| Euclides - 1862
...than the angle EDF. Conclusion. — Therefore, if two triangles, &c. QED PROPOSITION 26.— THEOREM. **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; namely, either the side adjacent to the equal angles... | |
| Benjamin Greenleaf - 1862 - 490 sider
...(Art. 34, Ax. 9) ; therefore GFE is equal to GCF, or DFE to BC A. Therefore the triangles ABC, DEF **have two angles of the one equal to two angles of the other,** each to each ; hence they are similar (Prop. XXII. Cor.). 266. Scholium. When the two triangles have... | |
| Henry Green - 1863
...to it in the other ; or nice versa.— LARDXEB.S Euclid, p. 56. PROP. 26.— THEOR. — (Important.) **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 in... | |
| Evan Wilhelm Evans - 1862 - 98 sider
...these two angles are equal. But the angle A is common to the two triangles BAD and BAC. Hence, these **triangles have two angles of the one equal to two angles of the other,** and are consequently similar (Cor., Theo. III). Therefore, AC : AB : : AB : AD. That is, if from a... | |
| Euclides - 1863
...and the right angle BED (I. Ax. 11) to the right angle BFD. Therefore the two triangles E BD and 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... | |
| Euclides - 1884
...truth of the sixteenth, it would be a proof of both the sixteenth and seventeenth. It shows us that, **if two triangles have two angles of the one equal to two angles of the other,** each to each or together, their third angles are also equal. The corollaries to this proposition are... | |
| Association for the improvement of geometrical teaching - 1884
...points C and E, such that AB is equal to AC, and AD to AE : shew that BE is equal to CD. THEOR. 6. **If two triangles have two angles of the one equal to two angles of the other,** each to each, and have likewise the sides between the vertices of these angles equal, then the triangles... | |
| Woolwich roy. military acad - 1884
...equal to one another. What other converse proposition may be obtained from Proposition V., Book I.? 3. **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, namely, the sides opposite to the equal angles in each,... | |
| Euclides - 1884
...two of tho cases of equality of triangles ; the first of which may be separately enunciated thus : **If two triangles have two angles of the one equal to two angles of the other,** each to each, and also the sides adjacent to these angles equal ; they shall have all their other elements... | |
| Palaestra Oxoniensis - 1884
...shall be equal to three given straight lines, of which any two are together greater than the third. (5) **If two triangles have two angles of the one equal to two angles of the other,** each to each, and have one side equal to one side, viz. either the sides adjacent to the equal angles... | |
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