| Horatio Nelson Robinson - 1869 - 276 pages
...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 - 172 pages
...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... | |
| Euclides - 1871 - 136 pages
...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, each to each,... | |
| Bernard Marks - Geometry - 1871 - 172 pages
...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
...mutually equilateral, they arc 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.... | |
| Edward Olney - 1872 - 270 pages
...that ABC may or may PROPOSITION IX. 292. Tlieorem.—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 are... | |
| Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...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
...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... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...are also equal. (Eucl. i. 6.) PBOP. C. THEOREM. If two triangles have the three sides of the one eqwl **to the three sides of the other, each to each, the triangles** must be equal in all respects. Let the three sides of the A s ABC, DEF be equal, each to each, that... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...(26, Ax. 12). Thus circles having equal radii are equal ; and triangles having the three sides of the **one equal to the three sides of the other, each to each,** are also equal. Equal figures are always similar; but similar figures may be very unequal. 175. In... | |
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