(1) The Algebra of Logic (2) An Algebra for Preparatory Schools (3) Test Papers in Elementary Algebra (4) Practical Mathematics for Technical Students (5) A Text-book on Spherical Trigonometry (6) Plane and Spherical Trigonometry

Abstract

(1) THIS is an excellent translation of M. Couturat's well-known “Algèbre de la Logique.” The conciseness and modernity of M. Couturat's book is very apparent when we compare it with the first two volumes of Schröder's bulky, prolix, and somewhat antiquated work. The book under review is, as is remarked in the preface (p. viii.; cf. pp. 92–93), an exposition of the beautiful and simple calculus of symbolic logic, regarded as a branch of universal algebra. Leibnitz distinguished the two most important aspects of a symbolic language designed for purposes of reasoning, under the names calculus ratio-cinator and characteristica universalis: the latter indicates broadly the route taken by Frege, Peano, Russell, and Whitehead; the former the route taken by Boole, Jevons, Venn, Schröder, and others, and is that described in the present work. Between these two routes, the “logic of relations” lies, and this is not dealt with here; but we are given a complete presentation of the important modern work of Whitehead (1898, 1901), Johnson (1901), Poretzsky (1899–1904), and Huntington (1904) on the logic of classes and propositions. Miss Robinson has added several valuable notes to her translation. The volume is neat and handy, and is an important addition to our English mathematical literature.

(1) The Algebra of Logic.

By Louis Couturat. Authorised English Translation by Lydia G. Robinson. With a Preface by P. E. B. Jourdain. Pp. xiv + 98. (London and Chicago: The Open Court Publishing Company, 1914.) Price 3s. 6d. net.

(2) An Algebra for Preparatory Schools.

By Trevor Dennis. Pp. viii + i55. (Cambridge University Press, 1913.) Price 2s.

(3) Test Papers in Elementary Algebra.

By C. V. Durell. Pp. viii + 233. (London: Macmillan and Co., Ltd., 1914.) Price 3s. 6d.

(4) Practical Mathematics for Technical Students.

Part I. By T. S. Usherwood C. J. A. Trimble. Pp. 370. (London: Macmillan and Co., Ltd., 1914.) Price 3s. 6d.

(5) A Text-book on Spherical Trigonometry.

By Prof. R. E. Moritz. Pp. vi + 67. (New York: John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1913.) Price 4s. 6d. net.

(6) Plane and Spherical Trigonometry

(with Five-Place Tables). By Prof. R. E. Moritz. Pp. xvi + 357 + 67 + 96. (New York: John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1913.) Price 10s. 6d. net.