Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1765 - 79 σελίδες |
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Σελίδα 4
... ference from 180 ° ( or a femicircle ) its fupple- ment . 5. A chord , or fubtenfe , is a right - line drawn from one extremity of an arch to the other : thus the right line BE is the chord , or fubtense , of the arch BAE or BDE . 3 6 ...
... ference from 180 ° ( or a femicircle ) its fupple- ment . 5. A chord , or fubtenfe , is a right - line drawn from one extremity of an arch to the other : thus the right line BE is the chord , or fubtense , of the arch BAE or BDE . 3 6 ...
Σελίδα 31
... ference , and AD L B HF GA PQ half the fum , of AB and AC : let the radii OD and OC be drawn , and also the chord CB , meeting OE in E and OA ( produced ) in P ; draw ES paral- lel to AO , meeting CH in S , and EF and OK per- pendicular ...
... ference , and AD L B HF GA PQ half the fum , of AB and AC : let the radii OD and OC be drawn , and also the chord CB , meeting OE in E and OA ( produced ) in P ; draw ES paral- lel to AO , meeting CH in S , and EF and OK per- pendicular ...
Σελίδα 58
... . IV . As the fum of the tangents of any two angles BAC , BAD , is to their difference , fo is the fine of the fum of thofe angles , to the fine of their dif- ference . Let . Let BC . and BD be the two pro- 58 Properties of.
... . IV . As the fum of the tangents of any two angles BAC , BAD , is to their difference , fo is the fine of the fum of thofe angles , to the fine of their dif- ference . Let . Let BC . and BD be the two pro- 58 Properties of.
Σελίδα 62
... ference of the fame angles . But ( by Theor . 3. ) AB : AD ( AC — BC ) :: fine D ( co - fine DCE , or C ) : fine ABD . 2. E. D .. PROP . IX . As the difference of the two fides AC , BC , of a plane triangle , is to the difference of the ...
... ference of the fame angles . But ( by Theor . 3. ) AB : AD ( AC — BC ) :: fine D ( co - fine DCE , or C ) : fine ABD . 2. E. D .. PROP . IX . As the difference of the two fides AC , BC , of a plane triangle , is to the difference of the ...
Σελίδα 73
... fo is the co - fine of the dif- ference of the angles at the hypothenufe , to the fine of the excess of their fum above a right - angle . COROL COROLLAR Y. Hence , if the angles be fuppofed equal Spherical Triangles . 73.
... fo is the co - fine of the dif- ference of the angles at the hypothenufe , to the fine of the excess of their fum above a right - angle . COROL COROLLAR Y. Hence , if the angles be fuppofed equal Spherical Triangles . 73.
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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