Page:Carroll - Euclid and His Modern Rivals.djvu/202

164 Min. An indefinite Line! What in the world do you mean? Is a curved Line more definite than a straight Line?

Nie. I don't know.

Min. Nor I. The rest of the sentence is slightly elliptical. Of course you mean 'the shortest which can be drawn'?

Nie. (eagerly) Yes, yes!

Min. Well, we have discussed that matter already. Go on.

Nie. Next we have an Axiom, 'that from one point to another only one straight Line can be drawn, and that if two portions of a straight Line coincide, these Lines coincide throughout their whole extent.'

Min. You bewilder me. How can one portion of a straight Line coincide with another?

Nie. (after a pause) It can't, of course, in situ: but why not take up one portion and lay it on another?

Min. By all means, if you like. Let us take a certain straight Line, cut out an inch of it, and lay it along another inch of the Line. What follows?

Nie. Then 'these Lines coincide throughout their whole extent.'

Min. Do they indeed? And pray who are 'these Lines'? The two inches?

Nie. (gloomily) I suppose so.

Min. Then the Axiom is simple tautology.

Nie. Well then, we mean the whole straight Line and—and—

Min. And what else? You can't talk of 'one straight Line' as 'these Lines,' you know.