 | Charles Davies - Geometry - 1854 - 436 pages
...ungula whose angle is BOD. PROPOSITION XVIII. THEOREM. Tlte 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... | |
 | Education - 1855 - 1124 pages
...products of their bases by their altitudes. 6. Prove that 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. 163 FEEE ACADEMY. EXAMINATION; PAPERS, JULY, 1354. LEGENDRE... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...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 the great circle DEFGHI, drawn... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Henry Barnard - Military education - 1862 - 410 pages
...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... | |
 | Education - 1862 - 752 pages
...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
...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... | |
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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. 
