 | Robert Woodhouse - 1819 - 470 pàgines
...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 - 1822 - 394 pàgines
...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, John Farrar - 1825 - 280 pàgines
...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 - 276 pàgines
...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 - 1825 - 570 pàgines
...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... | |
 | Adrien Marie Legendre - 1830 - 344 pàgines
...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,... | |
 | Richard Wilson - 1831 - 372 pàgines
...than . y ; 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 ;... | |
 | 1832 - 636 pàgines
...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...third side c until they meet again. The produced parts "• — a and *• — b will, with the third side c, form a triangle. Hence by the last proposition,... | |
 | John Radford Young - 1833 - 286 pàgines
...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... | |
 | Adrien Marie Legendre - 1836 - 394 pàgines
...shortest distance between B and A can lie out of the arc of the great circle BDA. PROPOSITION HI. THEOREM. 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,... | |
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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, AU, till they meet again in D. 
