Part 126

Footnote 146:

The literal translation instead of “in which the factors are the same,” is “which is able to become equally equal,” by which is meant a number multiplied by itself.

-----

Socr. Very well.

Theæ. But the intermediate numbers, such as three and five, and every one in which the factors are not the same, but a greater number is multiplied by a less, or a less by a greater, so that a greater and a lesser side always enclose them, we compared to an oblong figure, and called them oblong numbers.

Socr. Admirable. But what next?

Theæ. Such lines as square an equilateral and plane number, we defined to be length, and such as square an oblong number, powers, as not being commensurate with them in length, but with the planes which they produce. And the case is the same with solids.

15. Socr. Excellently done, my boys; so that Theodorus appears to me not liable to the charge of having given false testimony.

Theæ. However, Socrates, I shall not be able to answer your question about science, as I did that about length and power; though you appear to me to seek something of the same kind. So that Theodorus again appears to be a false witness.

Socr. How so? If, praising you for running, he should say that he never met with any youth who ran so swift, and afterwards you should be defeated in running by a man who is full grown and very swift, do you think he would have praised you with less truth?

Theæ. I do not.

Socr. But with respect to science, as I just now spoke of it, do you think it is a trifling matter to find out what it is, and not in every way difficult?

Theæ. By Jupiter, I think it difficult in the extreme.

16. Socr. Have confidence, then, in yourself, and think that Theodorus spoke to the purpose, and endeavour by all possible means to comprehend the notion both of other things, and also of science, what it is.

Theæ. As far as endeavour goes, Socrates, it shall be found out.

Socr. Come then: for you began very well just now; endeavour, in imitation of your answer about powers, as you comprised those, which are many, under one general idea, so likewise to designate many sciences by one notion.

Theæ. Be assured, Socrates, I have often attempted to examine this, on hearing the questions that are propounded by you; but I can neither persuade myself that I can say any thing satisfactory, nor can I hear any one else answering in the manner you require, though still I do not desist from the attempt.

17. Socr. You are in labour, my dear Theætetus, not because you are empty, but pregnant.

Theæ. I know not, Socrates; however I tell you how the case stands with me.

Socr. What, absurd youth, have you not heard that I am son of the very noble and awful midwife Phænarete?

Theæ. I have heard so.

Socr. And have you also heard that I study the same art?

Theæ. By no means.

Socr. Be assured, however, that it is so: but do not betray me to others. For they are not aware, my friend, that I possess this art? but they, since they are ignorant of it, do not say this of me, but that I am a most absurd man, and make men doubt. Have you not heard this?

Theæ. I have.

Socr. Shall I tell you the reason of it?

Theæ. By all means.

Socr. Consider, then, every thing that relates to midwives, and you will more easily understand what I mean. For you doubtless know, that not one of them delivers others, while she herself can conceive and bring forth, but those who can no longer bring forth.