283, Plat. Theaet. 277, Plat. Soph. 261
[20]: The second in order of the nine annual archons.
[21]: Cf. Hom. Il. 12.514: ἰητρὸς γὰρ ἀνὴρ πολλῶν ἀντάξιος ἄλλων. The image of the physician was used above, 293. The image of the captain (for the Greek κυβερνήτης had an importance commensurate with that of the captain, rather than of the pilot, in modern times) has just been used. See also Plat. Rep. 6.488 A; Plat. Laws 12.963 B.
[22]: This passage obviously refers to the trial of Socrates. The word μετέωρα was used by those who made all sorts of general accusations against Socrates (see Plat. Apol. 18 B, 19 B, with its reference to the Clouds of Aristophanes), and the reference of the words διαφθείροντα ἄλλους νεωτέρους to the accusation brought against him by Miletus, Anytus, and Lycon (Plat. Apol. 24 C: φησὶ γὰρ δὴ τοὺς νέους ἀδικεῖν με διαφθείροντα) is perfectly plain.
[23]: See 295 E.
[24]: See 292 E.
[25]: What are called five distinct forms of government are resolved into one—the one right form of which all others are imitations (297 C). This is to be sought in some small number or one person (ibid.). We have found it in the really scientific monarchy, and the other so-called forms of government, being merely imitations of this, require no names of their own.
[26]: The name is said to be twofold in meaning, probably because it was applied in cases in which there was a regularly constituted popular government and also in cases of mob rule.
[27]: The concentration of power in the hands of one man makes monarchy most efficient, but, since no human monarch is perfect, monarchy must be regulated by laws. Its efficiency makes it under such conditions the best government to live under. But without restraint of law monarchy becomes tyranny—the worst kind of oppression. Oligarchy occupies a position intermediate between monarchy and democracy—less efficient than the one and more efficient than the other, because power is distributed among a small number of persons—and is, therefore, when lawful less good, and when lawless less bad, than monarchy. Democracy, in turn, since power is too greatly subdivided, is inefficient, either for good or evil, and is, therefore, when lawful less good, and when lawless less bad, than either of the others.
[28]: 291 A.
[29]: Plat. Tim. 59 B, defines adamant as χρυσοῦ ὄζος a branch of gold. It was, then, a substance akin to gold. Platinum has been suggested.
[30]: Cf. 303 C.
[31]: See 287-290, 303-305.
[32]: The word ἀνδρεία has a much wider meaning than the English courage. Like the Latin virtus, it embraces all qualities which are desirable in a perfect man, especially the more active and positive virtues. When applied to one particular kind of virtue it is applied to courage, but throughout this discussion it is used in the wider sense, for which there is no single English equivalent.
[33]: More or less equivalent to naturalization. It apparently means the adoption into one state of children born to citizens of another. This was not, as a rule, practiced in the Greek city states, but Plato here seems to recommend it.