| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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... | |
| 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
...angles being always opposite to the equal sides. PROPOSITION XII. TIIEOR. If two triangles have two **sides, and the included angle of the one equal to...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 - 446 pages
...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 to two....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
...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, equal to...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
...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
...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.... | |
| Benjamin Greenleaf - 1869 - 516 pages
...by construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DEF, **having two sides and the included angle of the one...and the included angle of the other, each to each,** are themselves equal (Prop. V. Bk. I.). But the triangle AGH is similar to ABC ; therefore DEF is also... | |
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