Page:Elementary Trigonometry.djvu/13



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HE object of that branch of mathematical science, which is called Trigonometry, is the investigation of all geometrical properties and relations in which angular magnitude is concerned. In the earlier stages of its progress it was, as its name implies, applied exclusively to the measurement of triangles. and to the establishment of propositions connected immediately with them. Its methods, however, have now received an extension and a generality which render it a most valuable analytical instrument in the higher departments of mathematics. Of all the elementary branches of mathematical science it is perhaps the one of which the practical utility is most distinctly apparent. The student will, for instance, without difficulty foresee how indispensable such methods of calculation are to the surveyor, the navigator, and the astronomer.

2. Extension of the definition of an angle.

Euclid defines a plane rectilineal angle to be the inclination of two straight lines to one another, which meet together but are not in the same straight line. He does not in his definition take into account the direction in which this indication is supposed to be estimated, and, moreover, necessarily limits the signification of the word to angular magnitudes which are less than two right angles.

In Trigonometry, however, we regard an angle as capable of being of any magnitude whatever, and consequently H. T.