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THE

ELEMENTS OF EUCLID.

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WITH A FEW VARIATIONS AND IMPROVEMENTS, FROM THE

TEXT OF DR. SIMSON.

A NEW EDITION, CORRECTED AND REVISED.

BY WILLIAM RUTHERFORD, F. R. A. S.

ROYAL MILITARY ACADEMY, WOOLWICH.

* LONDON:
PRINTED FOR THOMAS TEGG, No. 73, CHEAPSIDE.

1841.

ALVALA

LONDON BALNE BROTHERS, PRINTERS, GRACECHURCH STREET.

THE EDITOR'S PREFACE.

In this edition of the Elements of Hadid, the text and arrangement of Dr. Simson have been strictly adhered to, with the exception of several corrections and modifications, where the language of total distinguisļed geometer is not in strict accordance ixjth geometrical accuracy.

In many instances Euclid employs an indirect method for establishing the truth of what he intends to prove, and deduces an inference which contradicts some self-evident, or demonstrated truth. Whenever an inference is contrary to a demonstrated truth, the language of Simson is frequently ambiguous, and does not clearly point out whether the inference or the demonstrated truth is impossible. In the present edition this ambiguity has been removed by a slight change of the language, and in every instance the inference has been stated to be inconsistent with the demonstrated truth.

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