| Robert Simson - Trigonometry - 1827 - 513 pages
...11 Ax. right angle BED is equal f to the right E/ angle BFD ; 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 • 26. 1. DOtn . therefore... | |
| Thomas Kerigan - Nautical astronomy - 1828 - 664 pages
...opposite angle CBF, — Euclid, Book I., Prop. 29. And, since the two triangles AFD and FBC have, thus, **two angles of the one equal to two angles of the other,** viz., the angle AFD to the angle FBC, and the angle FAD to the angle BFC, and the side AF of the one... | |
| JAMES HAYWARD - 1829
...mO' and M'N'O' are equal. The angle N'O'M' is common to the two triangles nmO' and N'M'O'; and having **two angles of the one equal to two angles of the other,** the other angles must be equal, that is, the angle O'M'N' is equal to the angle O' nm ; and this intersection... | |
| Pierce Morton - Geometry - 1830 - 272 pages
...together equal to the angles А С D, ACB, that is, to two right angles (2.). Therefore, &c. Cor. 1. **If two triangles have two angles of the one equal to two angles of the other,** their third angles will likewise be equal to one another. Cor. 2. (Eue. i. 2G, second part of.) Hence,... | |
| John Playfair - Euclid's Elements - 1832 - 333 pages
...angle BAG is greater than the angle EDF. Wherefore, if two triangles, &c. QED PROP. XXVI. THEOR. I/ **two triangles have two angles of the one equal to two angles of the other, each to each;** undone side equal lo one side, viz. either the sides adjacent to the equa tangles, or the sides opposite... | |
| William Sullivan - Ethics - 1833 - 352 pages
...it. It is a truth, for example, but not a self-evident one, that if one draw two triangles, having **two angles of the one equal to two angles of the other, each to each ; and** one side equal to one side, viz. either of the sides adjacent to the equal angles, or the sides opposite... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...reasoning, the like may be proved in all other triangles under the same conditions. Wherefore, universally, **if two triangles have two angles of the one, equal to two angles of the other** respectively ; &c. Which was to be demonstrated. PROPOSITION XXVII. THEOREM. — If a straight line... | |
| Euclides - 1834
...BAC is greater than the angle EDF. Wherefore, if two triangles, &c. QED PROPOSITION XXVL THEOR. — **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, or the sides opposite... | |
| Mathematics - 1835
...together equal to the angles А С D, ACB, that is, to two right angles (2.). Therefore, &c. Cor. 1. **If two triangles have two angles of the one equal to two angles of the other,** their third angles will likewise be equal to one another. Cor. 1. (Eue. i. 26, second part of.) Hence,... | |
| Euclid - 1835 - 513 pages
...by BD, and because the right angle BED is equal to the right angle BFD, the two triangles EBD, FBD **have two angles of the one equal to two angles of the other,** and the side BD, which is opposite to one of the equal angles in each, is common to both; therefore... | |
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