 | Peter Nicholson - Mathematics - 1825 - 372 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...angle BAG is greater than the angle EDF. Wherefore, if two triangles, &e. QED .5- PROP. XXVI. THEOR. If two triangles have two angles of the one equal to two angles of the other, eaeh to eaeh -, and one side equal to one side, viz. either the sides adjaeent to the equal angles,... | |
 | Robert Simson - Trigonometry - 1827 - 513 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 have... | |
 | 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
...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... | |
 | John Playfair - Euclid's Elements - 1833 - 333 pages
...the angle BAC is greater than the angle EDF. Wherefore, if two triangles, &c. QED PROP. XXVI. THEOR. If two triangles have two angles of the one equal...; and one side equal to one side, viz. either the side adjacent to the equal angles, or the sides opposite to the equal angles in each ; then shall the... | |
 | 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 ; and one side equal to one side, viz. either of the sides adjacent to the equal angles, or the sides opposite to the equal angles in each; then... | |
 | 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... | |
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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... 
