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GEOMETRY:

BY

G. A. WENTWORTH, A. M.,

PROFESSOR OF MATHEMATICS IN PHILLIPS EXETER ACADEMY.

BOSTON:
PUBLISHED BY GINN AND HEATH.

1881.

COPYRIGHT, 1877.
BY GINN AND HEATH,

38280

Press OF ROCKWELL AND CHURCHILL,

39 Arch St., Boston.

PREFACE.

Most persons do not possess, and do not easily acquire, the power of abstraction requisite for apprehending the Geometrical conceptions, and for keeping in mind the successive steps of a continuous argument. Hence, with a very large proportion

beginners in Geometry, jt depends mainly upon the form in which the subject is presented whether they pursue the study, with indifference, not to say aversion, or with increasing interest and pleasure.

In compiling the present treatise, this fact has been kept constantly in view. All unnecessary discussions and scholia have been avoided ; and such methods have been adopted as experience and attentive observation, combined with repeated trials, have shown to be most readily comprehended. No attempt has been made to render more intelligible the simple notions of position, magnitude, and direction, which every child derives from observation ; but it is believed that these notions have been limited and defined with mathematical precision.

A few symbols, which stand for words and not for operations, have been used, but these are of so great utility in giving style and perspicuity to the demonstrations that no apology seems necessary for their introduction.

Great pains have been taken to make the page attractive. The figures are large and distinct, and are placed in the middle of the page, so that they fall directly under the eye in immediate connection with the corresponding text. The given lines

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