| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...hypothesis, the shortest ; consequently the distance from A to M is less than the distance from A to N, **which is absurd, since the arc AM is greater than...sum of the three sides of a spherical triangle is** lets Hum the circumference of a great circle. Fig. 224. Demonstration. Let ABC (fig. 224) be any spherical... | |
| Robert Woodhouse - Geometrical optics - 1819 - 264 pages
...angle, as AC p *, is less than the two others AC q, pCq; .•• A p is less than Aq +pq. PROP. III. **The sum of the three sides of a spherical triangle is less than the circumference of a great circle** (2тг). Let ACB be the spherical triangle ; then, CB < CD + BD J> by the former Proposition, and AC... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...is itself the shortest distance between its two extremities. PROPOSITION IV. THEOREM. The sum of all **the three sides of a spherical triangle is less than the circumference of a great circle.** Let ABC be any spherical triangle ; produce the sides AB, AC till they meet again in D. The arcs ABD,... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...N to B. But the first way is, by hypolhesis, the shortest; consequently the distance from A to ./If **is less than the distance from A. to JV", which is...is less than the circumference of a great circle.** Fig. 224, Demonstration. Let ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...JVto B. But the first way is, by hypothesis, the shortest ; consequently the distance from A to Mis **less than the distance from A to JV, which is absurd,...is less than the circumference of a great circle,** Fig. 224. Demonstration. Let ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till... | |
| Adrien Marie Legendre - 1825 - 224 pages
...hypothesis, the shortest ; consequently the distance from A to M is less than the distance from A to N, **which is absurd, since the arc AM is greater than...is less than the circumference of a great circle.** Fig. 524. Demonstration. Let ABC (Jig. 224) be any spherical triangle ; produce the sides AB, AC, till... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...distance from Jl to M is less than the distance from A. to JV, which is absurd, since the arc AJ\1 **is greater than AN; whence no point of the shortest...is less than the circumference of a great circle.** Kg. 224. Demonstration. Let ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 317 pages
...difference of any two sides of, a spherical triangle is less than the third side. PROP. XLVII. (129.) **The sum of the three sides of a spherical triangle is less than the circumference of a great circle.** For let any two of the sides a, b, be produced through the third side c until they meet again. The... | |
| Adrien Marie Legendre - Geometry - 1828 - 316 pages
...A to B can lie out of the arc ANB ; hence this arc is itself the shortest distance between its two **extremities. THEOREM. 461. The sum of the three sides of a spherical' triangle is** leas than the circumference of a great circle. Let ABC be any spherical triangle ; produce the sides... | |
| Adrien Marie Legendre - Geometry - 1830 - 316 pages
...A to B can lie out of the arc ANB ; hence this arc is itself the shortest distance between its two **extremities. THEOREM. • 461 . The sum of the three sides of a spherical triangle is less** tha n the circumference of a great circle. Let ABC be any spherical triangle ; produce the sides AB,... | |
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