Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1765 - 79 Seiten |
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Seite 13
... co - fine and radius . 3. That the co - tangent is a fourth - proportional to the fine , co - fine , and radius . 4. And that the co - fecant is a third - proportional to the fine and radius . 5. It appears moreover ( because AT : AC :: CD ...
... co - fine and radius . 3. That the co - tangent is a fourth - proportional to the fine , co - fine , and radius . 4. And that the co - fecant is a third - proportional to the fine and radius . 5. It appears moreover ( because AT : AC :: CD ...
Seite 14
... co - tang . Q : tang . P ( by ro . 4. ) PROP . II . H If there be three equidifferent arches AB , AC , AD , it will be , as radius is to the co - fine of their common difference BC , or CD , fo is the fine CF , of the mean , to half the ...
... co - tang . Q : tang . P ( by ro . 4. ) PROP . II . H If there be three equidifferent arches AB , AC , AD , it will be , as radius is to the co - fine of their common difference BC , or CD , fo is the fine CF , of the mean , to half the ...
Seite 15
... AC be fuppofed that of 60 ° ; then OF being the co - fine of 60 ° , = fine 30 ° chord of 60 ° O , it is manifeft that DG - BE will , in this cafe , be barely Dm ; and confequently DG = Dm + BE . From whence , and the preceding corollary ...
... AC be fuppofed that of 60 ° ; then OF being the co - fine of 60 ° , = fine 30 ° chord of 60 ° O , it is manifeft that DG - BE will , in this cafe , be barely Dm ; and confequently DG = Dm + BE . From whence , and the preceding corollary ...
Seite 25
... AC , CF of BC , BD A ( or the angle F ) of AB E D B and EF of ED ( or the angle A ) . THEOREM I. In any right - angled Spherical triangle it will be , as radius is to the fine ... co - fine of the angle at the bafe , fo is the tangent of the ...
... AC , CF of BC , BD A ( or the angle F ) of AB E D B and EF of ED ( or the angle A ) . THEOREM I. In any right - angled Spherical triangle it will be , as radius is to the fine ... co - fine of the angle at the bafe , fo is the tangent of the ...
Seite 26
... AC the hypothenufe , and BAC ( or DAE DE DOE ) the angle at the base : moreover , let CG be the fine of the hypo ... co - fine of EOF ( or BAC ) :: tang . AC tang . AB . Q , E. D. COROLLARY I. Hence it follows , that the fines of the ...
... AC the hypothenufe , and BAC ( or DAE DE DOE ) the angle at the base : moreover , let CG be the fine of the hypo ... co - fine of EOF ( or BAC ) :: tang . AC tang . AB . Q , E. D. COROLLARY I. Hence it follows , that the fines of the ...
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4th rem AC by Theor AC-BC adjacent angle AF-co-f alfo known alſo arch bafe baſe becauſe bifecting cafe chord circle co-fecant co-fine AC co-fine BC co-fine co-tangent of half common logarithm confequently COROL COROLLARY diameter dius E. D. PROP equal to half excefs faid fame fecant fecond feries fhall fides AC fince fines firft firſt fquare fubtracted fuppofed garithms given gles great-circles half the difference half the fum half the vertical Hence hyperbolic logarithm hypothenufe interfect itſelf laft leffer leg BC likewife manifeft meaſure moreover oppofite angle pendicular perpendicular plane triangle ABC progreffion propofed propofition proportion radius rectangle reſpectively right-angled Spherical triangle right-line ſhall spherical triangle ABC tang tangent of half THEOREM theſe thofe thoſe Trigonometry verfed vertical angle whence whofe