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WOOSTER WOODRUFF BEMAN
PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF MICHIGAN
DAVID EUGENE SMITH
PRINCIPAL OF THE STATE NORMAL SCHOOL AT BROCKPORT
GINN & COMPANY, PUBLISHERS
The Athenæum Press
Ecduc Т 148.99, 203
HARVARD COLLEGE LIBRARY
PROF. WILLIAN FOOG OSGOOD
COPYRIGHT, 1895, 1899, BY
WOOSTER WOODRUFF BEMAN AND DAVID EUGENE SMITH
ALL RIGHTS RESERVED
THE demand of a large number of schools for a book confined to plane geometry leads the authors to issue this edition of the first part of their "New Plane and Solid Geometry." In offering it to the profession an explanation of its distinctive features may be of service.
It is sometimes asserted that we should break away from the formal proofs of Euclid and Legendre and lead the student to independent discovery, and so we find text-books that give no proofs, others that give hints of the demonstrations, and still others that draw out the demonstration by a series of questions which, being capable of answer in only one way, merely conceal the Euclidean proof. But, after all, the experience of the world has been that the best results are secured by setting forth a minimum of formal proofs as models, and a maximum of unsolved or unproved propositions as exercises. This plan has been followed by the authors, and the success of the first edition has abundantly justified their action.
There is a growing belief among teachers that such of the notions of modern geometry as materially simplify the ancient should find place in our elementary text-books. With this belief the authors are entirely in sympathy. Accordingly they have not hesitated to introduce the ideas of one-to-one correspondence, of anti-parallels, of negative magnitudes, of general figures, of similarity of point systems, and such other concepts as are of real value in the early