Page:Carroll - Euclid and His Modern Rivals.djvu/174

136 Min. You have simply to take, as an instance, a Pair of coincidental Lines, which most certainly answer to your description of 'not parallel.'

Nie. It is an oversight.

Min. So I suppose: it is a species of literary phenomenon in which your Manual is rich.

Your proof of Cor. 2. is a delicious collection of negatives.

Reads. 'Cor. 2. Hence also if the corresponding angles are equal, or the alternate angles equal, or the interior angles supplementary, the Lines will he parallel.

'For they cannot be not parallel, for then the corresponding and alternate angles would be unequal by Cor. 1.'

Should I be justified in calling this a somewhat knotty passage?

Nie. You have no right to make such a remark. It is a mere jest!

Min. Well, we will be serious again.

At p. 9, you stated more than the data authorised: we now come to a set-off against this, since we shall find you asserting less than you ought to do. I will read the passage:—

P. 26. Th. 15. 'If two Triangles are equiangular to one another and have a side of the one equal to the corresponding side of the other, the Triangles will be equal in all respects.'

This contains a superfluous datum: it would have been