| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...(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 their sides... | |
| Benjamin Greenleaf - Geometry - 1861 - 638 pages
...(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.). homologous. Thus, DE is homologous with AB, DP with AC,... | |
| Euclides - 1862 - 140 pages
...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 in sach, or the... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...(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.). homologous. Thus, DE is homologous with AB, DF with A... | |
| Euclides - 1863 - 122 pages
...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 both. Therefore... | |
| Euclides - 1863 - 74 pages
...; 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 each, or the... | |
| University of Oxford - Education, Higher - 1863 - 316 pages
...circle, parallelogram, plane superficies. Write out Euclid's three postulates. 2. If two triangles have two angles of the one equal to two angles of the other, each to each, and the sides adjacent to the equal angles also equal, then shall the other sides be equal, each to... | |
| Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...angles A and B by AF and BF, and the angles a and b by af and bf. Now, since the triangles ABF, abf, have two angles of the one equal to two angles of the other, they are similar (Cor., Theo. Ill) ; hence, ABF : abf : : AB2 : a&2 (Theo. VIII). Multiplying an extreme... | |
| Euclides - 1864 - 448 pages
...than the angle EDF. "Wherefore, if two triangles, &e. QED PROPOSITION XXVI. 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, viz, either the sides adjacent to the equal angles in each, or the... | |
| Euclides - 1884 - 214 pages
...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 not Euclid's.... | |
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