Jan. 20, 1887] 



NA TURE 



269 



tea plant. As there are diversities of soils and climates, 

 so there are also diversities of industrial plants exactly- 

 suited to them. Where all such considerations are 

 ignored, there is danger both to the plants and the 

 planter ; and this danger ought in the present case to be 

 avoided. D- M. 



GEOMETRY 

 The Elements of Euclid. Books I.-VI. and part of 



Books XI. and XII. By H. Deighton. (Cambridge: 



Deighton, Bell, and Co., 1886.) 

 Euclid Revised. Book I. with Additional Propositions 



and Exercises. Edited by R. C. J. Nixon. (Oxford: 



Clarendon Press, 1886.) 

 Euclid Revised. Books I. and II. (.Same Editor and 



Publishers.) 

 First Lessons in Geometry, for the Use of Technical, 



Middle, and High Schools. By B. Hanumanta Rau. 



(Madras : Addison and Co., 1885. J 

 The Origins of Geometry. By Horace Lamb, F.R.S. 



(Manchester: Cornish, 1886.) 

 ''P'HE author of the first of these books attempts to "give 

 '■ a translation of the Greek text of a somewhat more 

 modern form than the mere verbal ones [what does he 

 mean ?] in general use ; and, whilst strictly adhering to 

 Euclid's methods, to render his reasoning as clearly and 

 concisely as possible." Hence our presentment of the 

 title-page is supplemented in the original work by the 

 words " newly translated from the Greek text with supple- 

 mentary propositions, chapters on modern geometry, and 

 numerous exercises." It will be evident that this is 

 Euclid pure and, as far as the author is able to render it, 

 unadulterated ; there is no revision here such as Mr. 

 Nixon provides for the reader. Mr. Deighton has, how- 

 ever, studied the " Syllabus " (of the A. I.G.T.) and his 

 here and there introduced, with fitting acknowledgment, 

 extracts from it. Further, the author is evidently actuated 

 by the same motives as those which lead the Associa- 

 tion to attach so much weight to the solution of geo- 

 metrical problems as evidence of a student's grasp of the 

 text. .A strong feature is the large number of exercises 

 (1419 in all, besides worked out examples), especially of 

 an elementary character, in close proximity to the propo- 

 sitions upon which their solution depends. At the end of 

 the first book are given the enunciations of several pro- 

 positions which certainly should be mastered by anyone 

 who wishes to gain a sound acquaintance with elementary 

 geometry. Following, it may be, the example of other 

 recent text-books, an excellent collection of the most im- 

 portant propositions on the radical axis, poles and polars, 

 harmonic proportion and centres of similitude are given ; 

 there is also a chapter on transversals. The selection of 

 exercises is not confined to Cambridge papers, but levies 

 have been made on the well-known works of Catalan, 

 Rouchi^, de Comberousse, and Spieker. There are 

 also remarks on plane loci and on the solution of geo- 

 metrical questions. The letterpress is clear, and the 

 figures are in the main distinctly and carefully drawn, but 

 several monstrosities appear in the third book, as of old, 

 and the drawings on pp. 115, 153, 186 are incorrect as 

 to relative measurements. Perhaps when Mr. Nixon 



has examined the present book he will modify a state- 

 ment in his preface (p. vii., we refer to the work reviewed 

 in these columns, vol. xxxiv. p. 50, by R. B. H.) to the 

 effect that " there does not exist a modern edition which 

 gives Euclid pure and simple." 



The second and third books are the corresponding por- 

 tions of the larger work referred to above, reprinted page for 

 page, with the addition of an appendix, in which are given 

 proofs of omitted propositions, and also of i. 5 and of i. 8 

 as a deduction from i. 7. "This addition is made at the 

 request of several teachers. It is of course a concession 

 to the omnipotent examiner ; and, as such, is made with 

 much reluctance." One can only regret that a writer 

 who has taken up so advanced a position should have 

 yielded on this point. 



The fourth book is interesting as giving evidence of how 

 a modern movement has taken hold of able mathematical 

 teachers of the mild Hindoo. Mr. Rau candidly re- 

 pudiates all claim to originality for his matter, as in its 

 coinpilation he has consulted the best English and French 

 text-books both for pure as well as for practical geometry. 

 " If ' Euclid's Elements' is unsuited for beginners who 

 study it in their own native tongue, how much more so 

 should it be in this country, where it is taught in classes 

 consisting generally of lads between ten and twelve, 

 before they have had time to master the difficulties of a 

 foreign language, and before too, I may add, they can 

 benefit by its rigorous logic. The result, as may be 

 anticipated, has been highly prejudicial to the study of 

 geometry and of mathematics in general. With a view, 

 if possible, to remedy the evil, of which I had become 

 painfully conscious in the course of my several years' 

 experience as a mathematical teacher in schools and 

 colleges, I had long been aiixious to attempt a departure 

 from the established route." The worli consists of the 

 notes he drew up for the pupil-teachers and students 

 under his charge. " My success in the experiment is my 

 justification for publishing this little volume." The figures 

 are roughly drawn, and the cover is a paper one, but the 

 contents are carefully arranged, and furnish a very fair 

 amount of geometrical information for the class aimed at 

 all the propositions being looked at with an eye to their 

 practical utility. Such a class should know how to hold 

 an object "in an oblique position, not permitting it to 

 retrograde to the perpendicular." 



" The Origins of Geometry " is an address delivered at the 

 opening of the Owens College session, October 5, 1886. The 

 Professor of Mathematics casts " a rapid glance over the 

 early history of our science, more especially of that 

 branch of it which was first cultivated with success, 

 geometry." Taking Hankel as his guide, he glances 

 rapidly at mitters of which Dr. Allman has treated in 

 much fuller detail ; he then treats of what has proved 

 " the most formidable obstacle to the further progress of 

 Greek mathematics, the divorce between geometry on 

 the one hand, and arithmetic and algebra on the other. 

 This had its origin in the discovery of incommensurable 

 magnitudes by Pythagoras and his successors." He, by 

 the way, notes that " the greatest advances in mathe- 

 matics have been made by men whose interest in the 

 subject was of a speculative kind." The address winds 

 up with the question, " What is likely to be the relation 

 of mathematics to the science of the future ? " Prof. Lamb 



