| 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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