Excerpt from Plane Geometry
This book is written with the firm conviction that it is possible to give to high-school young people a more systematic training in the science of geometry than is furnished by any textbook on the market to-day. In this connection the two main features of the book should be noted:
1. The analytical method of attack is employed throughout.
Analyses of proofs serve several purposes. When it has been found by actual classroom experience that any particular proof is so difficult that the pupil cannot reasonably be expected to think it out for himself, the analysis gives him at the outset the gist of the argument, calls his attention to the method of proof employed, and gives him some idea of how the proof may have been originally invented. In such cases not only is the analysis given, but as much of the proof as experience has found necessary. In this connection the treatment of the proofs of Theorems 3, 4, 9, 14, 64, 77, 113, and 120 may be noted and compared with the usual treatment of these same proofs.
More important, however, is the fact that the pupil can, with proper training, invent many of his own proofs. While nothing can do away entirely with the element of inspiration in getting originals, the fact remains that the method of analysis is the method by which every trained mind attacks difficulties. The teacher should see to it that the pupil is continually asking himself the necessary questions, that he sees clearly how each step follows from the preceding, and that the results are set down in the orderly form here employed. The statements given in the analyses may seem formal, but clearness and definiteness are essential. No statement should be permitted which does not clearly indicate that the pupil sees all the essential steps of the argument. The proof should in every case be obtained by working backward from the analysis.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. Это и многое другое вы найдете в книге Plane Geometry (Classic Reprint) (Mabel Sykes)