Page:Carroll - Euclid and His Modern Rivals.djvu/109



Treatment of Parallels by revolving Lines.

Nie. I lay before you 'Elementary Geometry: Congruent Figures,' by, Ph.D., F.R.S., Professor of Pure Mathematics in University College, London, 1879.

Min. What is your Definition of a Line?

Nie. 'The boundary of a surface or of part of a surface is called a Line or a curve.' (p. 5.)

Min. Good—'Line,' I presume, meaning 'right Line.' But that throws us back upon 'surface.' Of course that is defined correctly?

Nie. I will tell you in a moment. (He turns over a few pages) Yes, here it is. 'A surface is the—' (He gives a perceptible start, stops reading, and turns a few pages back) Yes, it's all right. 'That which bounds a solid and separates it from other parts of Space is called its surface.' (p. 4.)

Min. (aside) There is more here than meets the eye! (Aloud) You will be good enough to read that other Definition of 'surface.'