| Olinthus Gregory - 1816 - 278 pàgines
...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... | |
| Richard Abbatt - 1841 - 234 pàgines
...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 - 1844 - 146 pàgines
...••••••'••••••••• \ ) 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 - 260 pàgines
...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 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 an elliptical... | |
| James Gordon (teacher of navigation.) - 1849 - 218 pàgines
...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 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 an ellipticnl... | |
| William Somerville Orr - 1854 - 534 pàgines
...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 - 1855 - 121 pàgines
...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 pàgines
...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 are 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... | |
| Isaac Todhunter - 1859 - 156 pàgines
...give an independent proof of this proposition in the following article. 42. The sines of the angles of a spherical triangle are proportional to the sines of the opposite sides. Let ABC be a spherical triangle, O the centre of the sphere. Take any point P in OA, draw PD... | |
| Woolwich roy. military acad - 1861 - 572 pàgines
...MATHEMATICS REV. CANON HEAVISIDE, MA Third Paper. — 11 1 AM to 1| PM 1. Show that the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides. In any spherical triangle, a, b, c being the sides subtending the angles A, B, C respectively,... | |
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