| Peter Nicholson - 1825 - 372 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 - 320 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 - 513 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 - 664 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
...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 - 272 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 - 150 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 - 352 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
...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... | |
| Euclid - 1835 - 513 sider
...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 Book IV. their... | |
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