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Abstract

WITHIN the limits of 267 pages it is not easy to make improvement in so vast a subject as that of this treatise. The chief novelty is the concurrent treatment of differential and integral calculus. A great step in perspicuity has been made by the use of the complete notation of hyperbolic trigonometry (sinh, cosh, &c., and sinh^-1, cosh^-1, &c.), which shows the perfect analogy of the circular and hyperbolic functions in both differentiation and integration. The gain is for mathematicians; its use to practical men may be doubted, as the numerical calculation of these functions is (at present) best done by the familiar logarithms. In the older treatises the applications were chiefly algebraic and geometric; the author's system is to introduce the student at once to a wide scope of applications in both geometry and physics, including some of the higher branches (e.g. central orbits, harmonic vibration, Fourrier's and Green's theorems, &c.). It is clear that the account of each must be very brief. In some cases (e.g. the article on “Curve-Tracing,” Art. 127) it amounts to merely a sketch of procedure and results with scarcely any proof. In an “introductory” work this seems a defect. It is, however, a masterly introduction to the subject, and the wide scope of the applications is well fitted to interest the student.

Differential and Integral Calculus, with Applications.

By A. G. Greenhill. Pp. xi. and 272. (London: Macmillan and Co., 1886.)