| War office - 1861 - 260 pages
...sovereign and a shilling ? MATHEMATICS. Voluntary Paper, No. II. REV. WN GRIFFIN, MA 1. If two triangles **have two angles of the one equal to two angles of the other,** and one side equal to one side, namely, the sides which are opposite to equal angles in each, then... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 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,... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 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... | |
| 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... | |
| 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... | |
| University of Oxford - Education, Higher - 1863 - 328 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... | |
| 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 - 72 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... | |
| 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 - 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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