Page:Carroll - Euclid and His Modern Rivals.djvu/251

§ 2.] Min. I heartily agree in your general principle, though I need scarcely remind you that it has been frequently charged against you, as fault, that you state as an Axiom what is really a Theorem.

Euc. That charge has been met (see p. 40). To return to my subject. I merely prove, once for all, in Prop. 2, that a Line can be drawn, from a given point, and equal to a given Line, by the original machinery alone, and without transferring distances. After that, my reader is welcome to transfer a distance by any method that comes handy, such as a bit of string &c.: and of course he may now transfer his compasses to a new centre. And this is all I expect him to do in Prop. 3.

Min. Then you don't expect these five Circles &c. to be drawn whenever we have to cut off, from one Line, a part equal to another?

''Euc. Pas si bête, mon ami''.

Min. Some of your Modern Rivals are, however, a little discontented with the very scanty machinery you allow.

Euc. 'A bad workman always quarrels with his tools.'

Min. Their charge against you is 'the exclusion of hypothetical constructions.' Mr. Wilson says (Pref. p. i.) 'The exclusion of hypothetical constructions may bementioned as a self-imposed restriction which has made the confused order of his first book necessary, without any compensating advantage.'

Euc. In reply, I cannot do better than refer you to Mr. Todhunter's Essay on Elementary Geometry (p. 186). 'Confused order is rather a contradictory expression,' &c. (see p. 241).