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. Elements of Geometry - Page 40by George Albert Wentworth - 1881 - 250 pagesFull view - About this book
| 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... | |
| Peter Nicholson - Mathematics - 1825 - 1046 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.... | |
| 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
...cases oí plane triangles, which are equal in every respect. PROP. 5. (Eue. i. 26, first part of.) **If two triangles have two angles of the one equal to two angles of the other,** each to each, and likewise the interjacent* sides equal ; their other sides shall he equal, each to... | |
| John Playfair - Euclid's Elements - 1832 - 358 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... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 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... | |
| 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,... | |
| Euclides - 1834 - 518 pages
...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... | |
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