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 11
... consequently half the radius . PROP . VI . 6. The tangent of an arc of 45 ° is equal to the radius . Suppose AB in the last figure but one were an arc of 45 ° ; then would ACB be half a right angle , and conse- quently its complement ...
... consequently half the radius . PROP . VI . 6. The tangent of an arc of 45 ° is equal to the radius . Suppose AB in the last figure but one were an arc of 45 ° ; then would ACB be half a right angle , and conse- quently its complement ...
Página 16
... consequently DK will in that case equal DF + D'K ' . From this conjointly with the preceding corol- lary result these two theorems : ( A ) . If the sine of the mean of three equidifferent arcs ( radius being unity ) be multiplied into ...
... consequently DK will in that case equal DF + D'K ' . From this conjointly with the preceding corol- lary result these two theorems : ( A ) . If the sine of the mean of three equidifferent arcs ( radius being unity ) be multiplied into ...
Página 20
... consequently , BD : BI :: de : ik ; that is , tan BCA + tan DCA : tan BCA 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 ...
... consequently , BD : BI :: de : ik ; that is , tan BCA + tan DCA : tan BCA 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 ...
Página 40
... consequently , when radius is unity we have AD = b cos a . In like manner BD a cos B. A There- If one fore , AD + BD = AB = c = a cos B + b cos a . of the angles , as A , were obtuse , the result would , not- withstanding , be the same ...
... consequently , when radius is unity we have AD = b cos a . In like manner BD a cos B. A There- If one fore , AD + BD = AB = c = a cos B + b cos a . of the angles , as A , were obtuse , the result would , not- withstanding , be the same ...
Página 41
... Consequently , a sin в = b sin a , sin A sin B In a similar manner , we may obtain a or = a sin A = and - = с sin c ' b sin B с sin c Or , changing the denomina- tors , the relations of all the six quantities may be thus expressed , sin ...
... Consequently , a sin в = b sin a , sin A sin B In a similar manner , we may obtain a or = a sin A = and - = с sin c ' b sin B с sin c Or , changing the denomina- tors , the relations of all the six quantities may be thus expressed , sin ...
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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