Page:Carroll - Euclid and His Modern Rivals.djvu/253

§ 3.] all retained, and those only are omitted which seem to be but the steps of a needlessly protracted ascent. The short road thus opened will be found perfectly solid inconstruction, and at the same time far less tedious and fatiguing than the circuitous one hitherto in vogue.'

Euc. I think Mr. Wilson's Th. 17 (p. 27), with its five figures (all necessary, though he only draws one), and still more his marvellous Problem, 'approached by four stages,' which fills pages 69 to 72, are pretty good instances of lengthy demonstration. And Mr. Cooley's 'short and solid road' contains, if I remember right, a rather breakneck crevasse!

Min. The next charge against you is 'too great brevity of demonstration.' Mr. Leslie (a writer whom I have not thought it necessary to review as a 'Modern Rival,' as his book is nearly seventy years old) says (Pref. p. vi.) 'In adapting it' (the Elements of Euclid) 'to the actual state of the science, I have … sought to enlarge the basis … The numerous additions which are incorporated in the text, so far from retarding will rather facilitate progress, by rendering more continuous the chain of demonstration. To multiply the steps of ascent, is in general the most expeditious mode of gaining a summit.'

Euc. I think you had better refer him to Mr. Wilson and Mr. Cooley: they will answer him, and he in his turn will confute them!

Min. The last charge relating to demonstration is, in Mr. Wilson's words (Pref. p. viii.) 'the constant reference to general Axioms and general Propositions, which are no clearer in the general statement than they are in the