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attack in the mind of the student. The exercises which have been taken from other authors are limited to such as appear in at least two of them.

Simplicity in wording and in demonstration have been sought; numerous notes are added ; leading thoughts, definitions, and methods are repeated so as to enforce them; the student is led, not driven; and he is encouraged to investigate and determine for himself.

The division of the work into fourteen chapters makes a natural arrangement of parts, although the chapters are quite unequal in length. The chapters have been divided into articles, and these have been numbered for convenience in cross-reference. But the student should refer to principles or facts by stating them in full.

The writer thinks that the proper place for the theory of proportion is in the Algebra, and for that reason has omitted it here.

The leading features of the book are, the development of, and the insistence on, method of attack in the solution of problems.

Logic, which is the science of orderly thinking, requires for its proper study, a development of mind beyond that which is necessary for the student of the ordinary Geometry. Geometry, however, does admirably illustrate the principles of Logic; and in it these principles are rigidly enforced at every step without the distractions that accompany investigations in any other

field of research. From the educational point of view Geometry is the most valuable study of the High School period.

Instructors are advised to proceed slowly with the earlier chapters, and more rapidly with the later ones; not abating at all in thoroughness.

Instructors and students are advised to read carefully the paragraphs on Demonstrative Geometry, pages 112116 of the “Report of the Committee on Secondary School Studies, appointed at the meeting of the National Educational Association, July 9, 1892”; and published by the United States Bureau of Education in 1893.

The writer will deem it a favor to have his attention called to errors. They will surely exist in the first writing, but the author hopes that the main features of the book will not be seriously injured thereby.


BERKELEY, March 23, 1895.

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