Page:Carroll - Euclid and His Modern Rivals.djvu/252

214 Min. Your reply is satisfactory. Mr. Wilson himself is an instance of the danger of such a method. Three times at least (pp. 46, 70, 88) he produces Lines to meet without attempting to prove that they will meet.

§ 3. Euclid's Demonstrations.

Min. The next heading is 'Demonstration.' You are charged with an 'invariably syllogistic form of reasoning.' (Wilson, Pref. p. i.)

Euc. Do you know, I am vain enough to think that a merit rather than a defect? Let me quote what Mr. Cuthbertson says on this point (Pref. p. vii.). 'Euclid's mode of demonstration, in which the conclusion of each step is preceded by reasoning expressed with all the exactness of the minor premiss of a syllogism, of which some previous proposition is the major premiss, has been adopted as offering a good logical training, and also as being peculiarly adapted for teaching large classes, rendering it possible for the teacher to call first upon one, then upon another, and so on, to take up any link in the chain of argument.' Perhaps even Mr. Wilson's own book would not be the worse if the reasoning were a trifle more 'syllogistic'!

Min. A fair retort. You are also charged with 'too great length of demonstration.' Mr. Wilson says (Pref. p. i.) 'The real objections to Euclid as a text-book are … the length of his demonstrations.' And Mr. Cooley says (Pref. p. 1.) 'The important and fertile theorems, which crown the heights in this field of knowledge, are here