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" If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal... "
Elements of Geometry and Trigonometry: With Applications in Mensuration - Page 84
by Charles Davies - 1886 - 324 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...on equal spheres, are equal in all their parts, when two sides and the included angle of the one are equal to two sides and the included angle of the other, each to each. . 230. Demonstration. Let the side AB = EF (Jig. 23O), the side AC = EG, and the angle BAC = FEG, the...
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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
...on equal spheres, are equal in all their parts, when two sides and the 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), the side AC = EG, and the angle BAC = PEG,...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...-vertical angles. 36. Two triangles arc. equal, -when two sides and the included angle of the one are equal to two sides and the included angle of the other, each to each. Demonstration. In the two triangles ABC, DEF (fig. 23), let Fig. 23. the angle A be equal to the angle...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...said to be right, when oblique 127 When said to be regular (its axis) 127 (a) Triangular prisms, which have two sides and the included angle of the one equal to two sides and the included angle of the other, are equal to one another . . . 138 (i) If the upper part of a triangular prism be cut...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...be right, when oblique 127 Л\ hen said to be regular (its axis) 127 () Triangular prisms, which have two sides and the included angle of the one equal to two sides and the included angle of the other, are equal to one another . . . 138 (V) If the upper part of a triangular prism be cut...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...angles, as by the successive angles ACB, BCD, DCE, ECF, FCA. PROPOSITION V. THEOREM. ' If two triangles have two sides and the included angle of the one,...and the included angle of the other, each to each, the two triangles will be equal. Let the side ED be equal to the side BA, the side DF to the side AC,...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 524 pages
...between them, are given, there are sufficient data for constructing the triangle ; and if two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other — it being understood that it is not the sum of the sides which is equal, hut that each...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 542 pages
...sufficient data for constructing the triangle ; 416 CONSTRUCTION OF TRIANGLE?. and if two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other — it being understood that it is not the sum of the sides which is equal, but that each...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 384 pages
...angles, as by the successive angles ACB, BCD, DCE, ECF, FCA. B PROPOSITION V. THEOREM. If two triangles have two sides and the included angle of the one,...sides and the included angle of the other, each to eac/i, the two triangles will be equal. Let the side ED be equal to the side BA, the side DF to the...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 264 pages
...of the Triangle. SECTION VI. PROPERTIES OF THE TRIANGLE. 1. If two triangles have two sides, and an included angle of the one, equal to two sides and the included angle of the other, each to each, the remaining parts will also be equal. That is, if we have the two triangles, .ABC and DEF, having...
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