Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 12
... equal to a rectangle under half the radius and the versed sine of the supplement of the whole arc or angle . This ... equal to the sum or the difference of the rectangles under their alternate sines and cosines . Let AB and BD be two ...
... equal to a rectangle under half the radius and the versed sine of the supplement of the whole arc or angle . This ... equal to the sum or the difference of the rectangles under their alternate sines and cosines . Let AB and BD be two ...
Página 13
... equal , then we have for the sum , rad x sin 2AB = sin AB X 2 cos AB , agreeing with prop . 2 of this chapter . PROP . IX . 9. The rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the ...
... equal , then we have for the sum , rad x sin 2AB = sin AB X 2 cos AB , agreeing with prop . 2 of this chapter . PROP . IX . 9. The rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the ...
Página 14
... equal rectangles being taken from the square of rc , there will remain , TC2 TC . TH , or TC . ( TC TH ) , or TC.CH = TC2 -TA . TR . Now , ― TC . CH ( or TC2 - TA . - TR ) : TC . RH ( or CA. TR ) :: CHI : RH :: CB ( or CA ) : BS :: CA2 ...
... equal rectangles being taken from the square of rc , there will remain , TC2 TC . TH , or TC . ( TC TH ) , or TC.CH = TC2 -TA . TR . Now , ― TC . CH ( or TC2 - TA . - TR ) : TC . RH ( or CA. TR ) :: CHI : RH :: CB ( or CA ) : BS :: CA2 ...
Página 15
... equal to the tangent of ( AE + AB ) , and b to the tangent of ( AE - AB ) , that is , of ( AD - AB . ) But , by reason of the parallels DE , LM , we have EN : DN :: bм : bL ; which is evidently the theorem enun- ciated above . - Cor ...
... equal to the tangent of ( AE + AB ) , and b to the tangent of ( AE - AB ) , that is , of ( AD - AB . ) But , by reason of the parallels DE , LM , we have EN : DN :: bм : bL ; which is evidently the theorem enun- ciated above . - Cor ...
Página 16
... equal to half their sum , and DE equal to half their dif- ference . By reason of the similar triangles CBH , cfe , DFE , we have , CB : CF :: BH : FG , and CB : DF :: CH : DE ; which are the analogies in the proposition . Cor . 1. From ...
... equal to half their sum , and DE equal to half their dif- ference . By reason of the similar triangles CBH , cfe , DFE , we have , CB : CF :: BH : FG , and CB : DF :: CH : DE ; which are the analogies in the proposition . Cor . 1. From ...
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altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith