Geometrie der Dynamen

Abstract

THE title of this book is somewhat misleading. Theobject of the first two parts is the discussion of certaingeometrical theorems. From these the laws for thecomposition of wrenches (Dynamen) can be deducedas particular cases. To this special application, fromwhich the book takes its title, only pp. 116 to 121 aredevoted. In the first part of the book the geometricaltheorems (which deal chiefly with the composition ofvectors, wedges, motors, &c.) are proved by purelygeometrical methods, and the reader is assumed tohave only a good working acquaintance with puregeometry, and in particular a knowledge of the theoryof the composition of screws and translations (such asis supplied, for instance, in Schoenflies's “Krystall-systeme und Krystallstructur,” pp. 326 to 340). Inthe second part the analytical proofs of the same geometrical theorems are given, but the author still confines himself to elementary methods. The third part,which contains the larger portion of the book, appealsto a more advanced class of readers who are familiarwith the method of modern analysis and the theoryof groups. Here the author seeks to supplement the work of Plücker, Ball, and Sturm, and to give a complete discussion and classification of linear line-complexes. A good index and table of contents are givenin the second volume. Geometrie der Dynamen. By E. Study. Two vols. Pp. xiii + 603. (Leipzig: B. G. Teubner, 1901 and 1903.)