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" If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects. "
Elements of Geometry - Page 164
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...included angle of the one are equal to two sides and the included angle of the other, each to each. Fig. 230. Demonstration. Let the side AB — EF (fig. 230),...parts which were supposed equal we shall have the sideBC= FG, the angle ABC - EFG, and the angle ACB = EGF. 481. Two triangles situated on the same sphere,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...being sides of the same square; and BF=^ BC, for the same reason ; consequently the triangles ABF, HBC, have two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are therefore equal (36). The triangle ABF is half of the rectangle BE], which...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...being sides of the same square; and BF = BC, for the same reason ; consequently the triangles ABF, HBC, have two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are therefore equal (36). The triangle ABF is half of the rectangle BE], which...
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Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - Geometry - 1836 - 242 pages
...determine such equality are comprised in the four following theorems. THEOREM VI. 38. If two triangles have two sides, and the included angle of the one...respectively equal to two sides and the included angle of the other, the remaining sides and angles are respectively equal. This theorem appears to be self-evident...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...triangle ABC, symmetrical to ABC. 452. Theorem. If two triangles on the same sphere, or on equal spheres, have two sides, and the included angle of the one respectively equal to the two sides and the included angle of the other, they are equal, or else they are symmetrical. Isosceles...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...being sides of the same square ; and BF= BC, for the same reason ; consequently the triangles ABF, HBC, have two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are therefore equal (36). The triangle ABF is half of the rectangle BE,* which...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...triangle ABC', symmetrical to ABC. 452. Theorem. If two triangles on the same sphere, or on equal spheres, have two sides, and the included angle of the one respectively equal to the two sides and the included angle of the other, they are equal, or else they are symmetrical. Proof....
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...confined to the second. PROP. IX. Two spherical triangles are either identical or symmetrical, 1. When they have two sides and the included angle of the one equal to the same in the other ; 2. When they have a side and two adjacent angles ; 3. When they...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...sides (594). 773. Corollary — The radius heing the same, two spherical triangles are equal, 1st. When they have two sides and the included angle of the one respectively equal to those parts of the other, and similarly arranged ; 2d. When they have one side and the adjacent angles...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 432 pages
...might be used indifferently. TWO SIDES AND INCLUDED ANGLE. 284. Theorem — Two triangles are equal when they have two sides and the included angle of...respectively equal to two sides and the included angle of the other. If the angle A is equal to D, and the side AB to the side DF, and AC to DE, then the...
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