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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 ... - Pągina 329
per John Bonnycastle - 1806 - 419 pągines
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## Mathematics: Compiled from the Best Authors and Intended to be the ..., Volum 2

1801 - 426 pągines
...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 Their ..., Volum 4

Thomas Leybourn - 1817
...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 - 1823 - 576 pągines
...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 - 1827 - 322 pągines
...been long meditated. PROPOSITION XV. 36. The sum of any two sides of a spherical triangle is gļeater' 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 - 1828 - 317 pągines
...(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.

JAMES HAYWARD - 1829
...(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 - 1830 - 120 pągines
...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 - 1834 - 428 pągines
...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 - 1834 - 631 pągines
...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 - 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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