| 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... | |
| 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... | |
| James Mitchell - Mathematics - 1823 - 666 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... | |
| William Galbraith - Astronomy - 1827 - 412 pages
...been long meditated. PROPOSITION XV. 36. The sum of any two sides of a spherical triangle is gïeater' **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... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 434 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... | |
| 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... | |
| Alexander Ingram - Mathematics - 1830 - 458 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... | |
| William Galbraith - Astronomy - 1834 - 454 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... | |
| 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... | |
| Nathan Scholfield - Conic sections - 1845 - 542 pages
...— 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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