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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... "
Carpentry Made Easy: Or, The Science and Art of Framing, on a New and ... - Pagina 33
di William E. Bell - 1857 - 134 pagine
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 pagine
...proposition the hypothesis is, that two sides and the included angle of one triangle are respectively equal to two sides and the included angle of the other ; and the conclusion deduced from this hypothesis is, that the remaining side and angles in the one triangle...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 pagine
...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 Pierce ...

1835 - 684 pagine
...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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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - 524 pagine
...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 - 1836 - 542 pagine
...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 - 1836 - 394 pagine
...the successive angles ACB, BCD, DCE, ECF, FCA. PROPOSITION V. THEOREM. ' 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. Let the side ED be equal to the side BA,...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - 1840 - 264 pagine
...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,...
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Psychology: Or, Elements of a New System of Mental Philosophy, on the Basis ...

Samuel Simon Schmucker - 1842 - 262 pagine
...demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz. : If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, they must be identical or equal in all respects. For it virtually consists in supposing...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 326 pagine
...the angle BAC is equal to its alternate angle DCA (Prop. xvii)t; hence the two triangles, having two sides and the included angle of the one equal to two sides and the included angle of the other, namely, the side AB equal to. the side CD, the side AC common, and the contained angle...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 372 pagine
...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, equal to two sides and the included angle of the other, each tc each, the two triangles will be equal Let the side ED be equal to the side BA,...
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