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 4
... difference from a quadrant ; and the complement of an angle is its differ- ence from a right angle . 12. The supplement of an arc is its difference from 4 Plane Trigonometry .
... difference from a quadrant ; and the complement of an angle is its differ- ence from a right angle . 12. The supplement of an arc is its difference from 4 Plane Trigonometry .
Página 5
... difference from a semicircle ; and the supplement of an angle is its differ- ence from two right angles . 13. The sine of an arc is a perpendicular let fall from one extremity upon a diameter passing through the other . 14. The versed ...
... difference from a semicircle ; and the supplement of an angle is its differ- ence from two right angles . 13. The sine of an arc is a perpendicular let fall from one extremity upon a diameter passing through the other . 14. The versed ...
Página 12
... difference of two arcs , is equal to the sum or the difference of the rectangles under their alternate sines and cosines . Let AB and BD be two unequal arcs , of the circle whose radius is AC ; and let BD ′ = BD . - - B Then is AD the ...
... difference of two arcs , is equal to the sum or the difference of the rectangles under their alternate sines and cosines . Let AB and BD be two unequal arcs , of the circle whose radius is AC ; and let BD ′ = BD . - - B Then is AD the ...
Página 13
... 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 : CH :: CF : CG ; whence CB ...
... 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 : CH :: CF : CG ; whence CB ...
Página 14
... difference , be what they may . This might be rendered evident by a suitable modification of the diagram ; and will still farther ap- pear in the fourth chapter of this work . PROP . X. 10. As the difference or sum of the square of the ...
... difference , be what they may . This might be rendered evident by a suitable modification of the diagram ; and will still farther ap- pear in the fourth chapter of this work . PROP . X. 10. As the difference or sum of the square of the ...
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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