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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. "
An Introduction to the Theory and Practice of Plain and Spherical ... - Page 136
by Thomas Keith - 1826 - 442 pages
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

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...
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An Introduction to the Theory and Practice of Plane and Spherical ...

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 Bę may...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

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...
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A Concise System of Mathematics ...

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...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

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...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

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,...
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The Element of Geometry

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,...
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Elements of Geometry and Trigonometry

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 bę equal, each to each, and the triangles themselves will be equal. Let the...
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An introduction to the theory ... of plane and spherical trigonometry ...

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...
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The Elements of Geometry, Symbolically Arranged

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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