| Mathematics - 1835
...describe (42.) the equilateral triangle BDC, and join A D. Then, because the triangles AB D, А С D have **the three sides of the one equal to the three sides of the other, each to each,** (7.) the angle BAD is equal to the angle CAD, Therefore, &c. Cer. By repeating this process with the... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...contradicts the hypothesis: 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... | |
| John Playfair - Geometry - 1836 - 114 pages
...COR. Hence, every 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... | |
| Euclides - 1840 - 194 pages
...triangles agree in having two sides, and the angle contained by those sides, equal (as in Prop. 4); or, in **having the three sides of the one equal to the three sides of the other** (as in Prop. 8) ; or, finally, in having two angles and a side, similarly placed with respect to the... | |
| Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...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 - 235 pages
...; but, by hypothesis, BC : EF : : AC : DF; consequently FG =DF; hence the triangles EGF, DEF, have **the three sides of the one equal to the three sides of the other, each to each** ; they are therefore equal (43). But, by construction, the triangle EGF is equiangular with the triangle... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...these are equal (Def. 4), therefore AD=DB (BI Prop. 19, Cor. 2); hence the two triangles ACD, BCD, **having the three sides of the one equal to the three sides of the other,** are equal, (B. I. Prop. 22), and the angles ACD, BCD,are equal ; and therefore the arcs AE, EB,are... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...will intersect in two points G and H, thus giving two triangles DGF and DHF ; but these two triangles, **having the three sides of the one equal to the three sides of the other,** are identical (Prop. vm). If two of the given lines are equal, the triangle will be isosceles ; when... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...also be equal, each to each, and the triangles themselves will be equal. Let ABC, DBF be two triangles **having the three sides of the one equal to the three sides of the other,** viz.: AB equal to DE, BC to EF, and AC to DF ; then will the three angles also be equal, viz.: the... | |
| Charles Davies - Logic - 1850 - 375 pages
...following, which have 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.... | |
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