Page:Carroll - Euclid and His Modern Rivals.djvu/198



§ 2.

Nie. I lay before you 'A Treatise on Elementary Geometry,' by W., LL.D., Professor of Mathematics and Astronomy in Washington University, published in 1876.

Min. I read in the Preface (p. 4) 'I have endeavoured to set forth the elements with all the rigour and completeness demanded by the present state of the general science, without seriously departing from the established order of the Propositions.' So there would be little difficulty, I fancy, in introducing into Euclid's own Manual all the improvements which Mr. Chauvenet can suggest.

P. 14. Pr. , and p. 18. Pr. , taken together, tell us that only one perpendicular can be drawn to a Line from a point. And various additions, about obliques, are made in subsequent Propositions. All these may well be embodied in a new Proposition, which we might interpolate as Euc. I. 12. B.