| War office - 1861 - 714 pages
...(f )2 to a decimal fraction. 10. Extract the square root of 4-20291001. Euclid. 1. If two triangles **have two angles of the one equal to two angles of the other, each to each,** and the side adjacent to the equal aii'/les in each triangle also equal, then shall the other sides... | |
| 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 - 1862 - 514 pages
...equal to the right angle EF С (Art. 34, Ax. 9) ; therefore GFE is equal to G С F, or DFE to В С А. **Therefore the triangles ABC, DEF have two angles of...each ; hence they are similar (Prop. XXII. Cor.).** 206. Scholium. When the two triangles have their sides parallel, the parallel sides are homologous... | |
| 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 - 1861 - 628 pages
...proportional ; and consequently the two triangles are similar (Art. 210). 260. Cor. Two triangles having **two angles of the one equal to two angles of the other, each to each,** are similar ; since the third angles will also be equal, and the two triangles be equiangular. 261.... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...proportional ; and consequently the two triangles are similar (Art. 210). 260. Cor. Two triangles having **two angles of the one equal to two angles of the other, each to each,** are similar ; since the third angles will also be equal, and the two triangles be equiangular. 261.... | |
| Benjamin Greenleaf - Geometry - 1863 - 502 pages
...together equal to two right angles (Prop. I. Bk. I.) ; hence the angle EDF is equal to BAG or BAC. B **The two angles, GFC, GCF, in the right-angled triangle...Cor.). homologous. Thus, DE is homologous with AB,** DP with AC, and EF with B C. PROPOSITION XXYI. — THEOREM. 267. In any triangle, if a line be drawn... | |
| 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 - 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.... | |
| Mathematical association - 1884 - 146 pages
...that the straight line joining their vertices bisects the vertical angles. THEOR. 19. If two triangles **have two angles of the one equal to two angles of the other, each to each,** and have likewise the sides opposite to one pair of equal angles equal, then the triangles are identically... | |
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