Page:Carroll - Euclid and His Modern Rivals.djvu/244

206 of its sides one less than that of the given figure; and thence to construct a Triangle equal to a given rectilineal Figure.' This I have already noticed (see p. 193). It really is not worth interpolating as a new Proposition. And its concluding clause is, if I may venture on so harsh an expression, childish: it reminds me of nothing so much as the Irish patent process for making cheap shoes—by taking boots and cutting off the tops!

Pr. (p. 103) is 'To divide a straight Line, either internally or externally, into two segments such that the rectangle contained by the given Line and one of the segments may be equal to the square on the other segment.' The case of internal section is Euc. II. 11, with the old proof. The other case is new, and worth interpolating.

I have now discussed, with as much care and patience as the lateness of the hour will permit, so much of this new Manual as corresponds to Euc. I, II, and I hope your friends are satisfied.

[A gentle cooing, as of satisfied ghosts, is heard in the air.]

I will now give you in a few words the net result of it all, and will show you how miserably small is the basis on which Mr. Wilson and his coadjutors of the 'Association' rest their claim to supersede the Manual of Euclid.

[An angry moaning, as of ghosts suffering from neuralgia, surges round the room, till it dies away in the chimney.]