Abstract
IN these books we have evidence of the growing demand for quaternion literature. Dr. Molenbroek's work is the promised sequel to his first volume on the Theory of Quaternions, and contains many admirable examples of the application of the method to geometry. All who are familiar with Hamilton's and Tait's classics on the subject will recognise many of these examples as old friends, taken almost verbatim from their original sources. In not a few of the applications, however, Dr. Molenbroek ventures into fresh fields, and shows that he can use quaternions with ease and power. It is interesting to notice the occasional effective use of the conjugate quaternion, an invention of the great master which is apt to be lost sight of after the foundations of the calculus have been laid. The treatment throughout is on the familiar Hamiltonian lines, the author's aim being development and not fancied improvements. The book consists of six chapters, in which are taken up—to name a few of the most important applications—spherical trigonometry, the plane and sphere, quadric surfaces, surfaces in general, curves in space, and the theory of rectilinear rays. The elementary properties of the remarkable operator ⇚ and the integration of partial differential equations of the first and second orders, are discussed as part of the general theory of surfaces. In the same chapter, Dr. Molenbroek, by means of two new differentiating operators, obtains a simple symbolic representation for the first, second, and higher polars of a point with regard to a given surface. These remarks will indicate sufficiently the scope of a work which, though not altogether above criticism in minor details, is a distinct addition to quaternion literature, and deserves a wide circulation.
Anwendung der Quaternionen auf die Geometrie.
Von Dr. P. Molenbroek. (Leyden: E. J. Brill, 1893.)
The Outlines of Quaternions.
By Lieut.-Colonel H. W. L. Hime. (London: Longmans, Green, and Co., 1894.)
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Quaternions. Nature 51, 76 (1894). https://doi.org/10.1038/051076a0
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DOI: https://doi.org/10.1038/051076a0