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number (the rest exc. I); (7) uñkos, length (all integral numbers after 1) which may be represented by straight lines, and used to form squares; (8) duvámers (irrational roots, N3, N5, VÕ «c.) which are incommensurable with the unit of length (Todcala), but can become sides of figures commensurable in area with squares. Socrates applauds this invention, and exhorts Theaetetus to apply his mind in the same way to discover a definition of knowledge.]
Theae. Yes, Socrates; this method now indeed appears easy. You seem to be asking the same sort of question that occurred some time since to us in our discussions ; to myself I mean, and your namesake, Socrates here.
So. What was that, Theaetetus?
Theae. Theodorus was writing out for us something about 'powers,' proving, as to the tripod" and the 'pentepod,' that in length they are not commensurable with the foot-unit: and so proceeding one by one as far as seventeen: but here he somehow came to a pause. We then bethought us of such a notion as this: since the 'powers' were evidently infinite in number, to try to comprise them under one term, by which we should entitle all these 'powers.'
So. Did you find any such term ?
Theae. We divided number generally into two classes, one, that which is capable of being formed by the multiplication of equal factors into one another, we likened in form to the square, and called it square and equilateral.
So. Very good.
1 Tρίπους, as Heindorf says, 1s ευθεία δυνάμει τρίπους, 1.e. W3, which is irrational (not commensurate with the foot-unit, not integral), but potentially rational (becoming so when squared: W3x73=3). So TEVTÉTOUS and the rest. The use of dúvauis is therefore different from the modern mathematical term "power" (**, 23...x").
Theae. All intervening numbers, to which belong 3 and 5 and every one that is incapable of being formed by the multiplication of equal factors, but is formed either by a larger number having a smaller-or by a smaller number having a larger -as its multiplier, we likened on the other hand to the oblong figure, which in every instance has greater and lesser sides, and called it oblong number.
So. Excellent. What next?
Theae. All lines which being squared form an equilateral plane figure we defined to be length'; all which form an oblong, we comprised under the name 'powers' (i.e. irrational roots), as not being commensurable with the others except through the surfaces which they have power to formo. And similarly with respect to the solids (cubes).
So. Nobody in the world could do better, my boys. So I do not think Theodorus will incur the guilt of perjury. Theae. But as
But as to your question about knowledge, Socrates, I could not answer it in the same way as that about length and power. Yet you seem to me to be looking for some such answer. So that now Theodorus again appears to be a false speaker.
So. Well, but if he had praised your running, and said he had never met with any young man so fleet, and then in
2 This appears as a general expression in the form
Example: 2x 11 (=11* 2) =3. As n is any integer, this includes all Oumbers greater than unity, τετράγωνος as well as προμήκης αριθμός.
3 Toîs ó ÉLTÉdous å dúvavtal. Thus vīz being 3.464 (nearly), Nizx/12=12=2x6 =3 * 4 =(geometrically represented) a rectangle with sides respectively either 2 and 6, or 3 and 4, or an imaginary square with side 3'464 (nearly).
a racing-match you had been defeated by one in the prime of life, and very fleet, do you think his praise would have been any
the less true? Theae. I do not.
So. And, as to knowledge, as I was saying a little while since, do you think it a small thing to discover its nature, and not one of the highest achievements ?
Theae. Nay indeed, Socrates, I do place it among the very highest of all.
So. Then be at ease about yourself: and consider that Theodorus speaks truly, and shew desire in every way to obtain a right definition of knowledge, as of all other things.
Theae. As for desire, Socrates, it will not be found wanting
6 [Theaetetus, though he has not yet succeeded in finding a definition of knowledge, confesses a mental feeling that he is always on the verge of
Socrates likens this feeling to the throes of impending child. birth in women: and reminding Theaetetus that he himself (Socrates) is the son of an excellent midwife, he claims the analogous function of assisting the labour of intellectual parturition in the minds of young men ; and describes the obstetric art in many of its details, with a view to illustrate and justify his own method as an educator.]
So. Come then: you made a good suggestion just now. Imitate your answer about the 'powers'. As you comprised their vast number under one term, so also try to describe the many kinds of knowledge by a single definition.
Theae. I assure you, Socrates, I have often endeavoured to gain insight into that matter, while listening to the questions you put. But, though I cannot persuade myself that I have anything important of my own to say, or that I have heard from some one else any such statement as you require,
nevertheless I cannot rid myself of the feeling that I am on the point of doing so'.
So. Oh! you are in the throes of labour, dear Theaetetus, through being not empty, but pregnant.
Theae. I do not know, Socrates. I tell you my feeling, at all events.
So. Have you not heard then, simpleton, that I am the son of a very famous and solid midwife, Phaenarete?
Theae. I have heard it before now.
So. I do really. But don't tell of me to other people. I am not known, my friend, to have this skill. And others, being unaware, do not say this of me, but only that I am a very strange person, and that I perplex people. Have you heard this too?
Theae. I have.
So. Reflect then upon the general situation of midwives, and
you will more easily learn what I mean. You know, I suppose, that none of them practise while they are still conceiving and bearing children, but those alone who are past child-bearing
So. This custom is said to be derived from Artemis, for that she, though a virgin, has the charge of parturition. Accordingly, she did not indeed allow barren women to become midwives, because human nature is too weak to acquire an art of which it has no experience: but she assigned it to
1 MEMEL is undoubtedly the true reading, giving the cue to the parable of the midwives. Melv would fail to do this.
those who are past the age of childbearing, in honour of their resemblance to herself.
So. Is not this also natural, that those who conceive and those who do not are better known by midwives than by others ?
Theae. Quite so.
So. Moreover also midwives, by giving drugs and chanting incantations, are able to excite the throes and to quell them, if they will, and to make those who have a hard time bring forth: and they produce abortion', if the case require it.
So. Have you furthermore noted this in them, that they are also very clever match-makers, being well skilled to know what woman uniting with what man must bear the finest children ?
Theae. I was not quite aware of that.
So. I assure you they pride themselves on this much more than on their special practice. Just consider. Do you think the care and collection of the fruits of the earth belongs to one art, and the knowledge of what soil you must plant or sow to another?
Theae. No, to the same.
So. And do you consider it different in the case of a woman?
Theae. Seemingly not.
1 Νέον όν. Prof. Campbell writes, ‘Sc. Tò Bpépos, said here of the embryo "at an early stage,” i.e. before it is dangerous to do so.' But most commentators do not believe that véov would be used of Tò kúnua. Heindorf conjectures déov for včov ởv. The words may be a gloss, and in translation no point is lost by neglecting them, as above.
2 Gr. ομφαλητομία.