 | Peter Nicholson - 1823 - 210 sider
...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 - 1825 - 1046 sider
...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 - 1826 - 326 sider
...the right angle BED, is equal to the right angle BFD, the two triangles EBD, FBD have two angli sof the one equal to two angles of the other ; and the side BD, whieh is opposite to one of the equal angles in eaeh, is eommon to both; therefore their other... | |
 | Robert Simson - 1827 - 546 sider
...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 - 1828 - 776 sider
...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 - 228 sider
...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 - 1830 - 584 sider
...angle DBF cannot but be equal to the angle DEG, that is, to ABC. And, because the triangles ABC, DEF have two angles of the one equal to two angles of the other, each to each, they are equiangular (1. 19. Cor. 1.), and therefore similar (31. Cor. 1.). Therefore,... | |
 | Thomas Perronet Thompson - 1833 - 168 sider
...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 - 1833 - 380 sider
...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 sider
...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... | |
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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. 
