 | Thomas Keith - Navigation - 1810 - 478 pages
...Consequently ( / A + s_ B + / c) - 1 80° : 1 80° : : m : $ surface of the sphere. QED (Z) COROLLARY. The measure of the surface of a spherical triangle...the sum of its three angles and two right angles. For if s=r^ of the surface of the sphere, 180°x wi=sx (A + B+C- 180°). SX(A + B4 c-180") S But the... | |
 | John Bonnycastle - Trigonometry - 1818 - 488 pages
...of the sphere = c d. PROBLEM 11. ; The area, or surface, of any spherical triangle, ABC, is equal to the difference between the sum of its three angles and two right angles, multiplied by the radius of the sphere. B< 409 For having completed the great circle AB ab A, produce... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...rvith the radius of the sphere, being proposed, if each of Us angles be diminieked by a third part of the difference between the sum of its three angles and two right angles, the angles so diminished may be taken as the angles of a rectilineal triangle, whose sides are equal... | |
 | Thomas Keith - Navigation - 1826 - 504 pages
...Consequently (LA + L в + Le)— 180° : 1 80° "от : ± surface of the sphere, g. ED (K) COROLLARY. The measure of the surface of a spherical triangle...the sum of its three angles and two right angles. For if s =-J- of the surface of the sphere, 180°xm=s X(A + B + C— 180°). SX(A + B + C-180°) S... | |
 | University of Cambridge - 1831 - 552 pages
...points of a parabola, and find what the equation becomes when the points are supposed to coincide. 19. The measure of the surface of a spherical triangle...the sum of its three angles and two right angles. 20. Having given two sides and the included angle of a spherical triangle, obtain the third side in... | |
 | Sir Richard Phillips - Encyclopedias and dictionaries - 1832 - 450 pages
...product of the diameterand circumference divided by 4. To ñnd the area of a spherical triangle, multiply the difference between the sum of its three angles and two right angles by the radius of the sphere. To find- the area of the segment of a parabola, multiply the base by the... | |
 | Mathematics - 1836 - 366 pages
...between the chords of those two sides. 30. The measure of the surface of a spherical triangle is the 1831 difference between the sum of its three angles and two right angles. 31. Having given two sides and the included angle of a spherical triangle, obtain the third side in... | |
 | Thomas Keith - 1839 - 498 pages
...the sphere : m .: LA + LB + L c — 180° : 180° : : m : ± surf, of the sphere. (642) COROLLARY. The measure of the surface of a spherical triangle...the sum of its three angles and two right angles. For if si= | of the surface of the sphere, 180°xm=sx (A + B + C — 180°) But the whole surface of... | |
 | John Gregory - 1842 - 328 pages
...to two right angles, as the area of the triangle is to one-fourth of the surface of the sphere. 3. The measure of the surface of a spherical triangle,...the sum of its three angles and two right angles. ( A+B+ C) - 180°=surface. The measure of the spherical angle contained between any two arcs of a great... | |
 | James Hann - Spherical trigonometry - 1849 - 82 pages
...hut S = area of 4 great Hall's Diff. Gal., page 370. 2 = 49T when radius is unity, о or - = 4 = 180. The measure of the surface of a spherical triangle...three angles and two right angles. Let the triangle be AB С, a, b, c, representing the magnitudes of the angles at A, B, С; let P=surface BСrreB, Q=mСnm,... | |
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The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles. 
