| Peter Nicholson - Architecture - 1823 - 210 pages
...parallel to CD, the alternate angles, GFE, FGH, are also equal; therefore the two triangles GEF, FHG, **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... | |
| Peter Nicholson - Mathematics - 1825 - 1058 pages
...takes place when in each triangle two sides respectively equal, form an equal angle ; and also when **two angles of the one, equal to two angles of the other,** are formed on an equal side. It is easy to demonstrate these propositions in the same manner as in... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...angle EBC: and the angle AEG is •15.1. equal* to the angle BEH: therefore the triangles AEG, BEH **have two angles of the one equal to two angles of the other, each to each,** and the sides AE, EB, adjacent to the equal angles, equal to one another: • 26. 1. wherefore they... | |
| Thomas Kerigan - Nautical astronomy - 1828 - 776 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 - Geometry - 1829 - 228 pages
...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 - 584 pages
...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,... | |
| William Sullivan - Ethics - 1833 - 380 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... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...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 - 518 pages
...and the right angle FHC equal to the right angle FKC, therefore in the triangles FHC, FKC there are **two angles of the one, equal to two angles of the other, each to each** ; and the side FC, which is opposite to one of the equal angles in each, is common to both ; there•... | |
| Euclid - 1835 - 540 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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