| Mathematics - 1835 - 684 pages
...last circle in F ; and join FA, F В. Then, because the triangles ECD, FAB have the three sides of the **one equal to the three sides of the other, each to each,** (7.) they are equal in every respect, and the angle at A is equal to the angle at C. Therefore, &c.... | |
| John Playfair - Geometry - 1836 - 148 pages
...equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the **one equal to the three sides of the other, each to each ; the** angles opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three sides... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the **one equal to the three sides of the other, each to each, the** three angles will also b« equal, each to each, and the triangles themselves will be equal. Let the... | |
| Thomas Keith - 1839 - 498 pages
...equally obtuse. PROPOSITION VII. (308) In any two spherical triangles, if the three sides of the one be **equal to the three sides of the other, each to each, the** angles which are opposite to the equal sides wiH be equal. Let ABC be any triangle on the surface of... | |
| Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...sides, a triangle would admit of two different forms. This proposition is usually enounced thus : — **If two triangles have the three sides of one equal to the three sides of the other each to each,** then the three angles will le equal each to each, and their areas will be equal. (63.) When two sides... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...AT) be drawn to the middle of the base, the two triangles ABD, ADC, will have the three sides of the **one equal to the three sides of the other, each to each,** namely, AD common, BD = DC,AB = AC; consequently, by the preceding theorem, the two triangles will... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one respectively **equal to the three sides of the other, each to each, the triangles are equal,** and the angles are equal which are opposite to the equal sides. In ^s CBA, CDA, if AB, BC, CA = AD,... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one re-spectively **equal to the three sides of the other, each to each, the triangles are equal,** and the angles are equal which are opposite to the equal sides. In ^s CBA, CDA, if AB, BC, CA = AD,... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...mutually equilateral, they are equivalent. Let ABC, DEF be two triangles which have the three sides of the **one, equal to the three sides of the other, each to each,** viz., AB to DE, AC to DF, and BC to EF; then will the triangle ABC be equivalent to the triangle DEF.... | |
| Charles Davies - Logic - 1850 - 398 pages
...been before proved ; viz. : Prop. X. (of Legendre). "When two triangles have the three sides of the **one equal to the three sides of the other, each to each, the** three angles will also be equal, each to each, and the triangles themselves will be equal." Prop. V.... | |
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