| William Sullivan - 1833 - 352 páginas
...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 - 1833 - 150 páginas
...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... | |
| Euclides - 1834
...angle EEC : and the angle AEG is equal * to the angle BEH ; * 15' l• 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 ; wherefore they have their other... | |
| 1835
...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. 1. (Eue. i. 26, second part of.) Hence,... | |
| Euclid - 1835 - 513 páginas
...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... | |
| Euclid, Robert Simson - 1835 - 513 páginas
...equal to KCF, and the right angle FHC equal to the right angle FKC; in the triangles FHC, FKC there are **two angles of the one equal to two angles of the other,** and the side FC, which is opposite to one of the equal angles in each, is common to both : therefore... | |
| 1836 - 472 páginas
...which has the greater base, shall be greater than the angle contained by the sides of the other. XXVI. **If two triangles have two angles of the one equal...viz. either the sides adjacent to the equal angles,** or the sides opposite to the equal angles in each; then shall the other sides be equal, each to each... | |
| John Playfair - 1836 - 114 páginas
...bisected by BD, and that the right angle BED is equal to the right angle BFD, the two Iriangles 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... | |
| Euclides - 1837 - 88 páginas
...be > Z EOF. PROPOSITION XXVI. (Argument ad absurdum). Theorem. If two triangles have two angles of **one equal to two angles of the other, each to each,...viz., either the sides adjacent to the equal angles,** or opposite to the equal angles in each : then shall the other sides be equal, A, each to each; and... | |
| Charles Reiner - 1837 - 215 páginas
...SECTION IV. two angles of the one is equal to the sum of the remaining two angles of the other. 2. **If two triangles have two angles of the one equal to two angles of the other, each to each,** the third angle of the one is equal to the third angle of the other ; that is, the triangles are equiangular.... | |
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