WITH PROBLEMS AND APPLICATIONS BY H. E. SLAUGHT, PH.D., Sc.D. PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF CHICAGO AND N. J. LENNES, PH.D. PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF MONTANA ALLYN AND BACON Boston and Chicago PREFACE. In writing this book the authors have been guided by two main purposes: (a) That pupils may gain by gradual and natural processes the power and the habit of deductive reasoning. (b) That pupils may learn to know the essential facts of elementary geometry as properties of the space in which they live, and not merely as statements in a book. The important features by which the Plane Geometry seeks to accomplish these purposes are: 1. The simplification of the first five chapters by the exclusion of many theorems found in current books. These five chapters correspond to the usual five books, and the most important omissions are the formal treatment of the theory of limits, the incommensurable cases, maxima and minima, and numerous other theorems, together with the deduction of complicated algebraic formulæ, such as the area of a triangle and the radii of the inscribed, escribed, and circumscribed circles, in terms of the three sides. Chapter VI contains a graphic representation of certain important theorems and an informal presentation of incommensurable cases and limits. The treatment of limits is based upon the graph, since the visual or graphic method appeals more directly to the intuition than the usual abstract processes. Chapter VII is devoted to advanced work and to a review of the preceding chapters. |