 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...triangle ABC is equivalent'to (A + B + C — 2) X T. Hence the area of a spherical triangle is equal to the excess of the sum of its three angles above two right angles multiplied by the quadrantal triangle. 564. Cor. If the sum of the three angles of a spherical triangle... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...triangle ABC is equivalent to (A + B + C — 2) X T. Hence the area of a spherical triangle is equal to the excess of the sum of its three angles above two right angles multiplied by the quadrantal triangle. 564. Cor. If the sum of the three angles of a spherical triangle... | |
 | Oliver Byrne - 1863 - 324 pages
...(2) is Girard•s Theorem, and shows that the area of a spherical triangle may be represented by e, the excess of the sum of its three angles above two right angles. e is technically termed the Spherical Excess. 1),A1 + B1+C,-ir=%, (3.) (3) expresses the spherical... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...many spherical triangles as it has sides less two. But the area of each of these triangles is equal to the excess of the sum of its three angles above two right angles multiplied by the quadrantal triangle (Prop. XX.) ; and the sum of the angles in all the triangles... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...Bis obtuse. SURFACE OP THE SFHERICAL TRIANGLE. 191. The surface of a spherical triangle is equal to the excess of the sum of its three angles above two right angles. This excess, which is also called the spherical excess, may be found from the sides, by the aid of... | |
 | Isaac Stone - Educational tests and measurements - 1869 - 272 pages
...right angles, and greater than two." P. XIV. B. IX. 4. "The surface of a spherical triangle is equal to the excess of the sum of its three angles above two right angles multiplied by the tri-rectaugular triangle. P. XVIII. B. IX. Many other questions and Propositions... | |
 | Harvard University - 1873 - 732 pages
...what is the ratio of the volume above to that below the cutting plane ? 9. Prove that the surface of a spherical triangle is measured by the excess of the sum of its angles over 180°. 10. The slant height of a right cone is 3 ; the radius of the base is j. Show that... | |
 | Harvard University - 1876 - 554 pages
...with respect to each other, they are also equilateral with respect to each other. 6. The surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles. Prove. 7. Given that the area of the surface, generated by a straight line revolving... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...lune whose angle is CBE. Therefore, if two great circles, etc. PROPOSITION XX. THEOREM. The area of a spherical triangle is measured by the excess of the sum of its angles above two right angles multiplied by the tri-vectangular triangle. Let ABC be any spherical... | |
 | Robert Fowler Leighton - 1880 - 428 pages
...six and eight feet. Give the ratio of their surfaces, and also of their volumes. 5. The surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles. ANALYTIC GEOMETKY. 1. PEOVE the formula for the tangent of the angle between... | |
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THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle. 
