Page:Carroll - Euclid and His Modern Rivals.djvu/194

156 to two curves, mnr and MNR, for the same abscissa; and let b and B be constants and represent their intercepts on the Y-axis; i.e. let On = b, and ON = B.



Does not this diagram fairly represent the data of the proposition? You see, when we take a negative abscissa, so as to make a greater than b, we are on the left-hand branch of the curve, and A is also greater than B; and again, when a is equal to b, we are crossing the Y-axis, where A is also equal to B.

Nie. It seems fair enough.

Min. But the conclusion does not follow? With a positive abscissa, A is greater than B, but a less than b.

Nie. We cannot deny it.

Min. What then do you suppose would be the effect on a simple-minded student who should wrestle with this terrible theorem, firm in the conviction that, being in a printed book, it must somehow be true?

Nie. (gravely) Insomnia, certainly; followed by acute Cephalalgia; and, in all probability, Epistaxis.

Min. Ah, those terrible names! Who would suppose