Page images
PDF
EPUB

PART I,

ELEMENTS OF PLANE TRIGONOMETRY.

CHAPTER I.

EXPLANATION OF THE TRIGONOMETRICAL LINES.

mathe

(Article 1.) PLANE TRIGONOMETRY is that branch of pure matics of which the primary object is to determine the several parts of a plane triangle from having certain other dependent parts given.

By the parts of a plane triangle we mean these six things, viz. the three sides and the three angles, and if any three of these six be given, provided only that a side be among them, the other three may always be determined either by geometrical construction, as shown in the Elements of Geometry, or by numerical computation, as will be seen hereafter.

From the foregoing definition it appears that quantities of two kinds, perfectly distinct from each other and admitting of no comparison, are concerned in Trigonometry, viz. straight lines and angles.

By means of certain happy contrivances, however, the whole business of trigonometry, and, indeed, the general theory of angular magnitude is conducted by help of linear quantities only; the angles themselves not entering into the computations, but certain straight lines dependent upon them and serving as indexes to them.

(2.) Before we explain the nature of these trigonometrical lines, it will be necessary first to show how angular magnitude is measured.

B

« PreviousContinue »