| 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... | |
| Robert Woodhouse - Geometrical optics - 1819 - 470 pages
...the manner of deducing 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 of... | |
| Naval art and science - 1872 - 1118 pages
...Time Aiinwt!; Problem. 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 done.... | |
| Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...triangles, from any three 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; also draw... | |
| James Thomson - Geometry, Analytic - 1844 - 146 pages
...••••••'••••••••• \ ) 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 multiplying extremes and means, we get sin A sin 6 = sin B sin a sin A sin c = sin... | |
| James Gordon (teacher of navigation.) - 1849 - 218 pages
...42, are deduced. Rule 3, page 42, is evidently deduced from the theorem in Spherical Trigonometry, that the Sines of the sides of a spherical triangle...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 an ellipticnl... | |
| James Gordon (Teacher of Navigation.) - 1849 - 260 pages
...42, are deduced. Rule 3, page 42, is evidently deduced from the theorem in Spherical Trigonometry, that the Sines of the sides of a spherical triangle...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 an elliptical... | |
| William Somerville Orr - Science - 1854 - 534 pages
...the following treatise. MATHEMATICAL SCIENCES— No. XIII. (1.) To show that the Sines of the Angles of a Spherical Triangle are proportional to the Sines of the opposite sides. Let ABC be the triangle, 0 the centre of the sphere, join OA, OB, 00 ; through A draw a plane... | |
| George Biddell Airy - Trigonometry - 1855 - 121 pages
...complemental triangle is also a right-angled triangle. Fig. 18. SECTION VI. SPHERICAL TRIGONOMETRY. (102.) THE sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Let ABC, (fig. 19), be any spherical triangle : from С draw С D perpendicular on the plane A 0 B,... | |
| Dublin city, univ - 1858 - 264 pages
...of the intersection of tangents to a conic section which cut one another at right angles. 3. Prove that the sines of the sides of a spherical triangle...proportional to the sines of the opposite angles. 3. Find the roots of the equation— x T — X* + x 3 - 1=0. 4. Find the locus of a point from which... | |
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