Page:Carroll - Euclid and His Modern Rivals.djvu/207

. § 4.] ; so that, if it requires a construction at all, it must be a 'fresh' one.

Nie. Be not hypercritical.

Min. Well, it is rather 'small deer,' I confess: let us change the subject.

Here is a pretty proof in Th. 4.

'Then m + o = m + x.

But m = m.

Therefore o = x.'

Isn't that 'but m = m' a delightfully cautious parenthesis? Your client seems to be nearly as much at home in Algebra as in Logic, which is saying a great deal!

At p. 9, I read 'The base of an isosceles Triangle is the unequal side.'

The unequal side! Is an equilateral Triangle isosceles, or is it not? Answer, mein Herr!

Nie. Proceed.

Min. At p. 17, I read 'From one and the same point three equal straight Lines cannot be drawn to another straight Line; for if that were the case, there would be on the same side of a perpendicular two equal obliques, which is impossible.'

Kindly prove the italicised assertion on this diagram, in which I assume FD, FC, FE, to be equal Lines, and