Page:Carroll - Euclid and His Modern Rivals.djvu/218

180 the sum of the two adjacent angles OIB, O’IB must be equal to two right angles, and consequently their sides IO, IO’ in the same straight Line. But since we can always draw one, and only one, straight Line between two points O and O’, it follows that from a point O we can always draw one, and only one, perpendicular to the line AB.'

Do you think you could make a more awkward or more obscure proof of this almost axiomatic Theorem?

Nie. (cautiously) I would not undertake it.

Min. All that about folding and re-folding the paper is more like a child's book of puzzles than a scientific treatise. I should be very sorry to be the school-boy who is expected to learn this precious demonstration! In such a case, I could not better express my feelings than by quoting three words of this very Theorem:—'I remains fixed'!

In conclusion, I may say as to all five of these authors, that they do not seem to me to contain any desirable novelty which could not easily be introduced into an amended edition of Euclid.

Nie. It is a position I cannot dispute.