Elementary Geometry Plane

Excerpt from Elementary Geometry Plane

This text-book aims to carry out the spirit of the admirable suggestions made by the Committee on Secondary School studies, appointed by the National Educational Association. While the book speaks for itself, some of its leading features may here be pointed out.

(1) It aims at a combination of Euclidean rigor with modern methods of presentation suitable for beginners in the study of demonstrative geometry; but the rigor is not regarded as consisting so much in excessive formality of expression as in soundness of structural development.

(2) It regards the postulates as a body of fundamental conventions that constitute a definition of Euclidean space, from which (with the definitions of particular figures) other properties of such space are to be unfolded by a series of logical steps.

(3) It regards the postulates of construction as determining or defining the province of elementary as distinguished from higher geometry. Accordingly no hypothetical figure is made the basis of an argument until its construction has been proved to be reducible to the construction postulates; and thus problems, no less than theorems, have their place in the logical development of the subject.

(4) The theorems and problems are arranged in natural groups and subgroups with reference to their underlying principle, thus exhibiting the gradual unfolding of the space relations.

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