 | Peter Nicholson - 1825 - 1046 σελίδες
...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 - 1827 - 546 σελίδες
...Ax. right angle BED is equal f to the right E/ angle BFD ; therefore the two triangles EBD, FBD have two angles of the one equal to two angles' of the other, each to each ; and the side BD, which is opposite to one of the equal angles in each, is common to • 26. 1. DOtn . therefore... | |
 | Thomas Kerigan - 1828 - 776 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1832 - 358 σελίδες
...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... | |
 | William Sullivan - 1833 - 380 σελίδες
...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, or the sides opposite... | |
 | Thomas Perronet Thompson - 1833 - 168 σελίδες
...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 - 518 σελίδες
...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 both ; there• 26. 1.... | |
 | Robert Simson - 1835 - 544 σελίδες
...the angle EBC : And the angle AEG is equal to the angle BEH" ; therefore the triangles AEG, BEH have two angles of the one equal to two angles of the other,...adjacent to the equal angles, equal to one another; wherec 26. l. fore, they shall have their other sides equalc: GE is therefore an. i. equal to EH, and... | |
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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. 
