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A

COURSE

OF

MATHEMATICS;

FOR THE

USE OF ACADEMIES

AS WELL AS

PRIVATE TUITION,

IN TWO VOLUMES.

BY

CHARLES HUTTON, LL.D. FR.S.

LATE PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY ACADEMY.

THE FIFTH AMERICKN, FROM THE NINTH
LONDON EDITION,

WITH MANY CORRECTIONS AND IMPROVEMENTS.
BY OLINTHUS GREGORY, LL.D.

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 Institution of Civil Engineers, &c. &c. Secretary to the Astronomical Society of London, and Professor of Mathematics in the Royal Military Academy.

WITH THE ADDITIONS

OF

ROBERT ADRAIN, LL.D. F.A.P.S. F.A.A.S, &c.
And Professor of Mathematics and Natural Philosophy.

THE WHOLE

CORRECTED AND IMPROVED.

VOL. I.

NEW-YORK:

W. E. DEAN, PRINTER."

T. AND J. SWORDS; T. A. RONALDS; COLLINS AND CO.; COLLINS AND HAN-
NAY; G. AND C. AND H. CARVILL; WHITE, GALLAHER, AND WHITE;
O. A. ROORBACH; AND M'ELRATH AND BANGS.

1831.

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Southern District of New-York, to wit:

BE IT REMEMBERED, That on the 22d day of February, Anno Domini 1831, W. E. DEAN, of the said district, hath deposited in this office the title of a book, the title of which is in the words following, to wit:

"A Course of Mathematics; for the use of Academies as well as private tuition. In Two Volumes. By Charles Hutton, LL.D. F.R.S., late Professor of Mathematics in the Royal Military Academy. The Fifth American from the Ninth London Edition, with many corrections and improvements. By Olinthus Gregory, LL.D. 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 Institution of Civil Engineers, &c. &c. Secretary to the Astronomical Society of London, and Professor of Mathematics in the Royal Military Academy. With the Additions of Robert Adrain, LL.D. F.A.P.S. F.A. A.S., &c. and Professor of Mathematics and Natural Philosophy. The whole corrected and improved."

the right whereof he claims as proprietor. In conformity with an Act of Congress, entitled "An Act to amend the several Acts respecting copy-rights."

FRED. J. BETTS,

Clark of the Southern District of New-York.

PREFACE.

THE present American edition is in part a reprint of the Ninth English edition by Dr. OLINTHUS GREGORY, with most of the improvements introduced into former American editions by Dr. ADRAIN, together with such modifications of the English editions as appeared calculated to increase the general usefulness of the work. At the same time two or three Chapters, devoted to subjects of no great value at present to the American student, have been omitted, to leave room for matter of more interest and importance,

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