 | Edward Atkins - 1876 - 130 pages
...shall be equal to the triangle DEF ; * QEF is an abbreviation for quod crat faciendum, that is " 3 to be done," And the otter angles to which the equal...ABC to the angle DEF, and the angle ACB to the angle DEE. PROOF. — For if the triangle ABC be applied to (or placed Suppose upon) the triangle DEF, "... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...Then shall the base J?Cbe equal to the base EF; and the triangle ABC to the mangle DEF; and the other angles to which the equal sides are opposite shall...viz. the angle ABC to the angle DEF, and the angle ACli to the angle DFE. V For, if the triangle ABC be applied to the triangle DEF, so that the point... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...angles BAC, EDF are also equal, the two triangles ABC, DEF are equal (Pr. 6), and their other angles are equal each to each, viz., the angle ABC to the^ angle DEF, and the angle ACB to the angle DFE. Therefore, if two triangles, etc. Scholium. In equal triangles, the equal angles are opposite to the... | |
 | Euclides - 1877 - 58 pages
...the triangle DEF, and the other angles, each to each, to which the equal sides are opposite, namely, the angle ABC to the angle DEF, and the angle ACB to the. angle DFE. A Demonstration. Let the triangle ABC be applied to the triangle DEF, so that the point A may be upon... | |
 | Āryabhaṭa - 1878 - 100 pages
...angles of the one coincide with the remaining angles of the other and are therefore equal to them, each to each ; viz., the angle ABC to the angle DEF, and the angle ACB to the angle DFE. Wherefore if two triangles have two sides of the one &c. QED Paot. IV. THEOEEM. (Prop. 5 and 6 : IE)... | |
 | Moffatt and Paige - 1879 - 428 pages
...the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal, each to each, namely, the angle ABC to the angle DEF, and the angle ACB to the angle DF E. For, if the triangle ABC... | |
 | Euclides - 1879 - 146 pages
...included L EDF. Then shall the base BC be equal to the base EF, and A ABC to A DEF, and the other L s, to which the equal sides are opposite, shall be equal, each to each, namely L ABC to L DEF, and L ACB to L DFE. 15 Dem. For if A ABC be applied to A DEF, So that the pt.... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...other angles of the one coincide with the other angles of the other, and are equal to them, namely, the angle ABC to the angle DEF, and the angle ACB to the angle DFE. Wherefore, if two triangles &c. QED PROPOSITION 5. THEOREM. T/te angles at the base of an isosceles... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...each to each ; viz., those to which the equal sides are opposite ; that is, the angle ABC is equal to the angle DEF, and the angle ACB to the angle DFE. For, if the triangle ABC be applied to the triangle D EF, BO thai the point A may be on the point D,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...other angles of the one coincide with the other angles of the other, and are equal to them, namely, the angle ABC to the angle DEF, and the angle ACB to the angle DFE. Wherefore, if two triangles &c. QED PROPOSITION' 5. THEOREM. TJie angles at the base of an isosceles... | |
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J which the equal sides are opposite, shall be equal, each to each, viz. the angle ABC to the angle DEF, and the angle ACB to DFE. 
