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ELEMENTARY GEOMETRY.

Cambridge: PRINTED BY C. J. CLAY, M.A.

AT THE UNIVERSITY PRESS.

PART 1.

ANGLES, PARALLELS, TRIANGLES, EQUIVALENT
FIGURES, WITH THE APPLICATION TO

PROBLEMS.

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PREFACE.

The lately published Report of the Schools Inquiry Commission has given an immediate importance to the question whether Euclid's Elements is the proper text-book for teaching Geometry to beginners. Euclid's recognised and acknowledged faults as a system of Geometry, and as a specimen of analysed reasoning, are of slight importance compared with others of greater magnitude. The real objections to Euclid as a text-book are his artificiality, the invariably syllogistic form of his reasoning, the length of his demonstrations, and his unsuggestiveness.

As to the first, he aimed, not at unfolding Geometry as a science, but at shewing on how few axioms and postulates the whole could be made to depend: and he has thus sacrificed, to a great extent, simplicity and naturalness in his demonstrations, without any corresponding gain in grasp or cogency. The exclusion of hypothetical constructions may be mentioned as a self-imposed restriction which has

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