Abstract
IN these 400 pages Mr. Johnston has ably succeeded in producing a very excellent treatise which leads the beginner by easy stages from the first principles of the subject to the more complicated theorems in trilinear coordinates. In the first ten chapters the student is made thoroughly familiar with the properties of the Ellipse, the Parabola, and the Hyperbola, after having been well exercised in the more preliminary parts of the subject as regards co-ordinates, the straight line, loci, &c. In these chapters it seems that the beginner can hardly fail to obtain a thorough grip of their contents, unless indeed he goes out of his way to do so, for more details could hardly be added. The numerous worked-out exercises should also be valuable, as they show him how to apply the knowledge gained from the various theorems learnt as book work. The next three chapters deal with the general equation of the second degree, confocal conies, and abridged notation, the last-mentioned including a large number of miscellaneous exercises; in these may be mentioned some additional methods of tracing a conic whose Cartesian coordinates are given, and an investigation of the equation of a diameter due to Prof. Purser. The remaining chapters treat of trilinear coordinates, envelopes, and methods of transformation. Here may be noticed Prof. Genese's proof of Feuerbach's theorem, Pascal's theorem, and many others of interest.
An Elementary Treatise on Analytical Geometry.
By W. J. Johnston (Oxford: Clarendon Press, 1893.)
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[Book Reviews]. Nature 49, 99 (1893). https://doi.org/10.1038/049099b0
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DOI: https://doi.org/10.1038/049099b0