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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. "
Elements of Plane and Spherical Trigonometry: With Its Applications to the ... - Page 69
by John Radford Young - 1833 - 264 pages
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A Treatise on Plane and Spherical Trigonometry

Robert Woodhouse - 1819 - 300 pages
...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 +...
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Elements of Geometry

Adrien Marie Legendre - 1819 - 574 pages
...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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1822 - 394 pages
...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...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 pages
...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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 294 pages
...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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 280 pages
...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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - 346 pages
...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....
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - 1828 - 434 pages
...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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1830 - 344 pages
...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....
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A System of Plane and Spherical Trigonometry: To which is Added a Treatise ...

Richard Wilson - 1831 - 372 pages
...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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