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COURSE

MATH E MATIC S.

IN TWO VOLUMES.

COMPOSĖD FOR THE

USE OF THE ROYAL MILITARY ACADEMY.

BY CHARLES HUTTON, LL.D. F.R.S.

LATE PROFESSOR OF MATHEMATICS IN THAT INSTITUTION.

VOL. II.

THE ELEVENTH EDITION,

WITH MANY CORRECTIONS AND IMPROVEMENTS.

BY OLINTHUS GREGORY, LL.D. F.R.A.S.
Corresponding Associate of the Academy of Dijon, Honorary Member of the Literary and Philosophical

Society of New York, of the New York Historical Society, of the Literary and Philosophical, and the
Antiquarian Societies of Newcastle upon Tyne, of the Cambridge Philosophical Society, of the Bristol
Philosophical Society, of the Institution of Civil Engineers, one of the Board of Visitors of the Royal
Observatory, &c. &c., and Professor of Mathematics in the Royal Military Academy,

LONDON:

PRINTED FOR LONGMAN, Rees, & co.; T. CADELL; J. RICHARDSON ; J. M. RICHARDSON;

BALDWIN & CRADOCK; J. G. & F. RIVINGTON ; BOOKER & DOLMAN; HARDING & co. ;
HARVEY & DARTON; HAMILTON, ADAMS, & co.; WHITTAKER & co.; J. DUNCAN;
SIMPKIN, MARSHALL, & co.; J. SOUTER; W. H. ALLEN & co.; AND STIRLING & co.,
EDINBURGH,

LONDON: GILBERT & RIVINGTON, PRINTERS,

ST. JOHN'S SQUARE,

CONTENTS

2n

74

334

339

PREFACE

TO

THE SECOND VOLUME.

In this New Edition of the Woolwich Course, the substance of the second and third volumes of the former Edition is, by a new arrangement, incorporated into one. The matter, also, of several portions of the volume is entirely remodified ; and my colleague, Mr. Davies, has been at the pains considerably to enlarge the part which relates to the Conic Sections; as well as to prepare a sketch of the Geometry of Co-ordinates. The doctrine of Fluxions is now introduced before the subject of Mechanics, a change which has enabled me to improve that department by introducing various propositions which could only be treated adequately by the fluxionary or an analogous calculus.

I had intended to attempt a concise sketch of the Elements of the Differential Calculus, according to my own view of the principle of limits, first defining the sense in which the term limit may be unobjectionably employed, and then, as occasion required, resorting to the familiar axiom, that “what is true up to the limit, is true at the limit;" but a very serious and continued indisposition, which commenced just at the time this should have been undertaken, compelled me to adopt another course. I got one of my own family to translate the Lehrbuch des Höhern Kalkuls, für Lehrer und Selbstlernende, of S. F. LUBBE of the University of Berlin : not because it was in all respects so satisfactory as I could have wished, for it sometimes falls into the paralogisms of various other authors in this department of science; but because several of its processes of investigation are both elegant and complete; and because it was

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