Page:Carroll - Euclid and His Modern Rivals.djvu/213



§ 5.

Nie. I lay before you 'Modern Methods in Elementary Geometry,' by E. M., M.A., Mathematical Master in Clifton College, Modern Side; published in 1868.

Min. The first remark I have to make on it is, that the Definitions and Axioms are scattered through the book, instead of being placed together at the beginning, and that there is no index to them, so that the reader only comes on them by chance: it is quite impossible to refer to them.

Nie. I cannot defend the innovation.

Min. In Th. (p. 3), I read 'the angles CDA, CDB are together equal to two right angles. For they fill exactly the same space.' Do you mean finite or infinite space? If 'finite,' we increase the angle by lengthening its sides: if 'infinite,' the idea is unsuited for elementary teaching. You had better abandon the idea of an angle 'filling space,' which is no improvement on Euclid's method.