[1]: Erineum was between Eleusis and Athens, near the Cephissus. Apparently Eucleides had walked some thirty miles.
[2]: The scene is evidently laid in a gymnasium; the young men have been exercising.
[3]: A simple form of the first statement would be: the square roots of 3, 5, etc., are irrational numbers or surds. The word δύναμις has not the meaning which we give in English to power, namely the result of multiplication of a number by itself, but that which we give to root, i.e. the number which, when multiplied by itself, produces a given result. Here Theaetetus is speaking of square roots only; and when he speaks of numbers and of equal factors he evidently thinks of rational whole numbers only, not of irrational numbers or fractions. He is not giving an exhaustive presentation of his investigation, but merely a brief sketch of it to illustrate his understanding of the purpose of Socrates. Toward the end of this sketch the word δύναμις is limited to the square roots of oblong numbers, i.e. to surds. The modern reader may be somewhat confused because Theaetetus seems to speak of arithmetical facts in geometrical terms. (Cf. Gow, Short History of Greek Mathematics, p. 85.)
[4]: That is, cubes and cube roots.
[5]: An allusion to the title of Protagoras’s book, Truth.
[6]: Hom. Il. 14.201, 302
[7]: Hom. Il. 8.18 ff. especially 26. In this passage Zeus declares that all the gods and goddesses together could not, with a golden chain, drag him from on high, but that if he pulled, he would drag them, with earth and sea, would then bind the chain round the summit of Olympus, and all the rest would hang aloft. This crowning argument is a reductio ad absurdum of the habit of using texts from Homer in support of all kinds of doctrine.
[8]: Eur. Hipp. 612ἡ γλῶσσ’ ὀμώμοχ’, ἡ δὲ φρὴν ἀνώμοτος, my tongue has sworn, but my mind is unsworn.
[9]: Hes. Theog. 750 Iris is the messenger of heaven, and Plato interprets the name of her father as Wonder (θαῦμα).
[10]: The rite called amphidromiatook place a few days after the birth of a child. After some ceremonies of purification the nurse, in the presence of the family, carried the infant rapidly about the family hearth, thereby introducing him, as it were, to the family and the family deities. At this time the father decided whether to bring up the child or to expose it. Sometimes, perhaps, the child was named on this occasion. In the evening relatives assembled for a feast at which shell-fish were eaten.
[11]: Truthwas apparently the title, or part of the title, of Protagoras’s book.
[12]: Sciron was a mighty man who attacked all who came near him and threw them from a cliff. He was overcome by Theseus. Antaeus, a terrible giant, forced all passersby to wrestle with him. He was invincible until Heracles crushed him in his arms.
[13]: Hom. Od. 16.121 Hom. Od.17.432 Hom. Od. 19.78
[14]: In Athenian legal procedure each party to a suit presented a written statement—the charge and the reply—at a preliminary hearing. These statements were subsequently confirmed by oath, and the sworn statement was called διωμοσία or ἀντωμοσία, which is rendered above by affidavit as the nearest English equivalent.
[15]: This may refer to Pind. Nem. 10.87 f.:ἥμισυ μέν κε πνέοις γαίας ὑπένερθεν ἐών, ἥμισυ δ’ οὐρανοῦ ἐν χρυσέοις δόμοσιν Thou (Polydeuces) shalt live being half the time under the earth and half the time in the golden dwellings of heaven, but it may be a quotation from one of the lost poems of Pindar.
[16]: The Athenians regarded the proper draping of the cloak as a sign of good breeding. The well-bred Athenian first threw his cloak over the left shoulder, then passed it round the back to the right side, then either above or below the right arm, and finally over the left arm or shoulder. See Aristophanes, Birds, 1567 f., with Blaydes’s notes.
[17]: Hom. Il. 18.104;Hom. Od. 20. 379
[18]: The legislator may call his laws advantageous, and that name, if it is given them when they are enacted, will belong to them, whatever their character may be.
[19]: See 168 B.
[20]: Parmenides, line 98 (ed. Mullach)
[21]: In its context the infinitive is necessary; but Plato may have quoted carelessly and may have used the indicative.
[22]: In the game referred to (called διελκυστίνδα by Pollux, ix. 112) the players were divided into two parties, each of which tried to drag its opponents over a line drawn across the palaestra.
[23]: A proverbial expression. An open plain is just what cavalry desires.
[24]: Il. 3.172;Od. 8.22; xiv. 234
[25]: Aesch. Lib. 197 ff. makes Electra recognize the presence of her brother Orestes by the likeness of his footprints to her own.
[26]: The similarity is in the Greek words κέαρ or κῆρ, heart, and κηρός, wax. The shaggy heart is mentioned in the Hom. Il. 2.851; Hom. Il. 16.554 The citation of Homer, here and below, is probably sarcastic—in reference to the practice of some of the sophists who used and perverted his words in support of their doctrines.
[27]: A man who was leading the way through a river was asked if the water was deep. He replied αὐτὸ δείξει, the event itself will show (i.e. you can find out by trying). The expression became proverbial.
[28]: The length of speeches in the Athenian law courts was limited by a water-clock.
[29]: Στοιχεῖον and συλλαβή originally general terms for element and combination, became the common words for letter and syllable.
[30]: The distinction here made is that which we make between vowels and consonants. The seven Greek vowels are α, ε, η, ι, ο, υ, ω called φωνήεντα.
[31]: Cf. Plat. Theaet. 204b
[32]: The reader is reminded that words στοιχεῖον and συλλαβή have the meanings element and combination as well as letter and syllable.
[33]: Hes. WD 456
[34]: In which perspective is the main thing.
[35]: The Mysians were despised as especially effeminate and worthless
[36]: A σκυτάλη was a staff, especially a staff about which a strip of leather was rolled, on which dispatches were so written that when unrolled they were illegible until rolled again upon another staff of the same size and shape.
[37]: Meletus was one of those who brought the suit which led to the condemnation and death of Socrates.