| Peter Nicholson - Cabinetwork - 1856 - 482 pages
...parallel to CD, the alternate angles, GFE, FGH, are also equal ; therefore the two triangles GEF, HFG, **have two angles of the one equal to two angles of the other, each to each ; and the** side FG, adjacent to the equal angles, common ; the triangles are therefore equal (theorem 6) ; and... | |
| Euclides - 1856 - 168 pages
...BAC, and the angle ABE is equal to the angle ABC (being both right angles), the triangles ABC, ABE **have two angles of the one equal to two angles of the other,** and the side AB common to the two. Therefore the triangles ABC, ABE are equal, and the side AE is equal... | |
| Elias Loomis - Conic sections - 1857 - 242 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.) ; and... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 pages
...consequently, the two equiangular triangles BA C, CUD, are similar figures. Cor. Two triangles which **have two angles of the one equal to two angles of the other,** are similar; for, the third angles are then equal, and the two triangles are equian gular (BI, p. 25,... | |
| Euclides - 1858 - 248 pages
...to assist in the demonstration of the following propositions. PROP. 26.— THEOR. — (Important.) **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 angles in each, or the sides... | |
| 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.) ; and... | |
| 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... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...the obverse of Prop. 8. From what Proposition is it an immediate inference ? PROPOSITION 26. THEOREM. **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, namely, either the sides adjacent to the equal angles or sides which are... | |
| Euclid - Geometry - 1890 - 442 pages
...necessitates that BC < EF. AA It remains .'. that A > D. Proposition 26. (First Part.) THEOREM — **If two triangles have two angles of the one equal to two angles of the other, each to each, and** have likewise the two sides adjacent to these angles equal ; then the triangles are identically equal,... | |
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