APPENDED NOTES.

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[The references are (1) to chapters in translation; (2) to pages in text and translation; (3) to pages in Ed. I. of Stephens, as shewn in margin of text.]

pp. 10, 109. St. 147. D. περὶ δυνάμεών τι ἡμῖν Θεί δωρος ὅδε ἔγραφε, τῆς τε τρίποδος πέρι καὶ πεντέποδος ἀποφαίνων ὅτι μήκει οὐ ξύμμετροι τῇ ποδιαίᾳ, Theodorus was describing to us something about powers, proving as to the root of 3 and root of 5, that they are not in length commensurable with the foot-unit:' i. e. shewing that √3 is greater than I and less than 2, and that √5 is greater than 2 and less than 3; that therefore they do not contain unity so many times; that they are fractions, not integers. With Todiala understand γραμμῇ.

H. Schmidt in his Exegetic Commentary tries to shew that what Theodorus taught was a corollary to the Pythagorean Theorem (Euclid I. 47); that dvváues mean the powers. a2, b3 &c. as in modern algebra, and that Todiaía here is a unit square a2, by which the squares of a series of hypotenuses of right-angled triangles, having for their kathetes a and the foregoing hypotenuse, are all commensurable: since

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b2 = 2a3, c2 = 3a2, d2 = 4a3, &c. Theodorus may have taught this truth, but it is certainly not introduced here, as the word μnke proves, shewing rodiaía to be the linear foot-unit. And that duvάues mean roots, not the modern 'powers,' is clear from what follows 148 A, ὅσαι δὲ τὸν ἑτερομήκη, δυνάμεις, ὡς μήκει μὲν οὐ ξυμμέτρους ἐκείναις, τοῖς δ ̓ ἐπιπέδοις ἃ δύνανται, i.e. √√3, √5 &c. are called 'powers,' because they have power, when squared, to form areas which are commensurable with the squares 4, 9, 16, 25, &c. So Professors Jowett and Campbell.

pp. 15, 116. St. 151 Ε. ὃν ἔλεγε καὶ Πρωταγόρας. The words in which Plato recites the famous doctrine of Protagoras on the relativity of knowledge (μέτρον ἄνθρωπος, homo mensura) are probably cited from that philosopher's treatise called 'Aλn@ela, Truth. But the identification of it with the suggestion of Theaetetus that knowledge is sensuous perception, I suppose with Grote, (Plato, II. p. 323 note) to be Plato's own view, which Grote considers unjust, contending at some length against it (322-336). His main argument is, that implication of object and subject is universal, affecting Noumena as well as Phaenomena: 'cogitata' suppose a 'cogitans,' as much as 'sensibilia' suppose a 'sentiens.' Therefore Protagoras would not have limited the application of his maxim to aïσ◊ŋoɩs alone. We must concur with Grote in lamenting that we get the statements and arguments of Protagoras at second hand only; and that the views of others, as of Heracleitus and his great opponent Parmenides, are known to us only in fragments and citations, and from the late biographies of Diogenes Laertius.

pp. 16, 117. St. 152 Α. "Ανθρωπος δὲ σύ τε καγώ; Socrates means: as Protagoras applies his doctrine to man generally, he applies it to you and me, seeing that we are

men.

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pp. 16, 117. St. 152 B.C. By the illustration here used Socrates proves that the maxim of Protagoras means that what appears to any one 'is' to him: and, as appearance implies perception, it follows that perception is knowledge.

pp. 16, 118. St. 152 C. "Ap' ovv K.T.λ. Why this outburst? Socrates has just drawn from Theaetetus the admission that αἴσθησις τοῦ ὄντος ἐστί, perception is of the existent, of that which 'is.' But the Heracleitean doctrine does not allow that anything 'is' (orí) but says that all things yiyveral 'come to be.' And Protagoras in his 'AλýDela adopts this: so we must infer from what follows. What? says Socrates: did Protagoras then teach an obscure exoteric doctrine (víaro) to the multitude, and tell the truth in esoteric confidence (ev ảπoppýτ eyev) to his disciples? Did he teach the one to believe in övra, the others in nothing but γιγνόμενα? Αινίττεσθαι, 'to speak in riddles, is used of obscure or purposely veiled language. That Plato considered the doctrines which now follow to be involved in the teaching of Protagoras, is evident; indeed he distinctly says so; nor can we doubt that he had foundation for his statement in the writings of that sophist. But it is evident also that he does not here quote his precise words: and it must always be doubtful how far Protagoras was committed to all the refinements of the Heracleitean school, which appear in the next passage and afterwards.

pp. 17, 119. The Platonic complication of the three doctrines (1) the Heracleitean (olov peúμara κiveîσlaι Tà πάντα) (2) the Protagorean (πάντων χρημάτων ἄνθρωπον μέτρον είναι) and that put forth by Theaetetus (αἴσθησιν ἐπιστήμην yiyveola) is summarised below, 15, pp. 28, 135. The following observations of Grote (Plato, II. p. 324) deserve special attention, and supply a valuable key to the difficulties occurring in Plato's treatment of this subject from 9 to 15

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and again from 15 to 30, where the definition aïolŋois is finally abandoned. Upon all the three opinions, thus represented as cognate or identical, Sokrates bestows a lengthened comment (occupying a half of the dialogue).... His strictures are not always easy to follow with assurance, because he often passes with little notice from one to the other of the three doctrines which he is examining: because he himself, though really opposed to them, affects in part to take them up and to suggest arguments in their favour: and further because, disclaiming all positive opinion of his own, he sometimes leaves us in doubt what is his real purpose-whether to expound or to deride the opinions. of others whether to enlighten Theaetetus, or to test his power of detecting fallacies. We cannot always distinguish between the ironical and the serious. Lastly, it is a still greater difficulty that we have not before us any one of the three opinions as set forth by their proper supporters.' pp. 21, 125. St. 155 E. St. 155 E. Tov aμvýτwv. Prof. Campbell in his learned Introduction to this dialogue examines at large the question, who are the men whom Plato glances at here in such uncomplimentary language. Had he in mind Antisthenes and the Cynics? or Democritus and the Atomists? If Plato had either of these two schools in view, it seems more probable that these were the followers of Democritus. The ymyeves mentioned in γηγενείς the Sophistes (p. 246 &c.) are evidently the same as the σκληροὶ καὶ ἀντίτυποι (εὖ μάλ ̓ ἄμουσοι) in this place. See Campbell, pp. xx, xxx.

pp. 22, 126. St. 156 D. I must retract the partial favour which my notes in the text and translation shew to the interpolated words of Cornarius. I find the view taken by Prof. Campbell and Prof. Jowett supported also by H. Schmidt (though Müller in his German translation