 | Euclides - 1883 - 176 σελίδες
...Assuredly the proposition is not complete without a proof of this fact. EU. I. 26. THEOR. 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 (1st) the side adjacent to the equal angles... | |
 | 1883 - 654 σελίδες
...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 - 428 σελίδες
...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 - 86 σελίδες
...[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 - 170 σελίδες
...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 - 214 σελίδες
...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 - 182 σελίδες
...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 - 204 σελίδες
...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 - 242 σελίδες
...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 - 148 σελίδες
...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,... | |
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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. 
