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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 - Σελίδα 160
των Adrien Marie Legendre - 1819 - 208 σελίδες
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 σελίδες
...included angle of the other, each to each. Fig. 230. Demonstration. Let the side AB — EF (fig. 230), the side AC = EG, and the angle BAC = FEG, the triangle...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,...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
...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...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre - 1825 - 224 σελίδες
...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...

Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - 1836 - 220 σελίδες
...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...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1837 - 159 σελίδες
...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...

Elements of geometry

Adrien Marie Legendre - 1841 - 235 σελίδες
...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...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1847 - 150 σελίδες
...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....

Elementary Course of Geometry ...

Charles William Hackley - 1847 - 103 σελίδες
...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...

Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 420 σελίδες
...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...

Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 420 σελίδες
...equal sides (594). 773. Corollary The radius being 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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