REVIEWS 



MATHEMATICS 



A Treatise on the Analytic Geometry of Three Dimensions. By George 

 Salmon, D.D., D.C.L., LL.D., F.R.S., late Provost of Trinity College, 

 Dublin. Revised by Reginald A. P. ROGERS, Fellow of Trinity College, 

 Dublin. [Pp. xxiv + 470, Sixth Edition, Vol. I.] (London : Longmans, 

 Green & Co., 1914. Price ox) 



A Treatise on the Analytic Geometry of Three Dimensions. By George 

 Salmon, D.D., D.C.L., LL.D., F.R.S., late Provost of Trinity College, 

 Dublin. Edited by Reginald A. P. Rogers, Fellow of Trinity College, 

 Dublin. [Pp. xvi + 334, Fifth Edition, Vol. II.] (London : Longmans, 

 Green & Co., 191 5. Price js. 6d.) 



The last edition of this work which appeared in one volume under the name of 

 George Salmon alone was the fourth. Mr. Cathcart, indeed, took the work of 

 revision almost entirely off Salmon's hands, so that the third edition was practically 

 the last edition at which Salmon worked. Mr. Rogers undertook the task of so 

 adding to Salmon's classical treatise as to make it a concise and comprehensive 

 survey of algebraic and differential Euclidean geometry of three dimensions. In 

 order to avoid delay it was thought advisable to publish the new edition in two 

 volumes, and accordingly the first volume of the fifth edition appeared in 1912. 

 A new edition of this volume became necessary in 1914, and the second volume of 

 the fifth edition appeared in 191 5. It is these two volumes which are reviewed 

 here. 



The sixth edition of the first volume only differs from the fifth by a few 

 corrections, and it may be convenient to summarise here the additions to both 

 volumes of the fifth edition. It is, of course, superfluous to dwell on the merits of 

 Salmon's book ; and, as regards Mr. Rogers's additions, which are enclosed in 

 square brackets as all additions ought to be, this summary, which is taken from 

 the two prefaces, is all that is needed. The additions include illustrations of 

 models of most of the different species of quadrics, with generators or lines of 

 curvature, and notices on the analytical classification of real quadrics, on projection 

 and Fiedler's projective co-ordinates, on the non-Euclidean theory of distance and 

 angle, and on the expression of twisted cubics and quartics by rational or elliptic 

 parameters. In differential geometry Mr. Rogers's aim has been to form a closer 

 connecting-link between Salmon's book and the more extensive and more purely 

 analytical methods used by Bianchi, Darboux, and others ; and he has therefore 

 added articles on the Frenet-Serret formulas, on the intrinsic equations of a twisted 

 curve, on Bertrand curves, and on the application of Gauss's parametric method 

 to conformal representation, geodesic curvature, and geodesic torsion. To the 

 portion dealing with the differential geometry of curves on quadrics, Mr. Rogers 

 has added Staude's thread-construction for ellipsoids, which is the three-dimensional 

 analogue of Graves's theorem ; and his definitions of confocal quadrics, which are 

 the analogues of the ordinary definitions of conies by means of focal radii. The 

 rest of the new matter in the first volume is of the nature of commentaries. The 



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