NA TURE 



577 



THURSDAY, APRIL 23, 1903. 



SCHOOL GEOMETRY REFORM. 

 Practical Exercises in Geometry. By W. D. Eggar, 



M.A. Pp. xii + 287. (London : Macmillan and Co., 



Ltd., 1903.) Price 25. 6d. 

 Geometry. An Elementary Treatise on the Theory and 



Practice of Euclid. By S. O. Andrew, M.A. Pp. 



xi + 182. (London : John Murray, 1903.) Price 2s. 

 Theoretical Geometry for Beginners. By C. H. 



Allcock. Pp. ix+ 135. (London : Macmillan and 



Co., Ltd., 1903.) Price is. 6d. 

 Elementary Geometry. By W. M. Baker, M.A., and 



A. A. Bourne, M.A. Books i. and ii., pp. xxix+ 126; 



price is. 6d. Books i.-iii., pp. xxix + 213 ; price 2s. 6d. 



Books i.-iv., pp. xxix + 272; price 3s. Books i.-vii., 



pp. xxix + 474; price 4s. 6d. (London : George Bell 



and Sons, 1903.) 

 The Elements of Geometry. By R. Lachlan, Sc.D., 



and VV. C. Fletcher, M.A. Pp. xii4-207- (London : 



Edward Arnold, n.d.) Price 2s. 6d. 

 Plane Geometry. Adapted to Heuristic Methods of 



Teaching. By T. Petch, B.A. Pp. vii+112. 



(London : Edward Arnold, n.d.) Price is. 6d. 

 Euclid: Books v., vi., xi. By Rupert Deakin, M.A. 



Pp. 144. (London : W. B. Clive, 1903.) Price is. 6d. 

 A Short Introduction to Graphical Algebra. By H. S. 



Hall, M.A. Pp. 49. (London : Macmillan and Co., 



Ltd., 1903.) Price is. 



THE movement having for its object the improve- 

 ment of the teaching of elementary geometry is 

 making rapid progress; witness the enthusiastic sup- 

 port of the teachers, the adhesion of important examin- 

 ing bodies, and the number of new text-books now 

 appearing in rapid succession. 



In the " Practical Exercises in Geometry," by Mr. 

 W. D. Eggar, we have a contribution of remarkable 

 freshness. In this valuable text-book the method pur- 

 sued is on lines indicated long ago by W. G. Spencer, 

 the father of Mr. Herbert Spencer, in his " Inventional 

 Geometry," 1 a little work that should be known to all 

 teachers. The principal advance on Spencer's geo- 

 metry is in the amount of quantitative measurement 

 introduced, and in the use of squared paper methods. 

 The author describes his book as " an attempt to adapt 

 the experimental method to the teaching- of geometry 

 in schools. " He says : — 



" The main object of this method, sometimes called 

 ' heuristic,' is to make the student think or himself, 

 to give him something to do with his hands for which 

 the brain must be called in as a fellow-worker. The 

 plan has been tried with success in the laboratory, and 

 it seems to be equally well suited to the mathematical 

 class-room." 



And readers of the book will agree that the author 

 has very good grounds for this opinion. 



The first five chapters are devoted entirely to the 

 measurements of lines, arcs and angles. The author 

 wisely uses only decimal scales. These are the inch 

 and the centimetre scales; in regard to the latter it is 

 no small advantage for a youth to be trained so as to 

 be able to think in metric units. The degree of 



1 Published by Williams and Norgale. 



NO. [747, VOL. 67] 



accuracy aimed at will appear from the requirement 

 that students are asked to measure lengths correctly 

 to within the one-hundredth part of an inch. This, 

 however, will prove to be rather trying for lines in 

 some of the figures, in the absence of short cross lines 

 denning their ends. Several methods are suggested 

 of how to measure the circumference of a circle, but 

 the use of tracing paper and a pricker, perhaps the best 

 of these, is overlooked. 



The student is next introduced to the use of set- 

 squares, and the notions of parallel and perpendicular 

 lines naturally follow. Explanations are then given 

 of how areas and volumes are measured, the subject 

 being illustrated by the use of squared paper, unit 

 cubes, graduated flasks, weighing, &c. The quantita- 

 tive work is here largely arithmetical. This free ad- 

 mixture of arithmetic and drawing is, in fact, a feature 

 throughout the book, and one marvels at the long un- 

 natural divorce which has existed between the two in 

 the past. 



Chapters xi. and xii. are devoted to some funda- 

 mental constructions, such as the bisection of lines and 

 angles, and the division of lines. The student by this 

 time is quite familiar with the notion of a locus. 



So far the work has been more or less of preparation. 

 The student is now led to study more particularly the 

 properties of triangles, quadrilaterals, circles, pro- 

 portionals and similar figures. But there is no change 

 in the method of treatment. By judicious directions, 

 by questions and suggestions, the reader all the while 

 seems to be discovering new truths for himself by draw- 

 ing and measurement, and his interest is secured and 

 maintained. Then follows the reason, given quite in- 

 formally, perhaps by a mere hint, but none the less 

 perfectly logical, and absolutely convincing and satis- 

 factory, and the student feels that he has, or could 

 have, discovered this also. 



The concluding chapters relate to mensuration rules, 

 the graphical solution of quadratic equations, the con- 

 struction of scales, and graphs. 



Material is provided at the ends of some of the 

 chapters for the student to exercise himself in riders, 

 constructions, and numerical examples. The answers 

 to the latter are collected at the end of the volume. 



The course above outlined is developed on satis- 

 factory lines, and may be regarded as a first important 

 instalment to the new literature of the subject. Taught 

 in this manner, geometry would seem likely to become 

 the most popular, as well as the most illuminating 

 branch of elementary mathematics. It ought to re- 

 place not only Euclid, but the wretched system of 

 practical plane geometry now in vogue in our elemen- 

 tary day schools. The course includes everything con- 

 tained in the first six books of Euclid that a boy need 

 know ; and he knows it so thoroughly that any sub- 

 sequent study of Euclid or its equivalent will add little 

 to his knowledge of geometry, whatever may be its 

 other merits or demerits. 



We notice that the use of the T-square is not intro- 

 duced at all. This seems a pity, in view of its great 

 utility and of future developments. 



While in general agreement with the author, we 

 should like to see his course of study extended. What- 



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