[Book Reviews]

Abstract

THIS is the second edition of a work which so accomplished a geometer as Prof. Henrici (vol. xxix. p. 453) has pronounced in these columns to be in many respects an “excellent” book. As the first edition contained 254 pages, and this one reaches 312 pages, it is manifest that the work has grown—and with its growth we find that it has acquired an accession of strength. We will indicate in what directions it has increased. First and foremost is the addition of the propositions of Euclid's Eleventh Book, which are generally read by junior students, and an appendix (well suited for candidates for the London Intermediate Examination) on the properties of the prism, pyramids, cylinder, sphere, and cone. There is also now given an explanation of the ratio of incommensurable quantities, and a still greater number, than in the first edition, of alternative proofs. Further, we can testify, by a careful perusal of the text, that the work has been “thoroughly revised as well as greatly enlarged.” One feature we note, that whereas in the first edition the syllabus of the Association for the Improvement of Geometrical Teaching was often referred to by quotation, in this edition the name occurs but once or twice. There are reasons for most actions—we presume there are for this course of action.

The First Six Books of the Elements of Euclid, and Props, i.—xxi. of Book xi., and an Appendix on the Cylinder, Sphere, Cone, &c.

With copious Annotations and numerous Exercises. By John Casey. (Dublin: Hodges, Figgis, and Co., 1884.)