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ENTERED, according to Act of Congress, in the year 1848, by
JEREMIAH DAY, In the Clerk's Oifice of the District Court of the United States for the
Southern District of New York.
THOMAS B. SMITH, STEREOTYPER,
216 WILLIAM STREET, N. Y.
J. D. BEDFORD, PRINTER,
138 FULTON STREET.
Pece 1-17-41. HT
SCARCELY any department of Mathematics is more important, or more extensive in its applications, than Trigonometry. By it the mariner traces his path on the ocean; the geographer determines the latitude and longitude of places, the dimensions and positions of countries, the altitude of mountains, the courses of rivers, &c., and the astronomer calculates the distances and magnitudes of the heavenly bodies, predicts the eclipses of the sun and moon, and measures the progress of light from the stars.
The section on right angled triangles in this treatise, may perhaps be considered as needlessly minute. The solutions might, in all cases, be effected by the theorems which are given for oblique angled triangles. But the applications of rectangular trigonometry are so numerous, in navigation, surveying, astronomy, &c., that it was deemed important, to render familiar the various methods of stating the relations of the sides and angles; and especially to bring distinctly into view the principle on which most trigonometrical calculations are founded, the proportion between the parts of the given triangle, and a similar one formed from the sines, tangents, &c., in the tables.
As this treatise is intended to form a part of Day and Thomson's Course of Mathematics for the use of Schools and Academies, the references to Algebra are made to Thomson's Abridgment; and the references to Geometry, to Thomson's Legendre, as well as to Euclid's Elements.