 | Nathan Scholfield - 1845 - 894 pages
...sum of the triangles AOC, BOD is equivalent to the lune OBNDO, whose angle is BOD. PROPOSITION XXII. 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. Let ABC be the proposed... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...BOD is equal to the lune OBNDO whose angle is BOD. Y PROPOSITION XXXV. THEOREM. The surface of any spherical triangle is measured by the excess of the sum of its three angles above two right angles. Let ABC be the proposed triangle : produce its sides till they meet... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...is equivalent to the lune whose angle is CBE. Therefore, if 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... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...AOC, BOD is equal to the lune OBNDO whose angle is BOD. PROPOSITION XXXV. THEOREM. The surface of any spherical triangle is measured by the excess of the sum of its three angles above two right-angles. Let ABC be the proposed triangle : produce its sides till they meet... | |
 | William Chauvenet - 1852 - 268 pages
...spherical triangle, to compute the area. This problem is solved in geometry, where it is proved that the surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles, by which is meant, that the area is as many times the area of the tri-rectangular... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...triangles AOC, BOD is equal to the lune OBKDO. whose angle is BOD. THEOREM XIX. The surface of any spherical triangle is measured by the excess of the sum of its three angles above two right angles. Let ABC be the proposed triangle : produce its sides till they meet... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...is equivalen-t to the lune whose angle is CBE. Therefore, if 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... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...equal spheres, are to each other as the angles of their rear ective lunes. PROPOSITION XVI. The area of a spherical triangle is measured by the excess of the sum of its angles over two right angles, multiplied by the tri-rectangular .triangle. SPHERICAL GEOMETRY. hence... | |
 | Elias Loomis - Conic sections - 1861 - 244 pages
...equivalent to the lune whose angle is CBE. Therefore, if two great circles, &c. PROPOSITION XX , THEOEEM. 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... | |
 | Henry Barnard - Military education - 1862 - 410 pages
...following enunciations: " A dihedral angle is measured by the plane angle included between its sides;" "The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles," etc.; enunciations which have no meaning in themselves, and from which... | |
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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. 
