Page:Carroll - Euclid and His Modern Rivals.djvu/200



§ 3.

Nie. I lay before you 'Elements of Geometry,' by, LL.D., Professor of Natural Philosophy and Astronomy in Yale College, a revised edition, 1876.

Min. I read in the Preface (p. 10) 'The present volume follows substantially the order of Blanchet's Legendre, while the form of the demonstrations is modeled after the more logical method of Euclid.' He has not, however, adopted the method of infinite series, which constitutes the crucial distinction between that writer and Euclid.

The Propositions are pretty nearly in Euclid's order: with a few changes in order and numeration, the book would be a modernised Euclid, the only important differences being the adoption of Playfair's Axiom and the omission of the diagonals in Euc. II. I have no hostile criticisms to offer. Our American cousins set us an excellent example in the art of brief, and yet lucid, mathematical writing.