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 pages |
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Page 10
... leg IAC and BC the angles The hyp . The an- gles 2 AC and one legBC The hyp . The other 3 AC and leg AB one legBC Solution . As radius is to the fine of A , fo is the hyp . AC to the leg BC ( by Theor . I. ) As AC : BC :: radius : fin ...
... leg IAC and BC the angles The hyp . The an- gles 2 AC and one legBC The hyp . The other 3 AC and leg AB one legBC Solution . As radius is to the fine of A , fo is the hyp . AC to the leg BC ( by Theor . I. ) As AC : BC :: radius : fin ...
Page 27
... BC } by the For let BC be perpendicular to AD ; then radius : fine A :: fine AC : fine BC s finceradius : fine D ... leg BC common , the tangents of the hypothenuses are to each other , inversely , as the co - fines of the adjacent ...
... BC } by the For let BC be perpendicular to AD ; then radius : fine A :: fine AC : fine BC s finceradius : fine D ... leg BC common , the tangents of the hypothenuses are to each other , inversely , as the co - fines of the adjacent ...
Page 28
... BC :: co - fin . AB : co - fineAC , fincerad : co - fin . BC :: co - fin . DB : co - fine DC , therefore , by ... leg to the co - fine of the oppofite angle . DEMON- C at 0- ve ar eir to as C , 28 Spherical Trigonometry .
... BC :: co - fin . AB : co - fineAC , fincerad : co - fin . BC :: co - fin . DB : co - fine DC , therefore , by ... leg to the co - fine of the oppofite angle . DEMON- C at 0- ve ar eir to as C , 28 Spherical Trigonometry .
Page 34
... leg BC The hyp . 2 AC and one angle A The adja- cent leg AB The hyp . 3 AC and one angle A The hyp . The other The other angle C 4AC and one leg BC leg AB As radius : co - ine of A : tang . AC ; tang . AB ( by the latter part of Thear ...
... leg BC The hyp . 2 AC and one angle A The adja- cent leg AB The hyp . 3 AC and one angle A The hyp . The other The other angle C 4AC and one leg BC leg AB As radius : co - ine of A : tang . AC ; tang . AB ( by the latter part of Thear ...
Page 35
... leg The other BC and the leg AB As tang . A : tang . BC :: ra- dius : fine AB ( by Theor . 4. ) 10 oppofite angle A One leg The adja- As co - fine BC radius :: BC and the cent angle II oppofite C co - fine of A Theor . 3. ) fine C ( by ...
... leg The other BC and the leg AB As tang . A : tang . BC :: ra- dius : fine AB ( by Theor . 4. ) 10 oppofite angle A One leg The adja- As co - fine BC radius :: BC and the cent angle II oppofite C co - fine of A Theor . 3. ) fine C ( by ...
Common terms and phrases
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