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MACMILLAN AND CO., LIMITED
LONDON · BOMBAY • CALCUTTA

MELBOURNE

THE MACMILLAN COMPANY

NEW YORK • BOSTON • CHICAGO

ATLANTA • SAN FRANCISCO

THE MACMILLAN CO. OF CANADA, LTD.

TORONTO

OF THE

HISTORY OF MATHEMATICS

BY

W. W. ROUSE BALL

FELLOW OF TRINITY COLLEGE, CAMBRIDGE

FOURTH EDITION

MACMILLAN AND CO., LIMITED
ST. MARTIN'S STREET, LONDON

First Edition 1888. Second Edition 1893. Third Edition 1901. Fourth Edition 1908.

PREFACE

The subject-matter of this book is a historical summary of the development of mathematics, illustrated by the lives and discoveries of those to whom the progress of the science is mainly due. It may serve as an introduction to more elaborate works on the subject, but primarily it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may yet desire to know.

The first edition was substantially a transcript of some lectures which I delivered in the year 1888 with the object of giving a sketch of the history, previous to the nineteenth century, that should be intelligible to any one acquainted with the elements of mathematics. In the second edition, issued in 1893, I rearranged parts of it, and introduced a good deal of additional matter. The third edition, issued in 1901, was revised, but not materially altered; and the present edition is practically a reprint of this, save for a few small corrections and additions.

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The scheme of arrangement will be gathered from the table of contents at the end of this preface. Shortly it is as follows. The first chapter contains a brief statement of what is known concerning the mathematics of the Egyptians and Phoenicians; this is introductory to the history of mathematics under Greek influence. The subsequent history is divided into three periods: first, that under Greek influence, chapters II to VII; second, that of the middle ages and renaissance, chapters VIII to XIII; and lastly that of modern times, chapters XIV to

XIX.

In discussing the mathematics of these periods I have confined myself to giving the leading events in the history, and frequently have passed in silence over men or works whose influence was comparatively unimportant. Doubtless an exaggerated view of the discoveries of those mathematicians who are mentioned may be caused by the non-allusion to minor writers who preceded and prepared the way for them, but in all historical sketches this is to some extent inevitable, and I have done my best to guard against it by interpolating remarks on the progress of the science at different times. Perhaps also I should here state that generally I have not referred to the results obtained by practical astronomers and physicists unless there was some mathematical interest in them. In quoting results I have commonly made use of modern notation; the reader must therefore recollect that, while the matter is the same

as that of any writer to whom allusion is made, his proof is

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