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" Thus the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides. "
Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous ... - Page 19
by Isaac Todhunter - 1879 - 158 pages
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Elements of Plane and Spherical Trigonometry

Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...therefore, f sin a sin 4 sin A sin 11 sine , . sin a sin b sin c ' ' ' ' * "' Hence, the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides. 21 . Draw CE and DF, respectively perpendicular and parallel to OB; then will the angle DCF = EOC =...
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A Treatise on Plane and Spherical Trigonometry

Robert Woodhouse - Geometrical optics - 1819 - 470 pages
...them, with the corresponding ones in Plane Trigonometry. ķing a proposition) The sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Right-angled spherical triangles may be considered as particular cases of oblique. The solutions...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - Mathematics - 1831 - 656 pages
...three angles of any spherical triangle is always greater than two right angles, but less than six, For, let ABC be a spherical triangle, o the centre of the sphere, and let the chords of the arcs AH, BC, AC, be drawn : these chords constitute a rectilinear triangle,...
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The Nautical Magazine: A Journal of Papers on Subjects Connected ..., Volume 41

Naval art and science - 1872 - 1118 pages
...REJIABKS. 1. The above Rules are directly deduced from the well-known analogy : the Sines of the sides of a spherical triangle are proportional to the Sines of the opposite angles. 2. I call it New, because I do not know of any author who has reduced it to practice as I have...
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The Elements of Plane and Spherical Trigonometry: And Its Application to ...

Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...known parts to determine the rest. SECTION VI. SPHERICAL TRIGONOMETRY. (85.) The sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Let ABC (fig. 22.) be a spherical triangle, 0 the centre of the sphere ; join A 0, BO, CO;...
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Elements of Plane and Spherical Trigonometry: With the First Principles of ...

James Bates Thomson - Plane trigonometry - 1844 - 148 pages
...sin 6 sine Hence, sin a : sin A : : sin 6 : sin B : : sin c : sin C ; that is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Hence, also, by multiplving extremes and means, we get sin A sin 6 = sin B sin a sin A sin...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845 - 542 pages
...To express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides. Let ABC be a spherical triangle, O the centre of the sphere. Let the angles of the triangles be denoted by the large letters A, B, C, and the sides opposite to...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...To express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides. Let ABC be a spherical triangle, O the centre of the sphere. Let the angles of the triangles be denoted by the large letters A, B, C, and the sides opposite to...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...To express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides. Let ABC be a spherical triangle, O the centre of the sphere. Let the angles of the triangles be denoted by the large letters A, B, C, and the sides opposite to...
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Lunar and Time Tables ...

James Gordon (Teacher of Navigation.) - 1849 - 260 pages
...page 42, is evidently deduced from the theorem in Spherical Trigonometry, that the Sines of the sides of a spherical triangle are proportional to the Sines of the opposite angles. From the explanation given at page 42, it appears that the limb of the Sun or Moon assumes...
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