Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 12
... latter being also a complement to the same angle . Hence , CB : CH :: DF : DE , and conseq . CB , DECH , DF . But , since as above , CB . EK = BH . CF , and CB . DE = CH . DF , we have , by addition , CB DK · BH 12 Plane Trigonometry .
... latter being also a complement to the same angle . Hence , CB : CH :: DF : DE , and conseq . CB , DECH , DF . But , since as above , CB . EK = BH . CF , and CB . DE = CH . DF , we have , by addition , CB DK · BH 12 Plane Trigonometry .
Página 16
... Hence , if the mean arc AB be one of 60 ° , its cosine CH , will ( prop . 5 ) be equal to CB , and DK — d'K ' ′ DF : consequently DK will in that case equal DF + D'K ' . From this conjointly with the preceding corol- lary result these ...
... Hence , if the mean arc AB be one of 60 ° , its cosine CH , will ( prop . 5 ) be equal to CB , and DK — d'K ' ′ DF : consequently DK will in that case equal DF + D'K ' . From this conjointly with the preceding corol- lary result these ...
Página 20
... G tan DCA :: sin ( BCA + DCA ) : sin ( BCA — DCA ) . Cor . Hence it follows , that the base of a plane tri- angle BCD , is to the difference of its two segments BA , AD , as the sine of the whole angle at 20 Plane Trigonometry .
... G tan DCA :: sin ( BCA + DCA ) : sin ( BCA — DCA ) . Cor . Hence it follows , that the base of a plane tri- angle BCD , is to the difference of its two segments BA , AD , as the sine of the whole angle at 20 Plane Trigonometry .
Página 21
... Hence , in △ ACB , sin C , or sin ( A Also , in △ acв , sin c , or sin ( a - A Da -- B - DA , BA B. + B ) : sin A :: AB : CB . - B ) : sin A :: aB : CB . Therefore , aB : AB :: sin ( AB ) : sin ( A + B ) . Again ( prop . 14 ) CB : CA ...
... Hence , in △ ACB , sin C , or sin ( A Also , in △ acв , sin c , or sin ( a - A Da -- B - DA , BA B. + B ) : sin A :: AB : CB . - B ) : sin A :: aB : CB . Therefore , aB : AB :: sin ( AB ) : sin ( A + B ) . Again ( prop . 14 ) CB : CA ...
Página 27
... . This , being an obtuse angle , its sine is to be found in the table by taking that of its supplement 80 ° 44 ' , which ( chap . i . 19 ) is the same . Hence , Logs . Logs . As sin c 99 ° 16 C 2 Solution of its Three Cases . 27.
... . This , being an obtuse angle , its sine is to be found in the table by taking that of its supplement 80 ° 44 ' , which ( chap . i . 19 ) is the same . Hence , Logs . Logs . As sin c 99 ° 16 C 2 Solution of its Three Cases . 27.
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Términos y frases comunes
altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith