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PLANE AND SPHERICAL
PROFESSOR OF MATHEMATICS IN THE UNITED STATES NAVAL ACADEMY; FELLOW OF THE AMERICAN ACADEMY
OF ARTS AND SCIENCES; MEMBER OF THE AMERICAN PHILOSOPHICAL SOCIETY, ETC.
Edue T 168.52.275
vard College Library,
22 May, 1030.
From the Library of
Entered according to Act of Congress, in the year 1850, by WILLIAM CHAUVENET, in the
STEREOTYPED BY L. JOHNSON AND CO.
I HAVE in this treatise endeavored to arrange a course of trigonometrical study sufficiently extensive to enable the student to comprehend readily any applications of trigonometry he may meet with in the works of the best modern mathematicians. With this object, some topics have been introduced which are not usually found in works devoted specially to this subject.
Among those topics, the most important is the solution of the general spherical triangle, or the triangle whose sides and angles are not limited, according to the usual practice, to values less than 180°. The advantage of introducing such triangles into astronomical investigations is sufficiently shown in the applications made of them in the works of BESSEL and other German mathematicians; and especially in the Theoria Motus Corporum Coelestium of GAUSS, who was the first to suggest their employment.
The subject of Finite Differences of triangles, plane and spherical, occupies a large space in Cagnoli's treatise, but. has not been admitted into more recent works. It here occupies only a few pages, but no important result of