 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.  Pure mathematics - Page 94by Edward Atkins - 1874Full view - About this book
 | Euclides - Geometry - 1853 - 334 pages
...that are equal to the same thing are equal to one another (Ax. i) : therefore the angle ABC is equal to the angle DEF, and the angle ACB to the angle DFE. Lastly, since the triangles ABC, DEF have been shewn to be equiangular to one another, they are similar... | |
 | Euclides - Geometry - 1853 - 176 pages
...angle baС equal to the angle edf, the base b С shall be equal to the base ef ; and the triangle ab С to the triangle def ', and the other angles to which the equal „ gf sides are opposite, shall be equal, each to each, viz. the angle ab С to the angle def, and... | |
 | Euclides - 1855 - 270 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. Therefore, if two triangles have two sides, &c. QED The demonstration of this proposition might have... | |
 | John Playfair - Euclid's Elements - 1855 - 340 pages
...to the triangle DEF; and the other angles, to 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. For, if the triangle ABC be applied to the triangle DEF, so that the point A may be on D, and... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...remaining angles of the one, will coincide with the remaining angles of the other, and be equal to them, viz. : the angle ABC to the angle DEF, and the angle ACB to the angle DFE. Therefore, if two triangles, &c. +. PROPOSITION VII. THEOREM. If two triangles have two angles, and... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...remaining angles of the one, will coincide with the remaining angles ol" the other, and be equal to them, viz. : the angle ABC to the angle DEF, and the angle ACB to the angle DFE. Therefore, if two triangles, &c. PROPOSITION VII. THEOREM. If two triangles have two angles, and the... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...equal to the included angle EDF. Then shall the base B Che equal to the base EF; and the triangle ABC to the triangle DEF; and the other angles to which...the angle DEF, and the angle ACB to the angle DFE. For, if the triangle ABC Toe applied to the triangle DEF, so that the point A may be on D, and the... | |
 | Euclides - 1860 - 288 pages
...equal to the angle EDF, to prove that 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 fe -- opposite, shall be equal, each to r ' Is •'-'' each; namely, the angle A* /H ABC to the angle... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...remaining angles of the one, will coincide with the remaining angles of the other, and be equal to them, viz.: the angle ABC to the angle DEF, and the angle ACB to tfte angle DFE. Therefore, if two triaii 0 ^s, &c. PROPOSITION VII. THEOREM. 11 If two triangles have... | |
 | Euclides - 1862 - 140 pages
...The base BC shall be equal to the base EF. 2. The triangle ABC shall be equal to the triangle DEF. 3. And the other angles to which the equal sides are...the angle DEF, and the angle ACB to the angle DFE. Demonstration. — 1. For if the triangle ABC be applied to (or placed upon) the triangle DEF, 2. So... | |
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