ANALYTIC GEOMETRY.

By John Wesley Young, Tomlinson Fort, and Frank Millett Morgan. Houghton Mifflin Company, 1936. x + 347 pp., 169 figs. $2.25.

The appearance of this textbook for a freshman course in mathematics will be of particular interest to Dartmouth alumni, for the late Professor Young, in addition to being one of America's most prominent mathematicians, was for many years a leading figure in the educational life of the college. The backbone of this book is a manuscript left unfinished by Professor Young, and Professor Fort and Dr. Morgan have undertaken the task of completing it and preparing it for publication.

The text covers ample material for a year course on analytic geometery, plane and solid, and includes as well a brief treatment of the first elements of the differential calculus. The topics and methods in analytic geometry which most teachers wish to teach are all included and thoroughly studied.

One of the most conspicuous features of the text is the accuracy and completeness of the proofs. The theorems and methods are profusely illustrated by well-chosen worked examples, and both text and worked examples are further clarified by one of the largest and most accurate assemblage of figures the reviewer has seen in a text of this kind. The problems for assignment to the student are also particularly profuse and varied in character, the latter third of each group being designed for the better students, but with an abundance of routine numerical problems for practice in technique.

The reviewer feels personally that the best chapter in the book is that on the conics, perhaps because he likes to teach that topic in essentially the same way. On the other hand, the reviewer prefers to reach the study of the circle in less than the 103 pages utilized here for the fundamentals and the treatment of the straight line.

From the point of view of typography this text is exceptionally easy on the reader's eyes, both esthetically and physically. The use of Clarendon type rather than italics for emphasis has a very fortunate effect as well. The publishers have reflected much credit on themselves in bringing out this fitting final tribute to one who long served them ably as editor of their mathematical series.

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