 | George Roberts Perkins - Geometry - 1856 - 460 pages
...and the sum of the triangles AOC, BOD is equal to the lune OBKDO. whose angle is BOD. THEOREM XIX. The surface of any spherical triangle is measured...produce its sides till they meet the great circle DEFGHI, drawn anywhere without the triangle. By the last proposition, the two triangles ADE, AGH are... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...whose angle is BOD. . / • PROPOSITION XVIII. THEOREM. 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•rectangular triangle. Let ABC be any spherical triangle : then will its surface... | |
 | John Hymers - Logarithms - 1858 - 324 pages
...180°. 14. The area of a spherical triangle is the same fraction of the area of a hemisphere, that the excess of the sum of its three angles above two right angles is of 360°. Let ABC (fig. 5) be a spherical triangle ; produce the arcs which contain its angles till... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...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 - 1860 - 472 pages
...the lune OBNDO. whose angle is BOD. THEOREM XIX. The surface of any spherical triangle is measured by excess of the sum of its three angles above two right...angles. Let ABC be the proposed triangle : produce ite sides till they meet the great circle DEFGHI, drawn anywhere without the triangle. By the last... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...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... | |
 | Education - 1862 - 752 pages
...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 every trace of homogeneity has... | |
 | Henry Barnard - Military education - 1862 - 410 pages
...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 every trace of homogeneity has... | |
 | Henry Barnard - Military education - 1862 - 412 pages
...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 every trace of homogeneity has... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...whose angle is DA E. PROPOSITION XX. — THEOREM. 563. 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 quadranlal triangle. Let А В С be a spherical triangle ; its area is equal to... | |
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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. 
