| Daniel Cresswell - Geometry - 1816 - 338 pages
...(75.) COR. In the same manner, it may be shewn, that the aggregate of the sides of a spherical polygon, **is less than the circumference of a great circle of the sphere,** if the polygon be bounded by arches of great circles, each of which is less than the semi-circumference... | |
| Robert Woodhouse - Geometrical optics - 1819 - 470 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 - 394 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 - 276 pages
...therefore this line is itself the shortest that can be drawn between its extremities. THEOREM. 461 . **The ,sum of the three sides of a spherical triangle...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, John Farrar - Geometry - 1825 - 280 pages
...therefore this line is itself the shortest that can be drawn between its extremities. THEOREM. 461. **The sum of the three sides of a spherical triangle 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... | |
| Adrien Marie Legendre - 1825 - 570 pages
...therefore this line is itself the shortest that can be drawn between its extremities. THEOREM. . * 461. **The sum of the three sides of a spherical triangle 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... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 430 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 - 1830 - 344 pages
...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,... | |
| Encyclopedias and dictionaries - 1832 - 636 pages
...20), that any two angles forming such a solid angle must be together greater than the third. (10.) **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... | |
| John Radford Young - Astronomy - 1833 - 286 pages
...B'OC', it follows that A'OD + B'OD = A' OB' < A'OC' + B'OC' ... AB < AC + CB. (39.) 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, then the arcs... | |
| |