 | Robert Woodhouse - 1819 - 470 pàgines
...the manner of deducing them, with the corresponding ones in Plane Trigonometry. íing 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.... | |
 | Charles Davies - 1830 - 318 pàgines
...into the calculations of the sides and angles of plane triangles. THEOREM. 43. The sides of a plane triangle are proportional to the sines of their opposite angles. Let ABC (PI. I. Fig. 2) be a triangle ; then, CB : CA : : sin. A : sin. B. For, with A as a centre, and AP,... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | George Salmon - 1862 - 494 pàgines
...-^—, . sin a> ' and P : P : : sin a> : sin w', an equation analogous to that which expresses that the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles; since P and P in the rectification of arcs on the ellipsoid answer to sin/a, sinp'... | |
 | George Salmon - 1862 - 490 pàgines
...= . . . sin o> ' and P : P : : sin co : sin co', an equation analogous to that which expresses that the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles; since P and P in the rectification of arcs on the ellipsoid answer to sinp, sin//... | |
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That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. 
