 | Robert Woodhouse - 1819 - 300 pàgines
...as ACp*, is less than the two others AC q, pCq; .-. Ap 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 (2ir). Let AC B be the spherical triangle ; then, CB < CD + BD by the former Proposition, and AC +... | |
 | Adrien Marie Legendre - 1819 - 574 pàgines
...triangle is lets Hum the circumference of a great circle. Fig. 224. Demonstration. Let ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be the semicircumferences of great circles, since two great circles always... | |
 | Adrien Marie Legendre - 1822 - 394 pàgines
...hence this arc is itself the shortest distance between its two extremities. PROPOSITION IV. THEOREM. The sum of all the three sides of a spherical triangle...produce the sides AB, AC till they meet again in D. The arcs ABD, ACD will be semicircumferences, since (1. VII. Cor.) two great circles always bisect... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 pàgines
...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 pàgines
...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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 pàgines
...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 - 1828 - 346 pàgines
...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...produce the sides AB, AC till they meet again in D. The arcs ABD, ACL) will be semicircutnffrences, since (454.) two great circles always bisect each other.... | |
 | Dionysius Lardner - 1828 - 434 pàgines
...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 - 1830 - 344 pàgines
...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...produce the sides AB, AC till they meet again in D. The arcs ABD, ACD will be semicircumferences, since (454.) two great circles always bisect each other.... | |
 | Richard Wilson - 1831 - 372 pàgines
...7Г 7Г that is, a + ß is greater than y : similarly, a + y ß, ß + У a• 30. PROP. The sum of the three sides of a spherical triangle is less than the circumference of a great circle of the sphere. By (Eue. XI. 21.) the sum of the plane angles at О is less than four right angles ;... | |
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The sum of 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, ACD, will be semicircumferenc.es, since (Prop. 
