 | Richard Wilson - Logarithms - 1831 - 372 pages
...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 ;... | |
 | 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... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...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,... | |
 | Andrew Bell - Mathematics - 1842 - 402 pages
...is less than 180°. 348. It is to be observed, in forming examples in spherical trigonometry, that the sum of the three sides of a spherical triangle is less than the circumference of a circle; and the sum of any two sides is greater than the third ; also the greater angle is opposite... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...hence this arc is itself the shortest distance between its two extremities. PROPOSITION IV. 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, AU, till they meet again in D. The arcs ABD,... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...hence this arc is itself the shortest distance between its two extremities. PROPOSITION IV. THEOREM. v 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, A(J, till they meet again in D. The arcs... | |
 | Nathan Scholfield - 1845 - 894 pages
...hence this arc is itself the shortest distance between its two extremities. PROPOSITION IV. 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, AU, till they meet again in D. The arcs ABD,... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...the arcs AB, AC, BC, which measures these angles, is less than the sum of the other two. PROP. VIII. 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 to / /^* iioset in D. Then, since two great... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...itself the shortest distance between its two extremities. PROPOSITION XVII. 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,... | |
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ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be... 
