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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.
A System of Plane and Spherical Trigonometry: To which is Added a Treatise ... - Page 190
by Richard Wilson - 1831 - 330 pages

## A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

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...

## A Treatise on Plane and Spherical Trigonometry

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...

## Elements of Geometry and Trigonometry: With Notes

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,...

## Elements of Geometry

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...

## Elements of Geometry...: Translated from the French for the Use of the ...

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...

## Elements of Geometry

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...

## An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

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...

## Elements of Geometry and Trigonometry: With Notes

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,...