The Elements of Euclid Euclid Revised Euclid Revised First Lessons in Geometry, for the Use of Technical, Middle, and High Schools The Origins of Geometry

Abstract

THE 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 supplementary 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, however, studied the “Syllabus” (of the A.I.G.T.) and has 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 Association to attach so much weight to the solution of geometrical 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 propositions upon which their solution depends. At the end of the first book are given the enunciations of several propositions 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 important 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, Rouché, de Comberousse, and Spieker. There are also remarks on plane loci and on the solution of geometrical 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 statement 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 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.

Book 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.)

The Origins of Geometry.

By Horace Lamb (Manchester: Cornish, 1886.)