This book is the outgrowth of an experience of many years in the teaching of mathematics in secondary schools. The text has been used by many different teachers, in classes of all stages of development, and under varying conditions of secondary school teaching. The proofs have had the benefit of the criticisms of hundreds of experienced teachers of mathematics throughout the country. The book in its present form is therefore the combined product of experience, classroom test, and severe criticism.
The following are some of the leading features of the book: The student is rapidly initiated into the subject. Definitions are given only as needed.
The selection and arrangement of theorems is such as to meet the general demand of teachers, as expressed through the Mathematical Associations of the country.
Most of the proofs have been given in full. In the Plane Geometry, proofs of some of the easier theorems and constructions are left as exercises for the student, or are given in an incomplete form. In the Solid Geometry, more proofs and parts of proofs are thus left to the student; but in every case in which the proof is not complete, the incompleteness is specifically stated.
The indirect method of proof is consistently applied. The usual method of proving such propositions, for example, as Arts.189 and 415, is confusing to the student. The method used here is convincing and clear.
The exercises are carefully selected. In choosing exercises, each of the following groups has been given due importance: (a) Concrete exercises, including numerical problems and problems of construction.(b) So-called practical problems, such as indirect measurements of heights and distances by means of equal and similar triangles, drawing to scale as an application of similar figures, problems from physics, from design, etc.