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 16
Side 13
... tangent is known . 2. CF : CE ( CA ) :: CA : CT ; whence the fecant is known . 3. EF CF : CD : DH ... half a right angle is equal to the ra- dius ; and that the co - tangents of ... co - tang . Q of Sines , Tangents , and Secants . 13.
... tangent is known . 2. CF : CE ( CA ) :: CA : CT ; whence the fecant is known . 3. EF CF : CD : DH ... half a right angle is equal to the ra- dius ; and that the co - tangents of ... co - tang . Q of Sines , Tangents , and Secants . 13.
Side 30
... co- tang . A. Q. E. D. LEMMA . As the fum of the fines of two unequal arches is to their difference , fo is the tangent of half the fum of thofe arches to the tangent of half their difference : and , as the fum of the co - fines is to ...
... co- tang . A. Q. E. D. LEMMA . As the fum of the fines of two unequal arches is to their difference , fo is the tangent of half the fum of thofe arches to the tangent of half their difference : and , as the fum of the co - fines is to ...
Side 31
... half the dif- ference , and AD O L D B H F GA half the fum , of AB and AC ... tangent of AD ) : DL ( the tangent of DC , by 20. 4. ) And 2OF ( OG + OH ) : 2HF ( OG - OH ) : : EI : EC :: DK ( the ... co - fine BC :: Spherical Trigonometry . 31.
... half the dif- ference , and AD O L D B H F GA half the fum , of AB and AC ... tangent of AD ) : DL ( the tangent of DC , by 20. 4. ) And 2OF ( OG + OH ) : 2HF ( OG - OH ) : : EI : EC :: DK ( the ... co - fine BC :: Spherical Trigonometry . 31.
Side 32
... co - fine BC :: co - fine ― Since co - fine AC : co - fine BC :: co - fine AD : co - fine BD ( by Cor . to Theor . 2 ... tangent of half the bafe , is to the tangent of half the fum of the fides , as the tangent of half the difference of the ...
... co - fine BC :: co - fine ― Since co - fine AC : co - fine BC :: co - fine AD : co - fine BD ( by Cor . to Theor . 2 ... tangent of half the bafe , is to the tangent of half the fum of the fides , as the tangent of half the difference of the ...
Side 33
... tangent of the distance of the perpendicular from the middle of the bafe . THEOREM VII . In any spherical triangle ABC , it will be , as the co - tangent of half the fum of the angles at the bafe , is to the tangent of half their ...
... tangent of the distance of the perpendicular from the middle of the bafe . THEOREM VII . In any spherical triangle ABC , it will be , as the co - tangent of half the fum of the angles at the bafe , is to the tangent of half their ...
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