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Association for tbe Improvement of Geometrical Teaching

THE

ELEMENTS OF PLANE GEOMETRY

PART I

(CORRESPONDING TO EUCLID BOOKS I.-II.)

Prepared by the Committee appointed by the Association

" Proficiency in Pure Geometry

perennially a symplom, not only of steady
application, but of a clear methodic intellect, and offering in all epochs good promise for all
manner of arts and pursuits.”—T. CARLYLE

LONDON
SWAN SONNENSCHEIN & CO., LIMITED

PATERNOSTER SQUARE

1903
(All rights reserved ]

HARVARD
UNIVERSITY

LIBRARY

First Edition, January 1884 ; Second Edition, May 1899; Third Edition,

May 1901 ; Fourth Edition, December 1903.

PREFACE

:0:

THE Association for the Improvement of Geometrical Teaching was formed in the year 1871, and published in the year 1875 a “Syllabus of Plane Geometry (corresponding to Euclid Books I.-VI.).” This Syllabus has received a considerable amount of favourable recognition at the hands of Teachers and others interested in the study of Geometry, as is proved by the fact that an edition of 3000 copies has recently been exhausted and, to meet a steadily continuing demand, a new edition has been published. It was felt, however, by many members of the Association that, in order to secure for the Syllabus more general consideration and acceptance, it was desirable that an authorised series of Proofs of the Propositions contained in it should be issued, and accordingly at the Annual Meeting in January, 1881, it was resolved

“ That a sub-committee be appointed to draw up Proofs of the Propositions of the Syllabus of Plane Geometry."

The result of the labours of the committee appointed in accordance with this resolution, extending over Books I. and II. of the Syllabus, was approved at a General Meeting of the Association, held on the 20th March last, and is submitted to the public in the following pages.

The Association is desirous that it should be clearly understood that the present work is not offered as a section of a complete treatise on Elementary Geometry, but simply as an edition of a part of the Syllabus with the demonstrations supplied and suitable exercises inserted.

Probably many teachers will find in this all that they require in a Text-Book for their pupils, being satisfied to supply the needful illustrations, explanations, and developments of the subject in their oral teaching. Still there is, doubtless, room for other treatises embodying such illustrative and explanatory matter; but the Association is of opinion that such treatises should rather be the work of individual authors than of an Association.

Accordingly, should any author desire to publish a further treatise, based on the present work, the Council of the Association would be glad to authorise his free use of the work on terms to be arranged by communication with them through the publishers or the honorary secretaries.

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BOOK II. Equality of Areas

Section 1. Theorems

Section II. Problems

Definitions

88

123

135

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