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CAMBRIDGE UNIVERSITY PRESS LONDON : Fetter Lane

NEW YORK The Macmillan Co. BONBAY, CALCUTTA and

MADRAS Macmillan and Co., Ltd.

TORONTO The Macmillan Co. of

Canada, Ltd.

TOKYO Maruzen-Kabushiki-Kaisha

All rights reserved

BASED ON THE VARIOUS GEOMETRY BOOKS

BY GODFREY AND SIDDONS

By

A. W. SIDDONS, M.A.
Late Fellow of Jesus College, Cambridge;
Senior Mathematical Master at Harrow School

and

R. T. HUGHES, M.A.
Assistant Master at Harrow School;

Late Scholar of Queen's College, Oxford;
Late Senior Mathematical Master at Northampton School

CAMBRIDGE
AT THE UNIVERSITY PRESS

1926

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Theoretical Geometry is based on the various Geometry books by Godfrey and Siddons. The order of the theorems is, with very slight modifications, that of Godfrey and Siddons' Elementary Geometry and Shorter Geometry, the order of which is followed very closely by the A.M.A. Schedule. A few theorems that were given as important riders in Elementary and Shorter Geometry are here proved in full; some examining bodies now include them in their schedules of theorems.

The object of this book is to provide a continuous course of logical Geometry, covering all the requirements of pupils at school, except the special requirements of mathematical specialists. The essential functions of the book are two:(i) The pupil, while reading Practical Geometry by the same

authors, should learn the proofs of many of the theorems and do many of the easy riders in Theoretical Geometry. He will thus acquire a knowledge of the principles and methods of Theoretical Geometry and be assured of the soundness of

many individual links in the logical chain. (ii) Towards the end of the school course, the pupil can read

straight through the book-work, looking at the subject as a whole; then he will see how the logical chain is linked

together. For the sake of completeness the proofs of the earlier theorems are all given; but the authors recommend that theorems 1-6, 10, 11, 14 should be taken as axiomatic (see Chapter I as to the soundness of this). The Mathematical Association has for many years recommended that proofs of certain of the early theorems should not be required in examinations; most examining bodies have for some years adopted the recommendation, but they do not all agree as to the list of theorems for which proofs shall not be required in their examinations. In this book some of these theorems are marked thus 1; but the teacher should consult the latest syllabus of the particular examination with which he is concerned.

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