Abstract
THIS work would have been more correctly described as being “by Eugène Roucheé and Ch. de Comberousse, translated and edited by Richard P. Wright,” &c. But, although Mr Wright can lay small claim to originality, he has shown judgment in the selection of an eminently logical and masterly treatise on geometry, and he has rendered it into clear and forcible English. The arrangement is excellent, and many of the conclusions for which Euclid found it necessary to reason geometrically on each particular case are treated generally by purely logical considerations. Many of the demonstrations, notably that of the pons asinommy are far more simple and convincing than those in Euclid. The difficulty of the twelfth axiom is met by the easy axiom that through a point without a line only one parallel can be drawn that line. In some points there seems to be an unnecessary alteration of the language of Euclid, as in the definition of a figure “Surfaces and Lines or combinations of them.” This definition seems to have been introduced to enable the authors to describe a locus as a figure; but it having been pointed out that a locus is not a figure, Mr. Wright has described it as a line, but has not restored the word figure to its ordinary acceptation. At the same time it is not quite correct to define a locus as a line, excluding such loci as a pair of parallel lines, the circumference of a circle with its centre, &c. Again, the word circumference is substituted for the word circle whenever the circumference only is intended. It is true that the word circle in Euclid is used in two different senses, but this leads to no ambiguity of ideas; while the use of the word circumference for the circumference of a circle only excludes its application to an ellipse or other closed curve. The word angle is not defined when first introduced, but we are told afterwards that it “may be regarded as the quantity of turning of a definite character around the vertex, which a movable line must receive in passing from the direction of one side to that of the other.” We fail to see the force of the words “of a definite character,” and would suggest the following definition: “When a straight line moves about a fixed point in itself so as to occupy a new position, the quantity of turning it has undergone is called the angle between the two positions.” The exercises are ingenious and instructive, but those of the earlier chapters are much too difficult for mere beginners. The treatment of proportion is good, and the work as a whole is an admirable introduction to the higher mathematics, and a great help to independent investigation. We especially recommend it to students who have found themselves discouraged by the cumbrous form and initial difficulties of Euclid. The second edition contains the alterations suggested by a late eminent mathematician in the Athenæum on the appearance of the first edition, with the addition of the substance of the second book of Euclid, and in a few cases the demonstrations of Euclid have been restored.
The Elements of Plane Geometry for the Use of Schools and Colleges.
By Richard P. Wright, Teacher of Mathematics in University College School, London, formerly of Queenwood College, Hampshire. With a Preface by T. Archer Hirst, F.R.S., &c., late Professor of Mathematics in University College, London. Second Edition. (Longmans, 1871.)
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N., H. The Elements of Plane Geometry for the Use of Schools and Colleges . Nature 5, 282 (1872). https://doi.org/10.1038/005282b0
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DOI: https://doi.org/10.1038/005282b0