 | 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... | |
 | 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... | |
 | Pierce Morton - Geometry - 1830 - 586 pages
...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
...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... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...AB С compose the lunary surface AB С A' which is measured by 2 A. Therefore the(890) sum of AB С and DEF is also measured by 2 A. 87. Theorem. The...Let ABC (fig. 10.) be the given triangle. Produce AC to form the circum(892) ference ACA'C', also produce AB and BU to form the semicircumferences ABA'... | |
 | Adrien Marie Legendre - Geometry - 1836 - 382 pages
...BOD, for 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... | |
 | Benjamin Peirce - Literary Criticism - 1837 - 216 pages
...surface ABCA' which is measured by 2 A. Therefore the sum of ABC and DEF is also measured by 2 A. 468. Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles, or 180°. Demonstration. Let ABC (fig. 190) be the given triangle. Produce... | |
 | Adrien Marie Legendre - Geometry - 1837 - 372 pages
...equivalent to the spherical ungula whose angle is BOD. PROPOSITION XX. THEOREM. The surface of a splierical 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... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...sum of the triangles AOC, BOD is equivalent to the lune OBNDO, whose angle is BOD. PBOPOSITION 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... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...BOD for bases, are together equivalent to the spherical ungula whose angle is BOD. PROPOSITION XXH. 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... | |
| |
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. 
