| 1883
...coincide with the vertex of the given angle and then the construction would fail. 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, viz., either the sides adjacent to the equal angles in... | |
| Euclid, Isaac Todhunter - 1883 - 400 sider
...I. n ; and therefore EF is less than EG. I. 26. It will appear after I. 32 that two triangles which **have two angles of the one equal to two angles of the other,** each to each, have also their third angles equal. Hence we are able to include thu two cases of I.... | |
| Mathematical association - 1883
...[Alternative proofs, (i) by Theors. 16 and 5. (ii) By Theors. 7 and 5.] 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... | |
| Evan Wilhelm Evans - 1884 - 155 sider
...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. IX). Therefore, Cor.—If from a point without a circle a secant... | |
| Euclides - 1884
...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... | |
| Euclides - 1884
...which is the greater of the angles R and V. TV 65. 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, namely, either the sides adjacent to the equal angles... | |
| Palaestra Oxoniensis - 1884
...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... | |
| Evan Wilhelm Evans - 1884 - 149 sider
...angles A and B by AF and BF, and the angles a and 6 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. IX) ; hence, ABF : abf= AB2 : o&2 (Theo. XIV). Multiplying first couplet... | |
| Woolwich roy. military acad - 1884
...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,... | |
| Association for the improvement of geometrical teaching - 1884
...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... | |
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