 | Elias Loomis - Conic sections - 1849 - 252 pages
...greater than the side AC, then will the angle ACB be greater than the angle ABC. PROPOSITION XIII. THEOREM. If two triangles have two sides of the one...equal to two sides of the other, each to each, but the included angles unequal, the, base of that which has the greater angle^will be greater than the base... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...line AB, the angle FAG is made equal to the given rectilineal angle DCE. PROP. XXIV. THEOR. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained-liy the two sides of the one greater than the angle contained by the two sides of the other... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...it has just been found that BO+ OC< BD +DC; therefore, still more isBO + OC<BA + AC. PROPOSITION IX. THEOREM. If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...two straight lines, a part AE has been cut off equal to c the less. Which was to be done. PROP. IV. THEOREM. If two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to one another; they shall likewise have... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...triangle abc, (fig. 14), ab is greater than ac, then is also /_ acb greater than £ abc, &c. 3. If two 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... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...St John's College. CHARLES OCTAVUS BCDD, MA, Pembroke College. THURSDAY, Jan. 6. 9... 12. 1. IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal, the angle which is contained by the two sides of the one shall... | |
 | 1851 - 716 pages
...triangle abc, (fig. 14), ab is greater than ac, then is also / acb greater than £ abc, &c. 3. If two 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... | |
 | Edward Adolphus Seymour (11th duke of Somerset.) - 1851 - 84 pages
...because the angles OVK and IVY -are vertical angles, they are equal Therefore the triangles KVO and IVY have two sides of the one equal to two sides of the other, each to each, and have likewise the angles contained by those sides equal to one another. Wherefore, by the 4th Proposition... | |
 | Janet Taylor - Nautical astronomy - 1851 - 674 pages
...observed of the sides AC and CD, and the angles ABC, BAC. O..KD Theorem VI II. [Eu. i. 24.] If two triangles have two sides of the one equal to two sides of the otlwr, Lu1 the included angle of the one greater than the included angle of the oilier, (Inn the side... | |
 | 1867 - 336 pages
...also the third angle of the one equal to the third angle of the other. Construct two triangles which have two sides of the one equal to two sides of the other, and the angles equal which are opposite to the less of the two sides. Are such triangles necessarily... | |
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IF two triangles have two sides of the one equal to two sides of the... 
