Association for the 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

perennially a symptom, not only of stead

"Proficiency in Pure Geometry
application, but of a clear methodic intellect, and offering in all epochs good promise for a
manner of arts and pursuits."-T. CARLYLE

LONDON

SWAN SONNENSCHEIN & CO., LIMITED
PATERNOSTER SQUARE

1903

[All rights reserved

PREFACE

-:0:

dition,

THE Association for the Improvement of Geometrical Teach was formed in the year 1871, and published in the year 18 "Syllabus of Plane Geometry (corresponding to Euclid Bo I.-VI.)." This Syllabus has received a considerable amoun favourable recognition at the hands of Teachers and ot interested in the study of Geometry, as is proved by the that an edition of 3000 copies has recently been exhausted = to meet a steadily continuing demand, a new edition has b published. It was felt, however, by many members of Association that, in order to secure for the Syllabus n general consideration and acceptance, it was desirable that authorised series of Proofs of the Propositions contained should be issued, and accordingly at the Annual Meeting January, 1881, it was resolved

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

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

The Association is desirous that it should be clearly unders

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.