A Synopsis of Elementary Results in Pure Mathematics, &c

Abstract

IN our last notice of this work (vol. xxxi. p. 100) we gave an account of Sections X., XI., and XII. The complete volume contains two additional sections. The first of these treats of plane co-ordinate geometry, under which heading we have systems of coordinates, analytical conies in Cartesian and trilinear coordinates (we miss the m equations for the parabola and the corresponding equations for chords, &c.). In the latter division we have, amongst the particular conics considered, the triplicate-ratio and seven-point circles (or, as they are more usually styled, the Lemoine and Brocard circles). The account is carefully drawn up from original authorities, and will help to bring this latest development of the geometry of the circle and triangle more into notice. At present this and Dr. Casey's books are the only source readily accessible to students. We are promised another presentment of these circles shortly, but of this more anon. The concluding portion of this section is devoted to the theory of plane curves. Here we have, inter alia, inverse and pedal curves, roulettes, and the various forms of transcendental curves. Considerable space is taken up with linkages and link-works: here we have accounts of Kempe's five-bar linkage, the six-bar inversor, the eight-bar double inversor, the quadruplane, the isoklinostat, the planimeter, and the pantograph (this Mr. Carr generally calls pentograph—evidently he has not consulted the “English Cyclopædia”—and in one place only, pantograph). The concluding section is mainly taken up with solid co-ordinate geometry, the final articles being devoted to Guldin's rules, moments and products of inertia, perimeters, areas, volumes, &c. Here we have the theorems which go by the names of Fagnani, Lambert, and Griffiths (not Griffith, as the “Contents” and “Index” print the name; the text, § 6096, is right).

A Synopsis of Elementary Results in Pure Mathematics, &c.

By G. S. Carr. M.A. Pp. xxxviii. + 936 + 20 folding Plates of Figures. (London: Francis Hodgson, 1886.)