 | James Bates Thomson - Geometry - 1844 - 268 pages
...AG from one side, and its equal AB from the other, there will remain GC<BC, or EF<BC. Hence, If two triangles have two sides of the one respectively equal to two sides of the other, while the included angle of the one is greater than the included angle of the other, then will the... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...from the vertex of a triangle to the point of bisection of the base, bisects the triangle ; ana if two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles (I. def. 38) supplemental, the triangles are equal. * lt follows from the first corollary... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...AB would by § 61 and the preceding demonstration, be equal to or less than AC. 63. Theorem. If two triangles have two sides of the one respectively equal to two sides of the other, and if die included angle of the first triangle is greater than the included angle of the second triangle,... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...~ "~ THEOREM XXXII. If two triangles have two sides of the one equal to two sides of the other, but the included angles unequal, the third sides will be unequal, and the greater will be in that triangle which has the greater included angle. Let ABC, DBF be two triangles in which... | |
 | 1851 - 730 pages
...and B. 6. Solve the following equations: — Sx+1 Sx-1 2г + 5 (1.) (2.) xl x -t-1 2xt-1 7. If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles equal, prove that the triangles will be equal in every respect. 8. The square constructed... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...triangles have two sides of the one equal to two sides of the other, each to each, and the included angle unequal, the third sides will be unequal, and the greater side will belong to the greater triangle, which has the greater included angle ; or if an angle of a triangle is increased,... | |
 | 1851 - 716 pages
...triangles have two sides of the one equal to two sides of the other, each to each, and the included angle unequal, the third sides will be unequal, and the greater side will belong to the greater triangle, which has the greater included angle ; or if an angle of a triangle is increased,... | |
 | Euclides - 1852 - 48 pages
...(Prop. 19.) ; but DG is equal to A c, therefore DF is greater than A c. WWD PBOP. XXV. THEOE. If two triangles have two sides of the one respectively equal to two sides of the other, and if the base of one be greater than the base of the other ; the angle opposite to the greater base is... | |
 | Euclid - Geometry - 1853 - 176 pages
...to be by the " reductio ad absurdum." PROPOSITION VIII. THEOREM. — If two triangles (ABC and DEF) have two sides of the one respectively equal to two sides of the other (AB and AC to DE and DF), and have aho their bases equal (BC to EF), then the angles (A and D) formed... | |
 | Euclides - Geometry - 1853 - 334 pages
...been cut off equal to c the less. Which was to be done. PEOP. IV. THEOEEM. ' If two triangles have (1) two sides of the one respectively equal to two sides of the other ; (2) the angle included by the two sides of the one equal to the angle included by the two sides of... | |
| |
If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side. 
