 | Euclid, John Playfair - 1846 - 334 pagina’s
...arcs AFD, DGB, subtending these angles, are equal. Join AD, DB ; then the triangles ACD, BCD, having two sides and the included angle in the one, equal to two sides and the included angle in the other, are equal : so that, if ACD be applied to BCD, there shall be an entire coincidence, the point A coinciding... | |
 | Charles William Hackley - 1847 - 248 pagina’s
...will 36 lines intersect, 24 of which pass through the same point? THEOREM I. If two triangles have two sides and the included angle in the one equal to two sides and the included angle in the other, the triangles will be identical, or equal in all respects. In the two triangles ABC, DEF, if the side... | |
 | Charles Davies - 1849 - 372 pagina’s
...the angle ACB, by hypothesis ;j and the side BC common : therefore, the two triangles, BDC, BAC, have two sides and the included angle in the one, equal...and the included angle in the other, each to each: hence they are equal (Prop. V.). But the part cannot be equal to the whole (Ax. 8.); hence, there is... | |
 | Adrien Marie Legendre - 1852 - 436 pagina’s
...diagonal DB divides the parallelogram into two equal triangles. Cor. 2. Two parallelograms which have two sides and the included angle in the one equal...and the included angle in the other, each to each, are equal. Let the parallelogram ABCD, have I) C the sides AB, AD, and the included angle BAD equal... | |
 | Charles Davies - 1854 - 436 pagina’s
...diagonal DB divides the parallelogram into two equal triangles. Cor. •2. Two parallelograms which have two sides and the included angle in the one equal...and the included angle in the other, each to each, are equal. Let the parallelogram ABCD, have DC the sides AB, AD, and the included angle BAD equal to... | |
 | Henry Philip Tappan - 1856 - 480 pagina’s
...then add as a minor, " The two triangles ADB and ABC, by the contradictory, are, two triangles having two sides and the included angle in the one, equal to two sides and the included angle of the other/' Hence the conclusion, " The two triangles ADB and AB 0 are equal/' Here we assumed the... | |
 | Horatio Nelson Robinson - 1860 - 470 pagina’s
...perpendiculars, we should have unequal righ angles, which is impossible. THEOREM XVI. Two triangles which have two sides and the included angle in the one, equal...and the included angle in the other, each to each, are equal in all respects. In the two A's, ABCund DEF, on the supposition that AB = DE, AC=DF, and... | |
 | Benjamin Greenleaf - 1862 - 518 pagina’s
...point, are together equal to four right angles. PROPOSITION V. — THEOREM. 52. If two triangles have two sides and the included angle in the one equal...and the included angle in the other, each to each, the two triangles will be equal. In the two triangles ABC, DEF, let the side AB .be equal to the side... | |
 | Benjamin Greenleaf - 1861 - 638 pagina’s
...equilateral. PROPOSITION XIV. — THEOREM. 549. If two triangles on the same sphere, or on equal spheres, have two sides and the included angle in the one equal...and the included angle in the other, each to each, the two triangles are equal in all their parts. In the two triangles ABC, DBF, let the side AB be equal... | |
 | Benjamin Greenleaf - 1863 - 504 pagina’s
...equilateral. PROPOSITION XIV. — THEOREM. 549. If two triangles on the same sphere, or on equal spheres, have two sides and the included angle in the one equal...and the included angle in the other, each to each, the two triangles are equal in all their parts. In the two triangles ABC, DEF, let the side AB be equal... | |
| |
If two triangles have two sides and the included angle in the one equal to two sides and the included angle in the other, each to each, the two triangles will be equal. 
