Page:Carroll - Euclid and His Modern Rivals.djvu/97

. II.] but we may as well have that stated, to complete the enquiry.

Nie. We give Euclid's 12th Axiom, which we prove from Prop. 32, using the principle of Euc. X. 1 (second part), that 'if the greater of two unequal magnitudes be bisected, and if its half be bisected, and so on; a magnitude will at length be reached less than the lesser of the two magnitudes.'

Min. That again is a mode of proof entirely unsuited to beginners.

The general style of your admirable treatise I shall not attempt to discuss: it is one I would far rather take as a model to imitate than as a subject to criticise.

I can only repeat, in conclusion, what I have already said, that your book, though well suited for advanced students, is not so for beginners.

Nie. At this rate we shall make short work of the twelve Modern Rivals!