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WE recently noticed with approval the volume containing the first seven parts. This eighth part carries on the articles from 1400 to 1868, and is concerned with the differential calculus. It contains an abstract of the usual processes, and besides gives a succinct account of the theory of operations, and an analysis of matters which are treated of in the higher algebra, as Jacobians and quantics, and closes with maxima and minima, the geometrical applications being reserved for the parts on Co-ordinate Geometry.A Synopsis of Elementary Results in Pure and Applied Mathematics.By G. S. Carr Vol. i. part viii. (C. F. Hodgson and Son, 1880.)