 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...second place, every spherical triangle is equivalent to a lunary surface whose angle is equal to half of the excess of the sum of its three angles over two right angles (503). Let P, Q, R, be the arcs of a great circle which measure the three angles of a spherical triangle... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...equivalent to the spherical ungula whose angle is BOD. PROPOSITION XXIII. 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 the great... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...second place, every spherical triangle is equivalent to a lunary surface whose angle is equal to half of the excess of the sum of its three angles over two right angles (503). Let P, Q, R, be the arcs of a great circle which measure the three angles of a spherical triangle... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...second place, every spherical triangle is equivalent to a lunary surface whose angle is equal to half of the excess of the sum of its three angles over two right angles (503). Let P, Q, R, be the arcs of a great circle which measure the three angles of a spherical triangle... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...AOC, BOD for bases, are together equivalent to the spherical ungula whose angle is BOD. THEOREM. 501. The surface of a 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... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...will be represented by half 2 A+ 2B + 2C-4R, that is, byA+B + C2 R. And hence, it is commonly said, that the surface of a spherical triangle is measured by the excess of the sum of ils angles above two right angles ; it being understood that the surface of the sphere is measured... | |
 | Mathematics - 1835 - 684 pages
...will be represented by half 2 Á+ 2B+2C-4R, that is, by A + B + C2 R. And hence, it is commonly said, that the surface of a spherical triangle is measured by the excess of the sum of its angles above two right angles ; it being understood that the surface of the sphere is measured by eight... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...bases, are together equivalent to the spherical ungula whose angle is BOD. PROPOSITION XX. 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 triangle... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...which is measured by 2 A. Therefore the(890) sum of AB С and DEF is also measured by 2 A. 87. Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three (891) angles over two right angles or 180°. Demonstration. Let ABC (fig. 10.) be the given triangle.... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...which is measured by 2 A. Therefore the (890) sum of ABC and DEF is also measured by 2 A. 87. Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three (891) angles over two right angles or 180°. Demonstration. Let ABC (fig. 10.) be the given triangle.... | |
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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. 
