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 |
Inni boken
Resultat 1-5 av 7
Side 19
... last remainder , and fo on 44 times . 3 ° . To the leffer extreme add the forementioned excess ; and , to the fum , add the first remainder ; to this fum add the next remainder , and fo on continually then the feveral fums thus arifing ...
... last remainder , and fo on 44 times . 3 ° . To the leffer extreme add the forementioned excess ; and , to the fum , add the first remainder ; to this fum add the next remainder , and fo on continually then the feveral fums thus arifing ...
Side 29
... last figure ) , the co - fines of the angles at the bafe will be to each other , directly , as the fines of the vertical angles : For radius : fine BCA :: co - fine CB : co - fine A , fince radius : fine BCD :: co - fine CB : co - fine ...
... last figure ) , the co - fines of the angles at the bafe will be to each other , directly , as the fines of the vertical angles : For radius : fine BCA :: co - fine CB : co - fine A , fince radius : fine BCD :: co - fine CB : co - fine ...
Side 64
... last of these equal quantities , we have DC - AD - 20DXDF ; orDC + ADXDC - AD = 20D × DF ( by 7. 2. ) and therefore 2OD : DC + AÐ : DC - AD : DF ; but ( by Theor . 2. ) as the tang . AOD = ACB ( by 10. 3. ) ; to radius ( : } AD : OD ...
... last of these equal quantities , we have DC - AD - 20DXDF ; orDC + ADXDC - AD = 20D × DF ( by 7. 2. ) and therefore 2OD : DC + AÐ : DC - AD : DF ; but ( by Theor . 2. ) as the tang . AOD = ACB ( by 10. 3. ) ; to radius ( : } AD : OD ...
Side 70
... of an angle ( Q ) ; and as ra- dius : co - tang . Q :: AG : AE . But ( by Theor . 2. ) EF EI co - tang . EFI ( ACD ) : radius ; which proportion being compounded with the last 3 but but one , & c . we fhall have , 70 Properties of.
... of an angle ( Q ) ; and as ra- dius : co - tang . Q :: AG : AE . But ( by Theor . 2. ) EF EI co - tang . EFI ( ACD ) : radius ; which proportion being compounded with the last 3 but but one , & c . we fhall have , 70 Properties of.
Side 72
... last figure . ) 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 ...
... last figure . ) 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 ...
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