...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...

...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. The solutions of...

...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....

...angle. When R = 1, this becomes simply b = c sin I! — c cosA. PROP. II. THEOR. THE sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be any triangle; a : b : : sinA : sin 15 ; a : c : : sin A : sinC ; and b : c : : sin I! : sinC. Draw...

...••••••'••••••••• \ ) 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...

...angle. When R=l, this becomes simply 6 = c sin B = c cos A. PROP. II. THEOR. — The sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be any triangle; then a : 6 : : sin A : sin B; a : c :: sin A : sin C ; and 6 : c : : smB : sin C....

...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...

...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...

...letters A, B, C, and the sides respectively opposite to them by the letters a, b, c. 52. The sides of any triangle are proportional to the sines of the opposite angles. Let ABC be the triangle ; from C draw CD perpendicular to AB or AB produced. In the first figure, A and B are...

...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...