December 8, 1910] 



NATURE 



167 



it would seem, in the substitution of a fresh title- 

 page, with a later date and the name of a diflerent 

 publisher, and the enlargement in the addition of eight 

 reproductions of photographs, some at least of which 



1 not appear for the first time. 



Anv value the book once possessed has now been 

 greatly diminished by simple lapse of time, and the 

 appearance of this reprint under the false colours of 



other edition can only be regarded as a breach of 

 ,.;rh on the part of those who are responsible for it. 



J. W. E. 



ELEMENTARY MATHEMATICS. 



(i) The Public School Geometry. By F. J. VV. 

 Whipple. Pp. xii+154. (London: J. M. Dent and 

 Sons, Ltd., 1910.) Price 2s. 6d. net. 

 _i The Sttidcfit's Mafriculation Geometry. By S. 

 ( iangopadhyaya. Second edition, revised and im- 

 proved. Pp. xviii + 348. (Calcutta: The Students' 

 Library, n.d.) Price 1.4 rupees. 



(3) First Stage Mathematics. Edited by W. Briggs. 

 Pp. vii+194. (London: \V. B. Clive, 1910.) Price 



25. 



:i Second Stage Mathematics (with Modern Geo- 

 metry). Edited by \\'. Briggs. Pp. viii+i28 + 

 102+ 186+ 14 (answers) + 2i (exam, papers). (Lon- 

 don : W. B. Clive, 1910.) Price 3s. 6d. 

 (5) Conic Sections. By S. Gangopadhyaya. Pp. 

 vui + 97. (Calcutta : The Students' Library, 1909.) 

 Price 8 annas. 

 ih) Public School Arithmetic. By W. M. Baker and 

 .\. A. Bourne. Pp. xii + 386 + 2. (London: G. Bell 

 and Sons, Ltd., 1910.) Price, with answers, 45. 6d., 

 without answers, 3s. 6J. 

 -1 .4 School Algebra. By H. S. Hall. Part L Pp. 

 xi + 299 + xxxvii. (London : Macmillan and Co., 

 Ltd., 1910.) Price 2s. 6d. 

 ^1 Elements of .Algebra. By A. Schultze. Pp. xii4- 

 309. (New York : The Macmillan Company ; Lon- 

 don : Macmillan and Co., Ltd., 19 10.) Price 4s. 6d. 

 I The Theory of Elementary Trigonometry. By 

 Prof. b. K. Picken. Pp. vii4-48. (Wellington, 

 N.Z., and London : Whitcombe and Tombs, Ltd., 

 1910.^ Price 2s. 6d. net. 

 : ) TZJ* REE use is made in this volume of inductive 

 X methods in establishing the fundamental 

 facts of geometry — the conditions for congruency and 

 parallelism. The opening chapters deal with the 

 measurement of lines an^ angles and with a few 

 nple constructions. Then follow the elementary pro- 

 pt rties of the triangle and parallelogram, the usual 

 theorems on inequalities, and a short account of areas, 

 ihe principles of similar figures are then discussed, and 

 are employed to prove Pythagoras's theorem. And 

 the book closes with the angle and metrical properties 

 of the circle. The author has succeeded in giving in a 

 \ery concise form a useful summary of the subject- 

 master of the first six books of Euclid. W'e regret the 

 introduction of two new terms — new at least so far as 

 elementary text-books are concerned — the use of the 

 word "stretch " for a segment of a straight line, and 

 of the word "cognate" for "corresponding"; while 

 the definition of » on p. 16 is not merely misleading 

 NO. 2145, VOL. 85] 



but is incorrect. It is most important that the student 

 should understand that x is a pure number and not an 

 angle. There are a very large number of numerical 

 examples, but most teachers will consider the supply 

 of riders inadequate. 



(2) The plan of this book conforms very closely to 

 the syllabus for the matriculation examination at Cal- 

 cutta, which is practically identical with the Cam- 

 bridge schedule for the previous examination, the sec- 

 tion on proportion being omitted. While due atten- 

 tion is paid to experimental and numerical work, the 

 author has ver}- wisely given chief place to the 

 theoretical developments of the subject. We welcome 

 the presence of a certain number of historical allu- 

 sions, which might with advantage be increased in a 

 future edition. Those who use this book will find 

 that it answers with uniform success the purpose for 

 which it was written. From its general workman- 

 ship it is evident that this volume comes from the 

 hand of an experienced teacher. 



(3 and 4) The two parts of this treatise are designed 

 to meet the requirements of the Board of Education 

 examinations in first- and second-stage mathematics. 

 The first part therefore contains the substance of 

 Euclid, book i., and the elementary algebraic pro- 

 cesses as far as simultaneous and literal equations. 

 In the second part will be found the substance of 

 Euclid, books ii.-iv., the section on algebra including 

 quadratics, indices, and proportion ; the remainder of 

 the volume provides the requisite course of trigono- 

 metrv up to and including the solution of triangles by 

 logarithms. We have no hesitation in saying that this 

 text-book is admirably suited to the needs of those 

 students who are reading by themselves for this 

 examination, or any other of a similar character. The 

 authors have made good use of their experience in 

 anticipating the nature of the difficulties which the 

 reader is likely to meet with, and in resolving them 

 in a lucid and accurate fashion ; and further, what is 

 equallv valuable, attention is directed to many points 

 of logical importance which a student is apt to over- 

 look, if working without any supervision. There is a 

 rich supply of well-graded e'xamples and a large 

 number of examination papers, which furnish the 

 student with opportunities for testing his progress. 



(5) This book falls into three sections. There is 

 first an introduction containing several preliminary 

 lemmas, together with a few remarks of a general 

 character bearing on geometrical procedure, the 

 second part relates to the parabola, and the concluding 

 chapter to the ellipse. The author has not aimed at 

 giving a complete account of the geometrical proper- 

 ties of conies, but rather a selection of the more useful 

 theorems, his objective being the syllabus for the 

 Calcutta intermediate examination. This leads to 

 some regrettable omissions ; there is, for example, no 

 mention of the auxiliary or director circle. Each pro- 

 position is followed by a number of simple applica- 

 tions and a few riders of a somewhat harder type 

 are given at the end of each chapter. The book will 

 serve as an admirable introduction to the subject. 

 Among other good features we note the introduction 

 of analysis at several stages, which is calculated 10 

 enlarge the outlook of the reader. 



