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
... rectangle under half the radius and the versed sine of the whole ; and the square of its cosine , equal to a rectangle under half the radius and the versed sine of the supplement of the whole arc or angle . This will be at once obvious ...
... rectangle under half the radius and the versed sine of the whole ; and the square of its cosine , equal to a rectangle under half the radius and the versed sine of the supplement of the whole arc or angle . This will be at once obvious ...
Página 13
... rectangles may , therefore , be expressed thus , CB . E'K ' BH . CF , and CB . D'E ′ = CH . DF , of which the ... rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the difference or ...
... rectangles may , therefore , be expressed thus , CB . E'K ' BH . CF , and CB . D'E ′ = CH . DF , of which the ... rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the difference or ...
Página 14
... rectangle under the tangents of two arcs , is to the square of the radius ; so is the sum or differ- ence of their ... rectangles being taken from the square of rc , there will remain , TC2 TC . TH , or TC . ( TC TH ) , or TC.CH = TC2 ...
... rectangle under the tangents of two arcs , is to the square of the radius ; so is the sum or differ- ence of their ... rectangles being taken from the square of rc , there will remain , TC2 TC . TH , or TC . ( TC TH ) , or TC.CH = TC2 ...
Página 19
... rectangle under GB , and BD E BF , is equal to the rectangle under AB and BE . Conse- quently ( Euc . vi . 16 ) ab : GB :: BF : BE ; which agrees with the proposition . PROP . XVII . 17. In any plane triangle it will be , as twice the ...
... rectangle under GB , and BD E BF , is equal to the rectangle under AB and BE . Conse- quently ( Euc . vi . 16 ) ab : GB :: BF : BE ; which agrees with the proposition . PROP . XVII . 17. In any plane triangle it will be , as twice the ...
Página 20
... rectangle BC . CA , is to twice the rectangle BC . CD , that is , to the difference of the sum of the squares of AC , BC , and the square of AB , as CA to CD ; that is , ( prop . 13 ) as radius to the sine of CAD , or , as radius to the ...
... rectangle BC . CA , is to twice the rectangle BC . CD , that is , to the difference of the sum of the squares of AC , BC , and the square of AB , as CA to CD ; that is , ( prop . 13 ) as radius to the sine of CAD , or , as radius to the ...
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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