previous next

[266a]

Stranger
And yet tame gregarious animals have all, with the exception of about two species, been already divided; for dogs are not properly to be counted among gregarious creatures.

Younger Socrates
No, they are not. But how shall we divide the two species?

Stranger
As you and Theaetetus ought by rights to divide them, since you are interested in geometry.

Younger Socrates
How do you mean?

Stranger
By the diameter, of course, and again by the diameter of the square of the diameter.1

Younger Socrates
What do you mean by that? [266b]

Stranger
Is the nature which our human race possesses related to walking in any other way than as the diameter which is the square root of two feet?2

Younger Socrates
No.

Stranger
And the nature of the remaining species, again, considered from the point of view of the square root, is the diameter of the square of our root, if it is the nature of twice two feet.3

Younger Socrates
Of course; and now I think I almost understand what you wish to make plain.

Stranger
Socrates, do we see that besides this something else has turned up [266c] in these divisions of ours which would be a famous joke?

Younger Socrates
No. What is it?

Stranger
Our human race shares the same lot and runs in the same heat as the most excellent and at the same time most easy-going race of creatures.4

Younger Socrates
Yes, I see that; it is a very queer result.

Stranger
Indeed? But is it not reasonable that they arrive last, who are the slowest?

Younger Socrates
Yes, that is true.

Stranger
And do we fail to notice this further point, that the king appears in a still more ridiculous light, running along with the herd and paired in the race with the man of all others [266d] who is most in training for a life of careless ease?5

Younger Socrates
Certainly he does.

Stranger
For now, Socrates, we have shown more clearly the truth of that which we said yesterday in our search for the sophist.6

Younger Socrates
What was it?

Stranger
That this method of argument pays no more heed to the noble than to the ignoble, and no less honor to the small than to the great, but always goes on its own way to the most perfect truth.

Younger Socrates
So it seems.

Stranger
Then shall I now, without waiting for you to ask me, guide you of my own accord along that shorter way referred to a moment ago that leads [266e] to the definition of the king?

Younger Socrates
By all means.

Stranger
I say, then, that we ought at that time to have divided walking animals immediately into biped and quadruped, then seeing that the human race falls into the same division with the feathered creatures and no others, we must again divide the biped class into featherless and feathered, and when that division is made and the art of herding human beings is made plain, we ought to take the statesmanlike and kingly man and place him as a sort of charioteer therein, handing over to him the reins of the state, because that is his own proper science.


1 The word “diameter” here denotes the diagonal of a square. The early Greek mathematicians worked out their arithmetical problems largely by geometrical methods (cf. Plat. Theaet. 147 D ff). The diagonal of the unit square (√2) was naturally of especial interest. It was called sometimes, as here simply διάμετρος, sometimes, as just below, διάμετρος δυνάμει δίπους, or, more briefly, διάμετρος δίπους. Given a square the side of which is the unit (i.e. one square foot), the length of the diagonal will be √2 and the square constructed with that diagonal as its side will contain two square feet. The length of the diagonal of this square will be √4=2 feet, and its area will be four square feet.

2 There is here a play upon words. Man, being a two-footed (δίπους) animal, is compared to the diagonal of the unit square (√2,διάμετρος δίπους).

3 i.e. the remaining species is four-footed. Our diameter is √2, and four is the area of the square constructed on the diagonal of the square which has √2 as its side. All this satirizes the tendency of contemporary thinkers to play with numbers.

4 The animal referred to is the pig. See P. Shorey, Classical Philology,1917, July, p. 308.

5 i.e. the swineherd, the pig belonging to γένει εὐχερεστάτῳ.

6 See Plat. Soph. 227B.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 United States License.

An XML version of this text is available for download, with the additional restriction that you offer Perseus any modifications you make. Perseus provides credit for all accepted changes, storing new additions in a versioning system.

load focus Greek (1903)
hide Places (automatically extracted)

View a map of the most frequently mentioned places in this document.

Download Pleiades ancient places geospacial dataset for this text.

hide Display Preferences
Greek Display:
Arabic Display:
View by Default:
Browse Bar: