 | Royal Irish Academy - Science - 1847 - 678 pages
...surface of an ellipsoid, of the fundamental property of plane and spherical triangles, that the sides (or the sines of the sides) are proportional to the sines of the opposite angles. 4. Let w be a right angle, and the corresponding geodetic vector will pass through... | |
 | William Chauvenet - 1852 - 268 pages
...deduce our fundamental formulae from a direct consideration of the solid angle itself. 3. In a spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let A В о, Fig. 1, be a spherical triangle, O the center of the sphere. The angles... | |
 | Elias Loomis - Trigonometry - 1855 - 192 pages
...17'29". ( B =96° 13' 23". OBLIQUE-ANGLED SPHERICAL TRIANGLES. THEOREM III. (215.) In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. In the case of right-angled spherical triangles, this proposition has already been... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...17' 29". ( B -96° 13' 23 OBLIQUE-ANGLED SPHERICAL TRIANGLES. THEOREM III. (215.) In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. In the case of right-angled spherical triangles, this proposition has already been... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...8h. 35m. 5.8s. RELATIONS BETWEEN THE SIDES AND ANGLES OF SPHERICAL TRIANGLES. 148. In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let А В С be any spherical triangle ; А, Д and С the angles opposite to its... | |
 | William Thomas Read - 1862 - 144 pages
...or two angles and an opposite side. This case depends on the following proposition. In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. In the right-angled triangle ABC, sin AB = sin AC . sin C, and sin BC = sin AC . sin... | |
 | Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1873 - 352 pages
...the ten working equations used in solving the various cases. 8. In any spherical triangle show that the sines of the sides are proportional to the sines of the angles opposite them. 9. In a quadrantal spherical triangle given the qaudrantal side and two other... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 218 pages
...Plane Trig. CHAPTEE II. FIG. 3. THE SPHERICAL TRIANGLE IN GENERAL. § 17. Theorem. In every spherical triangle the sines of the sides are proportional to the sines of the opposite ingles. Through c (Pig. 3) draw the great circle mcp perpendicular to c ; applying [2] to... | |
 | Henry Nathan Wheeler - Plane trigonometry - 1878 - 198 pages
...Plane Trig. CHAPTER II. FIG. 3. THE SPHERICAL TRIANGLE IN GENERAL. § 17. Theorem. In every spherical triangle the sines of the sides are proportional to the sines of the opposite angles. Through c (Fig. 3) draw the great circle arep perpendicular to c ; applying [2] to... | |
 | James Edward Oliver - Trigonometry - 1881 - 120 pages
...SPHEBICAL TRIAJSTGLES. § 3. GENERAL PROPERTIES OF SPHERICAL TRIANGLES. Тнм. 2. In any spherical triangle the sines of the sides are proportional to the sines of the opposite angles. \c Let ABC be any spherical triangle ; then will : 156] sin a : sin& = sin А : sinB... | |
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The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C... 
