NA TURE 



viu+284. 



Chambers, 



M.A 



and Co., 



March 30, 1905J 



£L£iV/£JVT.lR V M.4TH£A/.4T/CS. 



(1) Elementary Pure Geometry, '^'ith Mensuration 

 By E. Buddon, M.A., B.Sc. Pp. 

 (London and Edinburgh : W. and R. 

 Ltd., 1904.) Price 3^. ^ 



(2) Lessons in Experimental and Practical Geometry. 

 By H. S. Hall, M.A., and F. H. Stevens, 

 Pp. viii + 94+iii. (London: Macmi 

 Ltd., 1905.) Price is. 6d. 



(3) The Elements of Geometry, Theoretical and 

 Practical. Bv B. .\rnett, M.A. Books i., ii., and 

 iii. Pp. viii+193, viii + 238, and viii4-242. 

 (London: Simpkin, Marshall, Hamikon, Kent and 

 Co., Ltd., 1904.) Price 2.';. each volume. 



(4) The Elements of Trigonometry. By S. L. Loney, 

 M.A. Pp. xii + 339 + xiv. (Cambridge: The Uni- 

 versity Press, 1904; London: Macmillan and Co., 

 Ltd., 1904.) Price 35. 6d. 



(5) Elementary Algebra, Part II. By \V. >L Baker, 

 " M.A., and A. A. Bourne, M.A. Pp. viii + 277 to 



46S4-lxxvi. (London: George Bell and Sons, 

 1904.) 



(6) dive's Shilling Arithmetic. Edited by W. Briggs, 

 LL.D., M.A., &c. Pp. viii+154. (London: W. B. 

 Clive, 1905.) Price Js. 



(7) Graphic Statics. By T. Alexander, C.E., and 

 A. W. Thompson, D.Sc. Pp. viii + 50. (London: 

 Macmillan and Co., Ltd., 1904.) Price 2S. 



(i) T'HE geometry of Mr. Buddon is a notable addi- 

 ■'■ tion to the elementary text-books which owe 

 their appearance to the freedom of the last few 

 vears. The subject is introduced by experimental 

 work, very suggestive in character, and leading by 

 induction to fundamental definitions and theorems. 

 Thus from the sliding and folding of flat cards and 

 the like the author arrives at his definition of a plane 

 as " a surface, infinite in extent, which can be folded 

 about anv two points of the surface so that one part 

 lies entirely on the other." The definition of a 

 straight line naturally follows as the infinitely 

 extended fold of a plane. A plane angle is clearly 

 and rationally defined. Parallel lines are those having 

 the same direction in a plane, direction being measured 

 bv the angle made with any reference line. It is 

 pointed out that a plane, a plane angle, and a 

 straight line can in each case be reversed on itself, 

 and thus symmetrical properties are satisfactorily 

 established in which the two halves are alike but of 

 opposite aspect. Then follow general cases of 

 congruence. In dealing with ratio and proportion 

 the idea of a continually subdivided decimal scale is 

 introduced ; this enables all numbers which can be 

 expressed as continuous decimal fractions, e.g. 

 1. 4142. . . ., to be included, and to any degree of 

 approximation. In later chapters the subject-matter 

 comprises a very full treatment of the properties of 

 circles ; elementary trigonometrv ; an introduction to 

 projective geometry ; conic sections treated by modern 

 methods ; and solid geometry with the mensuration 

 of the simple geometrical solids. The book con- 

 tains in profusion sets of graphical and deduc- 

 tive exercises. The figures are drawn with 

 NO. 1848, VOL. 71] 



507 



thick, thin, and dotted lines on a systematic plan 

 to distinguish more readily between the data, the 

 constructron lines, and the result. The use of variable 

 type serves to differentiate parts of greater or less 

 importance. In fact, the book on every page bears 

 witness to the great care and thought bestowed 

 on its production. There is a stimulating freshness 

 in the matter and its method of presentation. Some 

 will doubt the wisdom of carrying on at school the 

 study of pure geometry to the extent covered in the 

 book ; others may wish that the geometry of vectors 

 had been included ; but all will agree that the author 

 has produced one of the most important of the new 

 elementary text-books, and one that should be known 

 to every teacher interested in the subject. 



(2) The " Lessons in Experimental and Practical 

 Geometry " by Messrs. Hall and Stevens might very 

 fittingly be incorporated in the authors' " School 

 Geometry," to which it forms an excellent introduction 

 as well as supplement. The subject is treated in the 

 masterly way that is found in the mathematical text- 

 books of these writers. Young pupils are fortunate 

 who obtain their first notions of geometry from a 

 course such as the one outlined in its pages. They 

 will become accustomed to the use of compasses, 

 squares, scales, and the protractor by interesting 

 quantitative and experimental work, fundamental 

 propositions being at the same time inductively 

 established. They will have practice in the applica- 

 tion of geometrical problems ; will learn how to 

 measure areas; and will be introduced to the simpler 

 geometrical solids. The authors make good use of 

 tracing paper. The list of instruments and apparatus 

 which they give might with advantage have included 

 the drawing and compass pencils, with a caution 

 added against the employment of soft blunt leads. 



(3) In" the preface of his elementary geometry Mr. 

 .\rnett states that the work " has been written for 

 the use of candidates who are being prepared by a 

 master for the different examinations conducted by the 

 universities and the Civil Service Commission." The 

 subject-matter is confined to plane geometry, and is 

 almost wholly deductive. The first book gives 

 definitions and axioms, and investigates some of the 

 properties of lines, angles, parallels, triangles, and 

 quadrilaterals. The second book deals mainly with tb'~ 

 circle and with ratio and proportion, and the last book 

 treats of areas and of similar figures. Tlie principal 

 feature of the work is the very large number of 

 exercises provided, a few of which are numerical or 

 graphical, the great bulk, however, being of the nature 

 of geometrical riders. The text-book is not at all suit- 

 able for beginners, for general school work, or for 

 private study except under the direction of a tutor 

 who could direct the student as to which parts should 

 be read and which omitted, and who would probably 

 re-arrange the order in which the theorems and 

 problems should be taken. 



(4) Mr. Loney's " Elements of Trigonometry " is 

 mainly taken from part i. of the author's " Plane 

 Trigonometry," and is designed as an easier text-book. 

 The subject is treated in the usual way, and there 

 is nothing to call for special mention. The first 

 chapters relate to acute angles and right-angled 



