 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC have two sides and the included angle of the one equal to two sides and the included angle of the other; hence they arc themselves equal (Prop. V. Bk. I.). EG ELEMENTS OF GEOMETRY. same altitude... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC have two sides and the included angle of the one equal to two sides and the included angle of the other ; hence they are themselves equal (Prop. V. Bk. I.). ELEMENTS OF GEOMETRY. K same altitude... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...similar. • Take AG equal to DE, and AH to DF ; also, join GH. Then the triangles AGH, DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, are equal throughout (Theo. VII, B. I). Now,- by hypothesis, AB : DE : : AC : DF. Therefore,... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...be greater nor less than D : hence, it must be equal to it. The two triangles have, therefore, two sides and the included angle of the one equal to two sides and the inclu* ded angle of the other, each to each ; and, consequently, they are equal in all their parts... | |
 | Euclides - 1865 - 80 pages
...the equal angles being always opposite to the equal sides. PROPOSITION XII. TIIEOR. If two triangles have two sides, and the included angle of the one...and the included angle of' the other, each to each, the triangles are equal (Def. 37). Let the two triangles ABC and EDF have the side AB equal to DE,... | |
 | Education - 1866 - 584 pages
...recitation on the morrow, to be that starting point in the properties of triangles, viz : If two triangles have two sides and the included angle of the one equal...and the included angle of the other, each to each, the two triangles will be equal in every respect. The teacher draws the diagram on the board, and desires... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...the other, each to each, the triangles will be equal in all their parts." Prop. V. " 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 in all their parts." Axiom 1. "Things which are equal to the same thing,... | |
 | C. Davies - 1867 - 342 pages
...the same manner we may prove that the angle AED ia equal to the angle CEBTHEOREM IV- If two triangles have two sides and the included angle of the one, equal to two sides and ike included angle of the other, each to each, the two triangles will be equalLet the triangles ABC... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC have two sides and the included angle of the one equal to two sides and the included angle of the other ; hence they are themselves equal (Prop. Y. Bk. I.). G same altitude BD (Prop. II. Cor.... | |
 | Bernhard Marks - Geometry - 1869 - 172 pages
...the angle ADC. Therefore the angle AB c is equal to the angle ADC. Then the two triangles AB c, AD c, have two sides, and the included angle of the one...and the included angle of the other, each \ to each, and are equal in all their parts ; that is, the three angles of the one are equal to the three angles... | |
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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... 
