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BY ORDER OF THE MASTER-GENERAL AND BOARD OF ORDNANCE.

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VOLUME I.

CONTAINING

.

ARITHMETIC AND ALGEBRA,

By W. RUTHERFORD, Esq. LLD. & F.R.A.S.
APPLICATION OF ALGEBRA TO GEOMETRY, PLANE TRIGONOMETRY,

SPHERICAL TRIGONOMETRY, MENSURATION,
AND COORDINATE GEOMETRY OF TWO DIMENSIONS,

BY STEPHEN FENWICK, F.R.A.S.
DIFFERENTIAL AND INTEGRAL CALCULUS.

By W. RUTHERFORD, Esq. LLD. & F.R.A.S.

LONDON:

PRINTED FOR HER MAJESTY'S STATIONERY OFFICE:

PUBLISHED BY

JOHN WEALE, 59 HIGH HOLBORN.

1853.

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MY LORD,

I HAVE the honour to lay before you the course of Mathematics for the Royal Military Academy, which in compliance with the directions given by the Marquis of Anglesey, while Master-General of the Ordnance, has been compiled under my superintendence. It will, I trust, not only meet the present wants of the Cadets, but also prove useful for such references and further studies as their professional duties may render necessary after they receive their commissions. The cordial co-operation of the gentlemen employed upon it, and the care bestowed by each of them on the subjects intrusted to him, induce a confident hope that this will be the case, and that their labours will deserve your Lordship’s approval.

The names of these gentlemen are published in the title-page of each volume to which they have contributed, but the valuable assistance afforded by Mr. Barlow, whose name is not thus recorded, also demands my grateful acknowledgment. The reluctance caused by a sense of my incompetency to undertake the editorship of a course extending far beyond the limits of my own information, disappeared when he consented to aid me. His great experience in the application of Mathematics to practical purposes-his long connexion with the Royal Military Academy as one of the Mathematical instructors—the numerous cases in which his former pupils have sought his assistance when their duties have compelled them to contend with difficult questions and the interest he has evinced

in their welfare and reputation by the kindness with which he has always been ready to give that assistance-marked him out as the best adviser during the preparation of the work required; to him it has in all its stages been submitted, and to him must be attributed whatever merit its general conception and arrangement may possess.

As the time, which has elapsed since the first communication on the subject of this course was made to me, may be considered unnecessarily long, I am desirous to state that although the wishes of the Marquis of Anglesey were conveyed to me at the end of October, 1847, it was not until the middle of May, 1849, that the various official difficulties which prevented the commencement of the work were removed, and its preparation authorized.

I remain,

My Lord,

Your obedient Servant,

H. D. HARNESS,

Captain Royal Engineers.

18th October, 1852.,

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