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 10
... cosine of any arc :: twice the sine of that are the sine of double the arc . In the preceding figure CH is the cosine of the arc BN , AB is twice the sine вH of that arc , and BD is the sine of AB the double arc . From the similar ...
... cosine of any arc :: twice the sine of that are the sine of double the arc . In the preceding figure CH is the cosine of the arc BN , AB is twice the sine вH of that arc , and BD is the sine of AB the double arc . From the similar ...
Página 11
... sine , and cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to double the radius . Let AB be an arc of 60 ° , AB its chord , CD its cosine , AD its versed sine , cr its secant . Then , = 1. Since ACB ...
... sine , and cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to double the radius . Let AB be an arc of 60 ° , AB its chord , CD its cosine , AD its versed sine , cr its secant . Then , = 1. Since ACB ...
Página 12
... sine of half any arc or angle is equal to a rectangle under half the radius and the versed sine of the whole ; and ... sines and cosines . Let AB and BD be two unequal arcs , of the circle whose radius is AC ; and let BD ′ = BD . - - B ...
... sine of half any arc or angle is equal to a rectangle under half the radius and the versed sine of the whole ; and ... sines and cosines . Let AB and BD be two unequal arcs , of the circle whose radius is AC ; and let BD ′ = BD . - - B ...
Página 13
... cosine of the sum or the difference of two arcs , is equal to the difference or the sum of the rectangles under their res- pective cosines and sines . Recurring to the same diagram , we have from the similar triangles CBH , CFG , CB ...
... cosine of the sum or the difference of two arcs , is equal to the difference or the sum of the rectangles under their res- pective cosines and sines . Recurring to the same diagram , we have from the similar triangles CBH , CFG , CB ...
Página 15
... sines of two unequal arcs , is to their difference , so is the tangent of half the sum of those two arcs , to the ... cosines of two arcs , is to their difference , as the cotangent of half the sum of those two arcs , is to the cotangent of ...
... sines of two unequal arcs , is to their difference , so is the tangent of half the sum of those two arcs , to the ... cosines of two arcs , is to their difference , as the cotangent of half the sum of those two arcs , is to the cotangent of ...
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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