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Principles of Geometry

Nature volume 114, pages 8384 (19 July 1924) | Download Citation



IT is an undoubted fact that greater intellectual satisfaction is to be obtained from the proof of a geometrical theorem by the methods of pure geometry than from an algebraical investigation of the same theorem, and treatises on the methods of protective geometry are not uncommon, even in English. But apparently the application of such methods to the study of three-dimensional problems is considered difficult, for English text-books either confine themselves to plane geometry or else devote a chapter at the end to a meagre account of quadrics. As for investigating by this means the properties of a space cubic curve or a cubic surface, that is never dreamt of. Salmon's “Geometry of Three Dimensions “is, we believe, the only English book which gives at all. a complete account of the cubic surface, and in Salmon, of course, the algebraical side preponderates. Prof. Baker's third volume fills, then, an undoubted gap. To get into 223 pages an account of quadrics, of the space cubic and of the cubic surface, has involved a great amount of compression which is perhaps to be regretted; the book makes difficult reading, but the matter is there, and whoever will take the trouble to study its pages with care will be amply rewarded.

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