Elements of geometry and trigonometry . e CP which is the cosine of thearc AM, has the origin of its value at the centre C, and is esti-mated in the direction from C towards A ; while CP, the cosineof AM has also the origin of its value at C, but is estimated ina contrary direction, from C towards \^. Some notation nmst obviously be adopted to distinguish theone of such ecjual lines from the other; and that lh<y may bothbe expressed analytically, and in the same gcncnil formula^ it isnecessary to consider all lints which are estimated in one di-rection as positive, and those which are estim
Elements of geometry and trigonometry . e CP which is the cosine of thearc AM, has the origin of its value at the centre C, and is esti-mated in the direction from C towards A ; while CP, the cosineof AM has also the origin of its value at C, but is estimated ina contrary direction, from C towards \^. Some notation nmst obviously be adopted to distinguish theone of such ecjual lines from the other; and that lh<y may bothbe expressed analytically, and in the same gcncnil formula^ it isnecessary to consider all lints which are estimated in one di-rection as positive, and those which are estimated in the con-trary direction as negative. If, therefore, the cosines wliicliare estinmt(?d from C towards A be considered as j)ositive,those estimated from C towards B, must be regarded as ne«ra-live. Hence, generally, we shall have, * cos A=—cos (180^~A)that is, the cosine of an arc or angle is equal tu the cosine (j Ussupplement taken negatively. The necessity of changing the algebraic sign to correspond 218 PLANE with the change of directionin the trigonometrical line,may be illustrated by the fol-lowing example. The versedsine AP is equal to the radiusCA minus CP the cosine AM :that is,ver-sin AM=R—cos when the arc AM be-comes AM the versed sineAP, becomes AF, that is equalto R + CP. But this expressioncannot be derived from theformula, ver-sin AM=R—cos AM,unless we suppose the cosine AM to become negative as soonas the arc AM becomes greater than a quadrant. At the point B the cosine becomes equal to —R ; that is,cos 180^=—R. For all arcs, such as ADBN, which terminate in the thirdquadrant, the cosine is estimated from C towards B, and isconsequently negative. At E the cosine becomes zero, and forall arcs which terminate in the fourth quadrant the cosines areestimated from C towards A, and are consequently positive. The sines of all the arcs which terminate in the first andsecond quadrants, are estimated above the diameter BA, whilethe s
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
