 | Euclides - 1858 - 248 pages
...demonstration of the following propositions. PROP. 26.— THEOR. — (Important.) If two triangles have two angles of the one equal to two angles of...viz., either the sides adjacent to the equal angles in each, or the sides opposite to them, then shall the other sides be equal, each to each, and also... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...is parallel to CD, the alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG have two angles of the one equal to two angles of the other, each to each, and the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.)... | |
 | Euclides - 1868 - 88 pages
...Hyp. Cone. Sap. HP 24. HypConol. D. 5. 9. Concl. Recap. PROP. XXVI. THEOR. If tu-o triangles have t\co angles of the one equal to two angles of the other, each to and one side equal to one side, viz., either the sides adjacent to the equal angles in each, or the... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...angle in each, contained by proportional sides, are similar to each other. Any two triangles having two angles of the one equal to two angles of the other, are similar triangles, because the three angles of the one triangle are equal to the three angles of... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...of it, either arc two right angles, or are together equal to two right angles. 2. If two triangles have two angles of the one equal to two angles of...other, each to each ; and one side equal to one side, namely, either the sides adjacent to the equal angles, or the sides which are opposite to equal angles... | |
 | John Playfair - Geometry - 1860 - 334 pages
...EDF. PROP. XXVI. THEOR. If two triangles have two angles of the one equal to two angles of the othtr, each to each; and one side equal to one side, viz....adjacent to the equal angles, or the sides opposite to the equal angles in each; then shall the other side be equal, each to each; and also the third angle... | |
 | Royal college of surgeons of England - 1860 - 332 pages
...less than the other two sides of the triangle, but shall contain a greater angle. 5. If two triangles have two angles of the one equal to two angles of...other, each to each, and one side equal to one side, namely, the sides adjacent to equal angles in each triangle ; then shall the other sides be equal,... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...the |_'s PFB and PEC, we have the remaining [_'s, AFC and AEB, equal. Hence, the A's, AFC and AEB, have two angles of the one equal to two angles of the other, each to each, and the included sides equal; the remaining sides and angles are therefore equal, (Cor., Prop. 9). Therefore,... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...right angle BED is equal to the right angle B FD ; (ax. 1 1 . ) therefore the two triangles EBD, FBD have two angles of the one equal to two angles of the other, each to each ; and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore their... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...angles A and B by AF and BF, and the angles a and 6 by af and bf. Now, since the triangles ABF, abf, have two angles of the one equal to two angles of the other, they are similar (Cor., Theo. IX) ; hence, ABF : abf= AB2 : o&2 (Theo. XIV). Multiplying first couplet... | |
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If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal... 
