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ROBERT REMINGTON GOFF
Director of Mathematics
New Britain, Conn.
HARYAAD COLLEGE 112,?ARY
Printed in the United States of America
The Riverdale Press, Brookline, Boston, Mass.
The special aim of this book is to increase emphasis on analysis, classification, and determination of method in geometry. The pupil is to be taught not the proof but how to find the proof. What is to be done? Then, what are the common methods of doing it?
For this purpose the propositions are arranged not, as usual, according to their conditions, but by their conclusions. The thing to be proved determines the class of proof. The given conditions determine the particular method. Consequently the principal theorems that prove any one thing, such as equality, parallel lines, etc., are grouped in one chapter. The basic principle, upon which all theorems in each chapter depend, is placed conspicuously at the head of that chapter. A Summary of Methods for that group is at the end of that chapter, and this is followed by selected exercises applying these methods. The most important theorems are marked by heavy type and are often followed by a note for emphasis.
This arrangement gives systematic drill in analysis and classification. The pupil soon begins to see that for doing certain things there are certain successful methods. He places a theorem in its class; he recalls the methods for that class; then selects the method for this particular case. He learns one group of methods before taking up another, and he knows the basic principles in each.
Another point of originality is in the explanation of the method of proof just before the proof. The plan is made clear at the beginning, and this fact reduces guessing and memorizing to the minimum.