MONTCLAIR, NEW JERSEY, CO-AUTHOR OF THE SOUTHWORTH-STONE ARITHMETIC, ALGEBRAS AND GEOMETRIES AND JAMES F. MILLIS, A.M. HEAD OF THE DEPARTMENT OF MATHEMATICS, FRANCIS W. PARKER SCHOOL SECONDARY ARITHMETIC ELEMENTARY ALGEBRA, FIRST COURSE ELEMENTARY ALGEBRA, SECOND COURSE ELEMENTARY ALGEBRA, COMPLETE COURSE HIGHER ALGEBRA PLANE GEOMETRY SOLID GEOMETRY PLANE AND SOLID GEOMETRY BENJ. H. SANBORN & Co., PUBLISHERS COPYRIGHT, 1916 BY BENJ. H. SANBORN & 00. 8 PREFACE THE STONE-MILLIS GEOMETRY-PLANE, SOLID, and PLANE AND SOLID — published in 1910, was a pioneer in its field, being the first of the group of American textbooks on geometry which in recent years have attempted in various ways to make the teaching of geometry conform to modern thought in education. It marked a wide departure from the traditional Greek geometry after which textbooks for secondary schools had for generations been patterned. This text has met with remarkable success. The educational ideals which it embodied are now recognized as national, and are summarized in the REPORT OF THE NATIONAL COMMITTEE OF FIFTEEN on the teaching of geometry. The present geometry, by the same authors, has been prepared in the attempt to produce a text which shall preserve the distinctive features of the older text, but which, if possible, shall be more simple, practical, and teachable. The following are some of the features which distinguish this text: I. SIMPLICITY.-1. The subject is graded so that the easier topics come first and so that the student is introduced to only one new difficulty at a time. The grading of geometry is made possible in this text by abandoning the Greek division of geometry into books and re-grouping the material in chapters. 2. Some of the theorems on fundamental properties of figures are treated informally at the beginnings of many topics. 3. The subject is also abbreviated and simplified by the omission of certain useless traditional theorems and the reduction to a reasonable minimum of the number of theorems, constructions, and corollaries requiring formal treatment. M305026 4. The use of the theory of limits in the proofs of incommensurable cases of theorems has been eliminated. II. PRACTICALITY.-1. Geometry is humanized by using as exercises a large number of practical problems. This phase of geometry, which was first introduced into American schools by the Stone-Millis text, is now universally recognized as an integral part of the subject. The STONE-MILLIS GEOMETRY contains a very large number and a very great variety of simple and genuine practical problems. They are selected from many fields of human activity, such as home life, art, architecture, astronomy, engineering, designing, navigation, science, the construction and use of implements and machinery, etc. 2. Directions are given for the construction of many homemade instruments and their use in out-of-door exercises. 3. Geometry is correlated with trigonometry by the introduction of simple work with trigonometric ratios, in the chapter on similar polygons. Application is made to practical problems in the solution of triangles. III. TEACHABLENESS. 1. A concrete approach to formal geometry is provided. This develops a body of experience and imagery as a basis of formal geometry, and the latter is not introduced until need for it is felt. In the approach to demonstrative geometry, familiarity with important geometric figures is secured through their accurate construction with drawing instruments. This development of clear imagery through accurate drawing of the figures involved in the formal theorems, etc., is continued throughout plane geometry. 2. Use is made of the suggestive method in the treatment of theorems. While complete model proofs of a large number of theorems are given-and whenever a proof is given it is given in complete form, with numbered steps-the proofs of many theorems are left, with suggestions, to the student. The suggestions in a large part of the theorems are given in the form of analyses. It is believed that suggestions of this nature are superior to those of the traditional kind, which are mere outlines of the proofs, because they give the student training in exactly the kind of thinking which he must do when attacking a proof unaided, and thus they teach method of attack and develop power of originality. 3. Exercises which demand technical knowledge have been eliminated. Many new exercises have been introduced. The exercises are grouped in every case immediately after the theorem, construction, or corollary to which they relate. Many miscellaneous review exercises are given. 4. Special care has been given to the illustrations in this text. When construction lines are required in drawing a figure, they show in the book. Throughout the SOLID GEOMETRY shaded drawings of models, are placed by the side of the more complicated geometric figures, to aid the student in visualizing the third dimension in the figures while looking at the flat drawings of them. The consistent plan of representing hidden parts of figures by thinner lines than the others is carried out, dotted lines being employed exclusively for auxiliary lines as in plane geometry. Grateful acknowledgment of the authors is due to all those who by timely suggestions have aided in the preparation of this text; especially to Professor H. E. Cobb and Professor A. W. Cavanaugh of Lewis Institute, Chicago; to Miss Alice M. Lord of the High School, Portland, Maine; and to Professor Guido H. Stempel of Indiana University. Special acknowledgment is due to Mr. Charles McCauley of Chicago, who has made the excellent illustrations. JOHN C. STONE, JANUARY, 1916. |