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 13
... co - tan- gent is known . 4. EF : EC ( CD ) :: CD : CH ; whence the co - fecant is known . Hence it appears , 1. That the tangent is a fourth proportional to the co - fine , the fine ... co - tang . Q of Sines , Tangents , and Secants . 13.
... co - tan- gent is known . 4. EF : EC ( CD ) :: CD : CH ; whence the co - fecant is known . Hence it appears , 1. That the tangent is a fourth proportional to the co - fine , the fine ... co - tang . Q of Sines , Tangents , and Secants . 13.
Side 14
... co - tang . Q : tang . Qtang . Pot as co - tang . P : tang . Q : co - tang . Q : tang . P ( by 10. 4. ) PROP . II . If there be three equidifferent arches AB , AC , AD , it will be , as radius is to the co - fine of their common ...
... co - tang . Q : tang . Qtang . Pot as co - tang . P : tang . Q : co - tang . Q : tang . P ( by 10. 4. ) PROP . II . If there be three equidifferent arches AB , AC , AD , it will be , as radius is to the co - fine of their common ...
Side 26
... co - fine of EOF ( or BAC ) :: : tang , AC : tang . AB . 2. E. D. COROLLARY I. Hence it follows , that the fines of the angles of any oblique fpherical triangles ADC are to one another , directly , as the fines of the oppofite fides ...
... co - fine of EOF ( or BAC ) :: : tang , AC : tang . AB . 2. E. D. COROLLARY I. Hence it follows , that the fines of the angles of any oblique fpherical triangles ADC are to one another , directly , as the fines of the oppofite fides ...
Side 27
... tang . DC : tang . AC . THEOREM II . In any right - angled fpherical triangle ( ABC ) it will be , as radius is to the co - fine of one leg fo is the co - fine of the other leg to the co - fine of the by- pothenufe . DEMON- F A ...
... tang . DC : tang . AC . THEOREM II . In any right - angled fpherical triangle ( ABC ) it will be , as radius is to the co - fine of one leg fo is the co - fine of the other leg to the co - fine of the by- pothenufe . DEMON- F A ...
Side 29
... co - fine BC : co - fine A. 2. E. D. COROLLARY . Hence , in right - angled fpherical triangles ABC , CBD , having ... tang . CF tang . FE ( by the latter part of Theor . 1. ) that is , radius : fine AB co - tang . BC : co - tang . A ...
... co - fine BC : co - fine A. 2. E. D. COROLLARY . Hence , in right - angled fpherical triangles ABC , CBD , having ... tang . CF tang . FE ( by the latter part of Theor . 1. ) that is , radius : fine AB co - tang . BC : co - tang . A ...
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