| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...construction, AG is equal to DE ; hence А П is equal to D F. Therefore the two triangles AGH, DEF, having two **¡sides and the included angle of the one equal to...and the included angle of the other, each to each,** are themselves equal (Prop. V. Bk. I.). But the triangle AGH is similar to А В С ; therefore DEF... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 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.). G ELEMENTS OF GEOMETRY. EG same altitude... | |
| 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,... | |
| Charles Davies - 1863 - 436 pages
...is equal to the angle CEB\ THEOREM IVIf two triangles have two sides and the included angle of tie **one, equal to two sides and the included angle of the other, each to each,** the two triangles will be equalLet the triangles ABC and DEF have the side AC equal to DF, CB to FE,... | |
| 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... | |
| Charles Davies - Geometry - 1864 - 358 pages
...Dl equal to AC and DG equal to AB, and join IG- Then the two triangles ABC and DIG, having two s1des **and the included angle of the one equal to two sides and the included** ingle of the other, each to each, will be equal (Bk- I Th- iv) Hence, the angles / and G are equal... | |
| Euclides - 1865 - 80 pages
...and C to DFE, the equal angles being always opposite to the equal sides. PROPOSITION XII. TIIEOR. If **two triangles have two sides, and the included angle...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,... | |
| Charles Davies - Mathematics - 1867 - 186 pages
...three sides of 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...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,... | |
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