Page:Carroll - Euclid and His Modern Rivals.djvu/215



§ 6.

Nie. I lay before you 'The Elements of Plane Geometry', by R. P., Teacher of Mathematics in University College School, London; the second edition, 1871.

Min. Some of the changes in Euclid's method, made in this book, are defended in the Preface.

First, he claims credit for having more Axioms than Euclid, whom he blames for having demonstrated 'much that is obvious.' I need hardly pause to remind you that 'obviousness' is not an invariable property: to a perfect intellect the whole of Euclid, to the end of Book XII, would be 'obvious' as soon as the Definitions had been mastered: but Geometricians must write for imperfect intellects, and it cannot be settled on general principles where Axioms should end and Theorems begin. Let us look at a few of these new Axioms. In p. viii of the Preface, I