SOC. Take this example. If anyone should ask us about some common everyday thing, for instance, what clay is, and we should reply that it is the potters’ clay and the oven makers’ clay and the brickmakers’ clay, should we not be ridiculous? THEAET. Perhaps. SOC. Yes in the first place for assuming that the questioner can understand from our answer what clay is, when we say clay, no matter whether we add the image-makers’ 
 
or any other craftsmen’s. Or does anyone, do you think, understand the name of anything when he does not know what the thing is? THEAET. By no means. SOC. Then he does not understand knowledge of shoes if he does not know knowledge. THEAET. No. SOC. Then he who is ignorant of knowledge does not understand cobblery or any other art. THEAET. That is true. SOC. Then it is a ridiculous answer to the question what is knowledge? when we give the name of some art; 
 
for we give in our answer something that knowledge belongs to, when that was not what we were asked. THEAET. So it seems. SOC. Secondly, when we might have given a short, everyday answer, we go an interminable distance round; for instance, in the question about clay, the everyday, simple thing would be to say clay is earth mixed with moisture without regard to whose clay it is. THEAET. It seems easy just now, Socrates, as you put it; but you are probably asking the kind of thing that came up among us lately when
 
your namesake, Socrates here, and I were talking together. SOC. What kind of thing was that, Theaetetus? THEAET. Theodorus here was drawing some figures for us in illustration of roots, showing that squares containing three square feet and five square feet are not commensurable in length with the unit of the foot, and so, selecting each one in its turn up to the square containing seventeen square feet and at that he stopped. Now it occurred to us, since the number of roots appeared to be infinite, to try to collect them under one name,
 
	by which we could henceforth call all the roots. 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.) SOC. And did you find such a name? THEAET. I think we did. But see if you agree. SOC. Speak on. THEAET. We divided all number into two classes. The one, the numbers which can be formed by multiplying equal factors, we represented by the shape of the square and called square or equilateral numbers. SOC. Well done! THEAET. The numbers between these, such as three

 
	
and five and all numbers which cannot be formed by multiplying equal factors, but only by multiplying a greater by a less or a less by a greater, and are therefore always contained in unequal sides, we represented by the shape of the oblong rectangle and called oblong numbers. SOC. Very good; and what next? THEAET. All the lines which form the four sides of the equilateral or square numbers we called lengths, and those which form the oblong numbers we called surds, because they are not commensurable with the others
 
in length, but only in the areas of the planes which they have the power to form. And similarly in the case of solids. That is, cubes and cube roots. SOC. Most excellent, my boys! I think Theodorus will not be found liable to an action for false witness. THEAET. But really, Socrates, I cannot answer that question of yours about knowledge, as we answered the question about length and square roots. And yet you seem to me to want something of that kind. So Theodorus appears to be a false witness after all. SOC. Nonsense! If he were praising your running and said he had never met any young man who was so good a runner, and then you were beaten in a race by a full grown man who held the record, do you think his praise would be any less truthful? THEAET. Why, no. SOC. And do you think that the discovery of knowledge, as I was just now saying, is a small matter and not a task for the very ablest men? THEAET. By Zeus, I think it is a task for the very ablest. SOC. Then you must have confidence in yourself, and believe that Theodorus is right,
 
