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i E From the two Ex- tremes of the Diameter Q AB, let the Chords AE and BE be drawn, and let the Radius CO bi

w sećtAE, perpendicularl S F operpendicularly, B C A. in D (Wid. I. 3.); then will AD be the Sine, and CD the Co-fine, of the Angle ACD, or ; ACE.

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The Sines and Coosines of two Arches being given, to find the Sines, and the Co-fines, of the Sum and Difference of those Arches. -

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Hence, if the Sines of two Arches be denoted by S and 3 ; their Co-fines by C and c; and Radius by R; then will

the Sine of their sum = % i. 3C

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Co Roll A R Y 2.

Hence, the Sine of the Double of either Arch

(when they are equal) will be = †, and its Cofine = cos. Whence it appears that the Sine of

the Double of any Arch, is equal to twice the Rečiangle of the Sine and Co-sine of . single Arch, divided by Radius; and that its Co-fine is equal to the Difference of the Squares of the Sine and Co-fine of the single Arch, also, divided by Radius.

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Hence, if Radius be supposed Unity, and the Tangents of two Arches be à: by Tand t, it follows that the Tangent of their Sum will be = #. and the Tangent of their Difference = I

T—t

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