 | Mathematics - 1835 - 684 pages
...let the line EG meet DF, or DF produced in G. Then, because the triangles ABC, DEG have two angles of the one equal to two angles of the other, each to each, they are equiangular : therefore (31.) DE : EG ••AB: В С, but AB:BC::DE:EF: therefore (12.) DE... | |
 | Mathematics - 1836 - 488 pages
...greater than the angle contained by the sides of the other. XXVI. 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 angles, or the sides opposite to the equal angles in each;... | |
 | John Playfair - Geometry - 1836 - 148 pages
...exterior angles are equal to four right angles. PROP. VI. THEOR. 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, the triangles shall be equivalent. Let ABC, DEF be two triangles which have the angles ABC, BC A, equal... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...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, and one side equal to one side; viz., either the sides adjacent to the equal angles, or opposite to the equal angles in each : then... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...is equal to the right angle FCL ; therefore in the two triangles FKC, FLC, there are two angles of one equal to two angles of the other, each to each ; and the side FC, which is adjacent to the equal angles in each, is common to both ; therefore the other... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...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.... | |
 | Euclides - 1838 - 264 pages
...is equal to the right angle FCL ; therefore, in the two triangles FKC, FLC, there are two angles of the one equal to two angles of the other, each to each ; and the side FC, which is adjacent to the equal angles in each, is common to both ; therefore «„ , the... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...is equal to the right angle FCL : therefore, in the two triangles FKC, FLC, there are two angles of one equal to two angles of the other, each to each, and the side FC, which is adjacent to the equal angles in each, is common to both ; therefore the other... | |
 | Euclides - Geometry - 1841 - 378 pages
...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, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another: therefore their other * 28. 1.... | |
 | Chambers W. and R., ltd - 1842 - 744 pages
...still further information on this useful subject. It shows that if two triangle* have two angles of the one equal to two angles of the other, each to each, and one side equal to one aide, namely, either the sides adjacent to the equal angles, or the sides opposite to the equal angles... | |
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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. 
