 | John Bonnycastle - 1806 - 464 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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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If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
