Page:Carroll - Euclid and His Modern Rivals.djvu/93



Treatment of Parallels by methods involving infinite series.

Nie. I lay before you Éléments de Géométrie by Mons. A. M., the 14th edition, 1860.

Min. Let me begin by asking you (since I consider you and your client as one in this matter) how you define a straight Line.

Nie. As 'the shortest path from one point to another.'

Min. This does not seem to me to embody the primary idea which the word 'straight' raises in the mind. Is not the natural process of thought to realise first the notion of 'a straight Line,' and then to grasp the fact that it is the shortest path between two points?