 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...: cos. ABC : sin. BCA. PROP. XXIV. In spherical triangles, whether right cngled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them. of the right angle at A), as the sine of the side AC to the sine of the angle... | |
 | 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 the vertex of the... | |
 | John William Colenso (bp. of Natal.) - 1851 - 148 pages
...TRIGONOMETRICAL PROPERTIES OF TRIANGLES, QUADRILATERALS, AND POLYGONS. 105. To shew that in any triangle the sides are proportional to the sines of the opposite angles. In future we shall use the letters a, J, c, to denote the sides BC, AC, AB, opposite to the angles A,... | |
 | William Chauvenet - 1852 - 268 pages
...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 of the triangle... | |
 | Elias Loomis - Trigonometry - 1855 - 192 pages
...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 demonstrated. Let,... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...( 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 demonstrated. Let,... | |
 | William Thomas Read - 1862 - 144 pages
...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 A. " Therefore, sin... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...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 sides a, b, and c,... | |
 | Sir Norman Lockyer - Astronomy - 1871 - 464 pages
...horizon. The angle osc is the parallax of the star s. It is one of the properties of triangles that the sides are proportional to the sines of the opposite angles : in the triangle esc, for instance, we have Sin. esc : sin. t os :: oc : ts. 544. The angle osc is the... | |
 | 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... | |
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In spherical triangles, the sines of the sides are proportional to the sines of the opposite angles. In... 
