:

ELEMENTS

OF

PLANE AND SPHERICAL

TRIGONOMETRY:

WITH

THEIR APPLICATIONS

TO

HEIGHTS AND DISTANCES, PROJECTIONS OF THE
SPHERE, DIALLING, ASTRONOMY, THE SOLUTION
OF EQUATIONS, AND GEODESIC OPERATIONS.

BY

OLINTHUS GREGORY, LL. D.

Of the Royal Military Academy,

VICE-PRESIDENT OF THE LONDON PHILOSOPHICAL SOCIETY, AND
HONORARY MEMBER OF THE LITERARY AND PHILOSOPHICAL, AND
OF THE ANTIQUARIAN, SOCIETIES AT NEWCASTLE UPON TYNE,

LONDON:

PRINTED FOR BALDWIN, CRADOCK, AND JOY,
47, PATERNOSTER-ROW;

W. BLACKWOOD, EDINBURGH ; AND J. CUMMING,

DUBLIN,

PREFACE.

HE who wishes to acquire any other reputation than that of being useful, will not devote his time to the preparation of an elementary work. Such, however, is the humble honour after which I here aspire: and if the small volume I now lay before the public shall contribute, in any degree, to increase the knowledge and improve the taste of the mathematical student in the earlier stages of his progress, I shall have attained my object.

Of late years the authors of elementary treatises on different branches of mathematics, and especially Dr. Hutton and Mr. Bonnycastle, in their compendious manuals for popular use, have shown that it is possible, by judicious arrangement and selection, to compress much interesting, valuable, and scientific matter, within the compass of a small duodecimo volume. There can, I think, be no doubt that to the extensive circulation of this class of books, together with the stimulus furnished by the annual problems in the Ladies' and Gentleman's Diaries, and those proposed in the Senate House at Cambridge, must principally be ascribed the circumstance that mathematical knowledge, to a certain extent, is more widely diffused over the middle classes of society in this country, than in any other part of Eu