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 6
... whence , dividing by CA , there results arc AB less than tangent AT . In a similar way it may be seen that chord AB , is less than arc AB , and sine BD , less than chord AB . The same is also evident from the consideration that a right ...
... whence , dividing by CA , there results arc AB less than tangent AT . In a similar way it may be seen that chord AB , is less than arc AB , and sine BD , less than chord AB . The same is also evident from the consideration that a right ...
Página 10
... whence the proposition is manifest . PROP . IV . E D T B G R 4. The sum of the tangent and secant of any arc , is equal to the tangent of an arc exceeding that by half its complement . Produce AT , the tangent of the assumed arc , till ...
... whence the proposition is manifest . PROP . IV . E D T B G R 4. The sum of the tangent and secant of any arc , is equal to the tangent of an arc exceeding that by half its complement . Produce AT , the tangent of the assumed arc , till ...
Página 12
... Whence AH2 = AC . AD . 2AC . AD . Also , 4CH2 = LB2 AL . LD = 2AC . LD . Whence CM2 AC . LD . PROP . VIII . 8. The rectangle under the radius and the sine of the sum or of the difference of two arcs , is equal to the sum or the ...
... Whence AH2 = AC . AD . 2AC . AD . Also , 4CH2 = LB2 AL . LD = 2AC . LD . Whence CM2 AC . LD . PROP . VIII . 8. The rectangle under the radius and the sine of the sum or of the difference of two arcs , is equal to the sum or the ...
Página 13
... whence CB . CG CH.CF : and the similar triangles CBH , and DEF , give CB : BH :: DF : EF or KG ; whence CB KG = BH . DF . The difference of these rectangles is , CB . CK CH.CF - BH . DF ; which is the first part of the proposition . The ...
... whence CB . CG CH.CF : and the similar triangles CBH , and DEF , give CB : BH :: DF : EF or KG ; whence CB KG = BH . DF . The difference of these rectangles is , CB . CK CH.CF - BH . DF ; which is the first part of the proposition . The ...
Página 14
... whence TC . RH = CA. TR , TC : TA :: TR : TH , whence TC . TH = TA . TR . Each of the last equal rectangles being taken from the square of rc , there will remain , TC2 TC . TH , or TC . ( TC TH ) , or TC.CH = TC2 -TA . TR . Now , ― TC ...
... whence TC . RH = CA. TR , TC : TA :: TR : TH , whence TC . TH = TA . TR . Each of the last equal rectangles being taken from the square of rc , there will remain , TC2 TC . TH , or TC . ( TC TH ) , or TC.CH = TC2 -TA . TR . Now , ― TC ...
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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