Page:Carroll - Euclid and His Modern Rivals.djvu/129

.] Nie. I fear not.

Min. At p. 74 I observe 'If two Lines be each perpendicular to a third, they will be parallel to one another.' This is not true. They might be coincidental. The same mistake is made in p. 75.

Now comes a wonderful specimen of slipshod writing. 'We understand by the angles of a Polygon those angles of which the part near the vertex lies within the Polygon.' Does not this oblige us to contemplate an angle as consisting of two parts—one 'near the vertex,' the other further off?

Nie. Undoubtedly.

Min. And if either part were gone, the angle would be less?

Nie. (uneasily) It would seem so.

Min. And this might be effected by shortening the Lines, so that they would not reach beyond the region 'near the vertex'?

Nie. I fear you have got us into a corner. Be merciful!

Min. You mean that I have driven you into 'that part of an angle which lies near the vertex.' Well, you may come out now. We will seek 'fresh fields and pastures new.'

At pages 91 to 96 I find no less than forty-six theorems on Symmetry, arranged in two columns—one headed 'Axial Symmetry,' the other 'Central Symmetry .' Here is a specimen pair, at p. 95.