Page:Carroll - Euclid and His Modern Rivals.djvu/234

196 sequence and numeration of our old friend. We must now examine the book seriatim. When we come to matters that have been already condemned, either in Mr. Wilson's book, or in the 'Syllabus,' I shall simply note the fact. We need have no new discussion, except as to new matter.

Nie. Quite so.

Min. In the 'Introduction,' at p. 2, I read 'A Theorem is the formal statement of a Proposition,' &c. Discussed at p. 189.

At p. 3 we have the 'Rule of Conversion,' which I have already endeavoured to understand (see p. 190).

At p. 6 is a really remarkable assertion. 'Every Theorem may he shewn to be a means of indirectly measuring some magnitude.' Kindly illustrate this on Euc. I. 14.

Nie. (hastily) Oh, if you pick out one single accidental excep

Min. Well, then, take 16, if you like: or 17, or 18

Nie. Enough, enough!

Min. (raising his voice)—or 19, or 20, or 21, or 24, or 25, or 27, or 28, or 30!

Nie. We abandon 'every.'

Min. Good. At p. 8 we have the Definitions of major conjugate and minor conjugate (discussed at p. 185).

At p. 9 is our old friend the straight angle (see p. 101).

In the same page we have that wonderful triad of Lines, one of which is regarded as lying between the other two (see p. 185).

And also the extraordinary result that follows when one straight Line stands upon another (see p. 186).