Excerpt from Plane Geometry
The addition of another text to the long list of existing geometry texts calls for an explanation of the motives underlying its preparation.
Briefly stated, this text aims to effect a compromise between the extreme demands of certain reformers and the equally untenable position of overconservative writers. Our educational troubles cannot be cured by a complete break with the past, nor by ignoring the legitimate demands of our times. Accordingly, the authors have tried to endow the subject with life and reality, and at the same time to retain, as far as possible, that spirit of careful reasoning for which geometry has always been famous.
To accomplish this double purpose, the authors depend mainly on the following features:
1. A Preliminary Course precedes the Demonstrative Course. It bad long been the experience of the authors that many pupils become permanently discouraged at the very beginning of demonstrative geometry by the simultaneous appearance of too many difficulties. The Preliminary Course is intended to serve as a preparation for formal geometry by vitalizing the content of all definitions by abundant illustration and discussion; by cultivating skill in the use of ruler and compasses through interesting drawing exercises; by presenting exercises requiring for their solution simple reasoning and inference; and by developing gradually the conviction that formal proof is necessary for further advance.
The actual time required by the Preliminary Course depends somewhat on the class and on the mode of procedure. A laboratory plan with individual notebooks may be followed, or the exercises may be solved on the blackboard. In either ease the Preliminary Course can be completed in five or six weeks.
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