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" The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. "
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... - Page 363
by John Bonnycastle - 1806 - 419 pages
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

Mathematics - 1801 - 658 pages
...sides of a plane triangle are the shortest distances between the angular points on a plane. Therefore the sum of any two sides of a spherical triangle is greater than the third. Q._ ED f DEMONSTRATION. Let the sides AB, AC, containing any angle A, be produced till they meet again...
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The Mathematical Questions Proposed in the Ladies' Diary: And ..., Volume 4

Thomas Leybourn - Mathematics - 1817 - 454 pages
...third zq л minimum, which is evidently the case when equal to the difference between qs, zs, because the sum of any two sides of a spherical triangle is greater than the third. Consequently, when the elapsed time is a minimum, gz i* equal to the difference between the altitudes...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 684 pages
...the less side. 2. Any side or angle of a spherical triangle is less than a semicircle, or 180░. 3. The sum of any two sides of a spherical triangle is greater than the third side; and their difference is less than the third side. 4. The dilference of any two Aides of a spherical triangle...
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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - Astronomy - 1827 - 448 pages
...been long meditated. PROPOSITION XV. 36. The sum of any two sides of a spherical triangle is g´eater' than the third side ; and the difference of any two sides is less than the third side. Cor. — The shortest distance between any two points on the surface of a sphere is the arc which passes...
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 438 pages
...(127.) Any two sides of a spherical triangle are together greater than the third side. (128.) Cor. The difference of any two sides is less than the third side. (129.) The sum of the three sides is less than the circumference of a great circle. (130.) Cor. The...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 pages
...(220) the sum of the arcs which measure them must be greater than the third arc (113) ; that is— The sum of any two sides of a spherical triangle, is greater than the third. Whence we infer that—The shortest way from one point to another, on the surface of a sphere, is in...
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A concise system of mathematics

Alexander Ingram - Mathematics - 1830 - 462 pages
...sides opposite to them are also equal. PROP. VIII. Any two sides of a spherical triangle are together greater than the third side, and the difference of any two sides is less than the third. Cor. The arc which passes through any two points on the surface of a sphere is the shortest distance...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - Astronomy - 1834 - 428 pages
...angles of another, each to each, their remaining sides and angles will be equal. PROPOSITION XV. 36. The sum of any two sides of a spherical triangle is...difference of any two sides is less than the third side. Cor. — The shortest distance between any two points on the surface of a sphere is the arc which passes...
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Inductive Geometry, Or, An Analysis of the Relations of Form and Magnitude ...

Charles Bonnycastle - Geometry - 1834 - 670 pages
...polygon. Whence the following propositions : RELATIONS COMMON TO ALL SPHERICAL TRIANGLES. 185 — 1. The sum of any two sides of a spherical triangle is greater than the third side ; art. 157 — 1. 2. The sum of the three sides is less than unity ; art. 157—2. 3. The sum of the...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...— cos. *' is always positive. Again, if a', 6', c', be the three sides of the polar triangle, since the sum of any two sides of a spherical triangle is greater than the third side : I b' + c1 > a1 .-. 180░ — B+1800 — C > 180░ — A .v B+ C — A< 180░ */ — cos. s' cos....
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