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 89
... sinc sinb ... sin c = sin B Case II . 33. Of these four things , viz . the three sides a , b , c , and an angle , any three being given , to find the fourth . This case comprises three problems . 1. When the three sides are given , to ...
... sinc sinb ... sin c = sin B Case II . 33. Of these four things , viz . the three sides a , b , c , and an angle , any three being given , to find the fourth . This case comprises three problems . 1. When the three sides are given , to ...
Página 95
... sinc ( sin A + sin B ) = sin c ( sin a + sin b ) , and sin c ( sin A sin B ) : - - = sin c ( sin a sin b ) . Dividing each of these two equations by the preced- ing , there will be obtained , sin A + sin B sin c sin a + sin b = COS ACOS ...
... sinc ( sin A + sin B ) = sin c ( sin a + sin b ) , and sin c ( sin A sin B ) : - - = sin c ( sin a sin b ) . Dividing each of these two equations by the preced- ing , there will be obtained , sin A + sin B sin c sin a + sin b = COS ACOS ...
Página 219
... sinc = ✓ sin ( sd ) sin ( s — d ' ) sin d sin d ' If h and h ' represent the angles of altitude ACA ' , BCB ' , the preceding expression will become sin c = = √ - - sin ( c + h — h ' ) sin § ( ċ + h ' − h ) . cos h cos h Or , in ...
... sinc = ✓ sin ( sd ) sin ( s — d ' ) sin d sin d ' If h and h ' represent the angles of altitude ACA ' , BCB ' , the preceding expression will become sin c = = √ - - sin ( c + h — h ' ) sin § ( ċ + h ' − h ) . cos h cos h Or , in ...
Página 221
... sinc . = ( 1 And in like manner cos a = 1- - - 2 sin2a , and cos b = 1 2 sin2 6. Therefore the preceding equa- - tion becomes 1 - 2 sin2 a 4 sin b cos 6 sin c cos c cos a + ( 1-2 sin2 16 ) ( 1 ― 2 sin2 c ) . ja , sin } = } , sản Ęc ...
... sinc . = ( 1 And in like manner cos a = 1- - - 2 sin2a , and cos b = 1 2 sin2 6. Therefore the preceding equa- - tion becomes 1 - 2 sin2 a 4 sin b cos 6 sin c cos c cos a + ( 1-2 sin2 16 ) ( 1 ― 2 sin2 c ) . ja , sin } = } , sản Ęc ...
Página 222
... sinc ) = √ ( L - - y2 ) , equa . 2 will , in this case , reduce to Pow sin A ' sin A = √ ( 1 − §y ) . ( 1 + έy ) ( 4. ) Cor . 3. From the equa . 3 , it appears that the vertical angle of an isosceles spherical triangle , is always ...
... sinc ) = √ ( L - - y2 ) , equa . 2 will , in this case , reduce to Pow sin A ' sin A = √ ( 1 − §y ) . ( 1 + έy ) ( 4. ) Cor . 3. From the equa . 3 , it appears that the vertical angle of an isosceles spherical triangle , is always ...
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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