Page:Carroll - Euclid and His Modern Rivals.djvu/222

184 Nos. No. We have the Axiom (p. 10, Ax. 2) 'Two straight lines that have two points in common lie wholly in the same straight line.'

Min. Well! That is certainly the strangest Axiom I ever heard of! The idea of asserting, as an Axiom, that Right Lines answer to their Definition!

Nos. (bashfully) Well, you see there were several of us at work drawing up this Syllabus: and we've got it a little mixed: we don't quite know which are Definitions and which are Axioms.

Min. So it appears: not that it matters much: the practical test is the only thing of importance. Do you adopt Euc. I. 14?

Nos. Yes.

Min. Then we may go on to the next subject. Be good enough to define 'Angle.'

P. 8. Def. 11. 'When two straight lines are drawn from the same point, they are said to contain, or to make with each other, a plane angle.'

Min. Humph! You are very particular about drawing them from a point. Suppose they were drawn to the same point, what would they make then?

Nos. An angle, undoubtedly.

Min. Then why omit that case? However, it matters little. You say 'a plane angle,' I observe. You limit an angle, then, to a magnitude less than the sum of two right angles.

Nos. No, I can't say we do. A little further down we