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PLANE AND SPHERICAL
WITH THEIR APPLICATIONS TO
MENSURATION, SURVEYING, AND
BY ELIAS LOOMIS, LL.D.,
PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN THE UNIVERSITY OF THE CITY
Entered, according to Act of Congress, in the year one thousand eight hundred and fifty-three, by
HARPER & BROTHERS,
in the Clerk's Office of the District Court of the Southern District
of New York.
THE following treatise constitutes the third volume of a course of Mathematics designed for colleges and high schools, and is prepared upon substantially the same model as the works on Algebra and Geometry. It does not profess to embody every thing which is known on the subject of Trigonometry, but it contains those principles which are most important on account of their applications, or their connection with other parts of a course of mathematical study. The aim has been to render every principle intelligible, not by the repetition of superfluous words, but by the use of precise and appropriate language. Whenever it could conveniently be done, the most important principles have been reduced to the form of theorems or rules, which are distinguished by the use of italic letters, and are designed to be committed to memory. The most important instruments used in Surveying are fully described, and are illustrated by drawings.
The computations are all made by the aid of natural numbers, or with logarithms to six places; and by means of the accompanying tables, such computations can be performed with great facility and precision. This volume, having been used by several successive classes, has been subjected to the severest scrutiny, and the present edition embodies all the alterations which have been suggested by experience in the recitation room.