| Horatio Nelson Robinson - 1869 - 276 pages
...ED = CF, (Ax. 3); but BE = AC, and AF= BD, (Th. 24); hence we have two A's, CAF and EBD, which have the three sides of the one equal to the three sides of the other, each to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
| Bernhard Marks - Geometry - 1869 - 170 pages
...side A B. 'D It PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove, that, If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| Charles Davies - Geometry - 1870 - 394 pages
...called a direct, and the latter an indirect demonstration. THEOREM via. If two triangles have tlie three sides of the one equal to the three sides of the other, each to each, the three angles will aho be equal, each to each. Let the two triangles ABC, ABD, have the side AB equal... | |
| Euclides - 1871 - 136 pages
...triangle be.equal, the sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. -25 q _ Let the three sides of the A s ABO, DEF be equal,... | |
| Bernard Marks - Geometry - 1871 - 172 pages
...ILLUSTRATED. PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are equal in all their part's. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...eqi. il, each to each, and the triangles themselves will be • •qua', Let ABC, DEF 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... | |
| Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...equal to each other, the £s opposite to them are also equal. (Prop. V.) Let ABO and DEF be the two As having the three sides of the one equal to the three sides of the other, each to each. Let the ADEF be applied to the AABC so that the point D may coincide with the point A, and the line... | |
| Edward Olney - Geometry - 1872 - 472 pages
...attention. A BD rV H E EQUALITY OF TRIANGLES. PROPOSITION IX. 292. Theorem. — Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEM. — Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BC = EF ; then... | |
| Edward Olney - Geometry - 1872 - 562 pages
...special attention. EQUALITY OP TBIANGLES. PROPOSITION IX. 292. Theorem. — Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEM. — Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BC =' EF ; then... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...chord EG, the arcs AD, EG will be equal. For, if the radii CD, OG are drawn, the triangles ACD, EOG, having the three sides of the one equal to the three sides of the other, each to each, are themselves equal (Theo. XIII. Bk. I.) ; therefore the angle A CD is equal to the angle EOG (Theo.... | |
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