 | Charles Davies - 1854 - 436 pàgines
...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... | |
 | 1855 - 1124 pàgines
...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 - 1856 - 460 pàgines
...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 - 1858 - 324 pàgines
...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 - 1860 - 472 pàgines
...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... | |
 | Henry Barnard - 1862 - 410 pàgines
...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... | |
 | 1862 - 752 pàgines
...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 - 1862 - 412 pàgines
...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 - 1862 - 518 pàgines
...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 - 1862 - 532 pàgines
...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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... third of the excess of the sum of its three angles above two right angles... 