and try earnestly in every way to gain an understanding of the nature of knowledge as well as of other things. THEAET. If it is a question of earnestness, Socrates, the truth will come to light. SOC. Well then—for you pointed out the way admirably just now—take your answer about the roots as a model, and just as you embraced them all in one class, though they were many, try to designate the many forms of knowledge by one definition. THEAET. But I assure you, Socrates, I have often tried to work that out, when I heard reports of the questions that you asked, but I can neither persuade myself that I have any satisfactory answer, nor can I find anyone else who gives the kind of answer you insist upon; and yet, on the other hand, I cannot get rid of a feeling of concern about the matter. SOC. Yes, you are suffering the pangs of labor, Theaetetus, because you are not empty, but pregnant. THEAET. I do not know, Socrates; I merely tell you what I feel. SOC. Have you then not heard, you absurd boy, that I am the son of a noble and burly midwife, Phaenarete? THEAET. Yes, I have heard that. SOC. And have you also heard that I practise the same art? THEAET. No, never. SOC. But I assure you it is true; only do not tell on me to the others; for it is not known that I possess this art. But other people, since they do not know it, do not say this of me, but say that I am a most eccentric person and drive men to distraction. Have you heard that also? THEAET. Yes, I have. SOC. Shall I tell you the reason then? THEAET. Oh yes, do. SOC. Just take into consideration the whole business of the midwives, and you will understand more easily what I mean. For you know, I suppose, that no one of them attends other women while she is still capable of conceiving and bearing but only those do so who have become too old to bear. THEAET. Yes, certainly. SOC. They say the cause of this is Artemis, because she, a childless goddess, has had childbirth allotted to her as her special province. Now it would seem she did not allow
 
barren women to be midwives, because human nature is too weak to acquire an art which deals with matters of which it has no experience, but she gave the office to those who on account of age were not bearing children, honoring them for their likeness to herself. THEAET. Very likely. SOC. Is it not, then, also likely and even necessary, that midwives should know better than anyone else who are pregnant and who are not? THEAET. Certainly. SOC. And furthermore, the midwives, by means of drugs
 
and incantations, are able to arouse the pangs of labor and, if they wish, to make them milder, and to cause those to bear who have difficulty in bearing; and they cause miscarriages if they think them desirable. THEAET. That is true. SOC. Well, have you noticed this also about them, that they are the most skillful of matchmakers, since they are very wise in knowing what union of man and woman will produce the best possible children? THEAET. I do not know that at all. SOC. But be assured that they are prouder of this
 
than of their skill in cutting the umbilical cord. Just consider. Do you think the knowledge of what soil is best for each plant or seed belongs to the same art as the tending and harvesting of the fruits of the earth, or to another? THEAET. To the same art. SOC. And in the case of a woman, do you think, my friend, that there is one art for the sowing and another for the harvesting? THEAET. It is not likely. SOC. No; but because there is a wrongful and unscientific way of bringing men and women together, which is called pandering, the midwives, since they are women of dignity and worth, avoid matchmaking, through fear of falling under the charge of pandering. And yet the true midwife is the only proper match-maker. THEAET. It seems so. SOC. So great, then, is the importance of midwives; but their function is less important than mine. For women do not, like my patients, bring forth
 
at one time real children and at another mere images which it is difficult to distinguish from the real. For if they did, the greatest and noblest part of the work of the midwives would be in distinguishing between the real and the false. Do you not think so? THEAET. Yes, I do. SOC. All that is true of their art of midwifery is true also of mine, but mine differs from theirs in being practised upon men, not women, and in tending their souls in labor, not their bodies. But the greatest thing about my art is this,
 
that it can test in every way whether the mind of the young man is bringing forth a mere image, an imposture, or a real and genuine offspring. For I have this in common with the midwives: I am sterile in point of wisdom, and the reproach which has often been brought against me, that I question others but make no reply myself about anything, because I have no wisdom in me, is a true reproach; and the reason of it is this: the god compels me to act as midwife, but has never allowed me to bring forth. I am, then, not at all a wise person myself,
 
nor have I any wise invention, the offspring born of my own soul; but those who associate with me, although at first some of them seem very ignorant, yet, as our acquaintance advances, all of them to whom the god is gracious make wonderful progress, not only in their own opinion, but in that of others as well. And it is clear that they do this, not because they have ever learned anything from me, but because they have found in themselves many fair things and have brought them forth. But the delivery is due to the god and me. And the proof of it is this: many before now,
 
being ignorant of this fact and thinking that they were themselves the cause of their success, but despising me, have gone away from me sooner than they ought, whether of their own accord or because others persuaded them to do so. Then, after they have gone away, they have miscarried thenceforth on account of evil companionship, and the offspring which they had brought forth through my assistance they have reared so badly that they have lost it; they have considered impostures and images of more importance than the truth, and at last it was evident to themselves, as well as to others, that they were ignorant.