| Adrien Marie Legendre - Geometry - 1822 - 367 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 - 584 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 - 92 pages
...and ABC compose the lunary surface ABC A' which is measured by 2 A. Therefore the (890) sum of ABC **and DEF is also measured by 2 A. 87. Theorem. The...Let ABC (fig. 10.) be the given triangle. Produce** А С to form the circum(892) ference ACA'C', also produce AB and B С to form the semicircumferences... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 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 - Geometry - 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 - Conic sections - 1845
...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... | |
| 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... | |
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