Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S.F. Wingrave, successor to Mr. Nourse, 1799 - 79 sider |
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Side 32
... Since co - fine AC : co - fine BC :: co - fine AD : co - fine BD ( by Cor . to Theor . 2. ) there- fore , by compofition and divifion , co - fine AC + co - fine BC : co - fine AC AD + co - fine BD : co- fine AD co - fine BD , But ( by ...
... Since co - fine AC : co - fine BC :: co - fine AD : co - fine BD ( by Cor . to Theor . 2. ) there- fore , by compofition and divifion , co - fine AC + co - fine BC : co - fine AC AD + co - fine BD : co- fine AD co - fine BD , But ( by ...
Side 61
... Since CD = CB , therefore is the angle A B A EF D DBC ( by 12. 1. ) and , confequently , half- the vertical angle ACB = = D. D + CBD ( by 9. 1. ) Moreover , feeing DCB is the fum of the angles A and CBA , at the bafe ( by 9. 1. ) it is ...
... Since CD = CB , therefore is the angle A B A EF D DBC ( by 12. 1. ) and , confequently , half- the vertical angle ACB = = D. D + CBD ( by 9. 1. ) Moreover , feeing DCB is the fum of the angles A and CBA , at the bafe ( by 9. 1. ) it is ...
Side 65
... Since the diameter HG is perpendicular to AB , therefore is AE = BE ( by 2. 3. ) AH BH , and the angle ACH BCH ( by 12. 3. ) ; whence , alfo , CD Cd , and HD Hd ( by 15. 1. ) Therefore , the right - angled triangles HAD and HBd , having ...
... Since the diameter HG is perpendicular to AB , therefore is AE = BE ( by 2. 3. ) AH BH , and the angle ACH BCH ( by 12. 3. ) ; whence , alfo , CD Cd , and HD Hd ( by 15. 1. ) Therefore , the right - angled triangles HAD and HBd , having ...
Side 72
... Since rad .: co - fine BC :: co - fine AB : co - fine AC ( by Theor . 2. ) , it will be ( by comp . and div . ) radius + co - fine BC : rad . - co - f . BC :: co - f . AB + co - f AC : co - f . AB - co - f . AC . But the radius may be ...
... Since rad .: co - fine BC :: co - fine AB : co - fine AC ( by Theor . 2. ) , it will be ( by comp . and div . ) radius + co - fine BC : rad . - co - f . BC :: co - f . AB + co - f AC : co - f . AB - co - f . AC . But the radius may be ...
Vanlige uttrykk og setninger
5th rem AB by Theor AC by Theor AC-BC AC+BC adjacent angle alfo alfo known alfo let alſo arch bafe baſe becauſe bifecting cafe chord circle co-f co-fecant co-fine AC co-tangent of half common logarithm confequently COROL COROLLARY diameter dius equal to half excefs fame fecant fecond feries fhall fides AC fince fines firft firſt fpherical triangle ABC fquare fubtracted fupplement fuppofed garithms gles great-circles half the difference half the fum half the vertical Hence hyperbolic logarithm hypothenufe interfect laft leffer leg BC likewife LUKE HANSARD moreover oppofite angle pendicular perpendicular plane triangle ABC progreffion PROP propofed proportion radius reafon refpectively right-angled spherical triangle right-line ſhall ſphere tang tangent of half THEOREM theſe thofe Trigonometry verfed vertical angle whence whofe