The Calculus of Extension


ABOUT a hundred years ago, when Boole and Hamilton were extending algebra by symbolizing logical and physical entities, a similar but independent investigation was begun in Germany by Grassmann. Unlike the quaternions of Hamilton, which aroused considerable interest and became very well known, the calculus of extensive magnitudes of Grassmann attracted very little attention until the close of the nineteenth century. The appearance of Whitehead's “Universal Algebra” first made this theory well known to English readers, and the book still remains a classic, by providing an interesting and readable approach to the philosophy both of Boolean and Grassmannian algebra. The aim of the work now under review is to give a more detailed account of Grassmann's methods, and particularly to exhibit their power in all forms of geometry, metrical, kinematical and projective. The book is the outcome of many years experience and appreciation of the methods: it was begun twelve years ago as a result of perusing some mathematical notes on Grassmann left by the late Prof. Genese, and its publication has tarried through no fault of the author. The book, which goes far beyond the scope of the original notes, is full of information, and shows very clearly the power of the method and its surprisingly wide range of applications.

The Calculus of Extension

By Prof. Henry George Forder, including Examples by Robert William Genese. Pp. xvi + 490. (Cambridge: At the University Press, 1941.) 30s. net.

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TURNBULL, H. The Calculus of Extension. Nature 148, 299 (1941).

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