| John Bonnycastle - 1806 - 464 pages
...THEOREM VI. 1 20. If the three sides of one spherical triangle be equal to the three sides of another, **each to each, the angles which are opposite to the equal sides will be equal.** AD c K o Let ABC, DBF be two spherical triangles, having the side AB = DE, AC = DF, and BC = EF ; then... | |
| Thomas Keith - 1810 - 478 pages
...construetion, also AB is common to the two triangles ABC and ADB, therefore the three sides of the one are **equal to the three sides of the other, each to each....The angles -which are opposite to the equal sides** in each triangle are equal. For, Produce the sides BC and BD to m and to n, so that Em and B« may... | |
| Daniel Cresswell - 1816 - 352 pages
...points : from which construction there will result six isosceles spherical triangles, three of which are **of the one be equal to the three sides of the other, each to each.** For (Art. 86.) the angle contained by any two sides of the one is equal to the angle contained by the... | |
| Alexander Ingram - 1830 - 458 pages
...meet in the poles of that circle. PROP. V. If two spherical triangles have the three sides of the one **equal to the three sides of the other, each to each, the angles which are opposite to the equal sides** are likewise equal ; and conversely. PROP. VI. If two sides and the included angle of one spherical... | |
| Pierce Morton - 1830 - 584 pages
...perpendicular to Ce; and join OQ. Then, because the triangles С P с, С Q с have the three sides of the one **equal to the three sides of the other, each to each, the** angle PC Ois equal (1. 7.) to the angle Q С О. And because (he triangles P С О, О С О have two... | |
| 1835 - 684 pages
...1.) is equal to the chord С В : and, because the triangles CDA, CDB have the three sides of the one **equal to the three sides of the other, each to each, the** angle CDA is equal to CDB : therefore, the line CD bisects AB at light angles. Therefore reversely,... | |
| John Playfair - 1836 - 148 pages
...equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the one **equal to the three sides of the other, each to each ; the angles** opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three sides equal,... | |
| Adrien Marie Legendre - 1836 - 394 pages
...therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one **equal to the three sides of the other, each to each, the** three angles will also b« equal, each to each, and the triangles themselves will be equal. Let the... | |
| Thomas Keith - 1839 - 498 pages
...through two given points on the surface of the sphere. Hence, the three sides of the one triangle being **equal to the three sides of the other, each to each, the** triangles are equal. (Prop. VH.) Secondly, let the triangles be situated on contrary sides of the centre... | |
| Great Britain. Admiralty - 1846 - 128 pages
...triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one respectively **equal to the three sides of the other, each to each, the** triangles are equal, and the angles are equal which are opposite to the equal sides. In ^s CBA, CDA,... | |
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