...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....

...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,...

...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...

...••••••'••••••••• \ ) 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...

...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...

...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...

...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...

...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...

...= . . . 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//...

...-^—, . 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'...