 | Thomas Leybourn - Mathematics - 1830 - 630 pages
...\a sin ¿6 sin \c sin ^d hence the diagonal б is given in terms of а, Ъ, с, and d. Again, since the area of a spherical triangle is proportional to the excess of the sum of its three angles above two right angles, technically termed the spherical excess, which (spherical excess)... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...respectively equal to the three angles of the triangle . . t 195 (с) Every spherical triangle is measured by the excess of the sum of its angles above two right angles . cor. 196 (¿0 A spherical triangle, whose angles are A, I!, and C, is equal to a lunc whose angle... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...an ellipse is equal to the sum of the squares of the two semiaxes. 12. The area of a spherical ^*V is proportional to the excess of the sum of its angles above two right angles. 13. In any lever, the two forces required to keep it at rest, are inversely as the perpendiculars from... | |
 | Mathematics - 1835 - 684 pages
...respectively equal to the three angles of the triangle . . . . 195 (e) Every spherical triangle is measured by the excess of the sum of its angles above two right angles . cor. 196 (d) A spherical triangle, whose angles are A, B, and C, is equal to a lune whose angle is... | |
 | James Thomson - Geometry, Analytic - 1844 - 146 pages
...180° : A+B + C— 180° :: wr" : area of ABC; and it appears, therefore, that (in the same sphere) the area of a spherical triangle is proportional to...excess of the sum of its angles above two right angles, or to what is called its SPHERICAL EXCESS.* It is also plain, that, when the spherical excess or the... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...triangle ADE, and, therefore, of -the same surface. QED PROP. xvii. The measure of a spherical triangle is the excess of the sum of its angles above two right angles. Let ABC be a spherical triangle ; its measure will be A + B + G-2.* For (by the last two propositions),... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...two great circles, &c. PROPOSITION XX. THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its angles above two right angles, multiplied by the quadrantal triangle. Let ABC be any spherical triangle ; its •urface is measured... | |
 | 1851 - 716 pages
...right angles ; likewise the sum of the three sides is less than the entire circumference or 360°. The area of a spherical triangle is proportional to the excess of the sum of its angles over two right angles (called the spherical excess). A spherical triangle, def, is called the polar... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...right angles ; likewise the sum of the three sides is less than the entire circumference or 360°. The area of a spherical triangle is proportional to the excess of the sum of its angles over two right angles (called the spherical excess). A spherical triangle, de.f, is called the polar... | |
 | William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...and x" - 1 = 0 have no common root but unity. 2. Shew that the area of a spherical triangle varies as the excess of the sum of its angles above two right angles ; and prove Llhuillier's theorem, ss - as - b ten = an tan EI/ T = vv 2 ~ 3. If straight lines, represented... | |
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The area of a spherical triangle is proportional to the excess of the sum of its angles over two right angles (called the spherical excess). 
