The Science and Art of Arithmetic for the Use of
Schools. Part I. Integral. By A. Sonnenschein and H. A. Nesbitt, M.A. (Whittaker and Co.)—Mr. Sonnenschein is a pupil, and a thoroughly taught pupil, of Mr. de Morgan's, and it is scarcely necessary to say more in order to convince all who know Mr. de Morgan's works that there is nothing like half-digested work in this arithmetic. This first part of Mr. Sonnen- schein's book is admirable of its kind, and better fitted for ordinary school use than Mr. de Morgan's Arithmetic, which is more suitable to students and teachers. Brevity and lucidity in the exposition of principle are its main characteristics as a scientific book ; and great care in the expla- nation of simple practical rules for shortening or verifying calculations is its main characteristic in reference to the art of computation. It gives a clear proof of all the rules,—insisting on the exact meaning of the various operations and their interpretation,—and contains a remarkably good chapter on the general properties of numbers, so far as they can be explained to beginners who have only mastered the arithmetic of integers. We think Mr. Sonnenschein might usefully have insisted more on general or symbolical arithmetic than he has done,—might have dwelt more, for instance, on the general rules for multiplying numbers broken up into parts, squaring numbers broken up into parts, and so forth, without trenching on any properly algebraic ground. But all that he has done, he has done admirably. We are not quite satisfied with his purely pictorial proof (p. 45) that m x n ra x m. A more general proof could easily be given without this appeal to the eye. But on the whole, it is hardly possible to speak too well of this little book, which we have examined very carefully.
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