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GORGIAS: Exactly.

SOCRATES: And yet I do not believe that you really mean to call any of these arts rhetoric; although the precise expression which you used was, that rhetoric is an art which works and takes effect only through the medium of discourse; and an adversary who wished to be captious might say, ‘And so, Gorgias, you call arithmetic rhetoric.’ But I do not think that you really call arithmetic rhetoric any more than geometry would be so called by you.

GORGIAS: You are quite right, Socrates, in your apprehension of my meaning.

SOCRATES: Well, then, let me now have the rest of my answer:—seeing that rhetoric is one of those arts which works mainly by the use of words, and there are other arts which also use words, tell me what is that quality in words with which rhetoric is concerned:—Suppose that a person asks me about some of the arts which I was mentioning just now; he might say, ‘Socrates, what is arithmetic?’ and I should reply to him, as you replied to me, that arithmetic is one of those arts which take effect through words. And then he would proceed to ask: ‘Words about what?’ and I should reply, Words about odd and even numbers, and how many there are of each. And if he asked again: ‘What is the art of calculation?’ I should say, That also is one of the arts which is concerned wholly with words. And if he further said, ‘Concerned with what?’ I should say, like the clerks in the assembly, ‘as aforesaid’ of arithmetic, but with a difference, the difference being that the art of calculation considers not only the quantities of odd and even numbers, but also their numerical relations to themselves and to one another. And suppose, again, I were to say that astronomy is only words—he would ask, ‘Words about what, Socrates?’ and I should answer, that astronomy tells us about the motions of the stars and sun and moon, and their relative swiftness.