 | John Farrar - Trigonometry - 1833 - 276 pages
...projections, mm' being joined, the two triangles Smm', Emm', will be equal in all respects, since they have two sides. of the one respectively equal to two sides of the other, and one side common. Consequently m Sm' = mEm'. Therefore, since these tangents make the same angle with... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...(4) Constr. & Hypoth. (5) Prop. 5. (6) Prop. 19. (7) Constr. & Prop. 4. If two triangles (EFD, BAC) have two sides of the one respectively equal to two sides of the other (FE to AB, and FD to AC}, and if one of the angles (BAC) contained by the equal sides be greater than... | |
 | Euclides - 1833 - 304 pages
...cannot be bisected in any point but G. PROP. 15. THEOR. Of all the triangles, that can be formed having two sides of the one respectively equal to two sides of the other, the greatest is that, which has those two sides at right angles to one another. Fig. 14. ANALYSIS.... | |
 | Eugenius Nulty - Geometry - 1836 - 242 pages
...each of two triangles, the only cases of the kind entitled to particular notice. THEOREM X. 43. J/ two triangles have two sides of the one respectively equal to two sides of the other, but the angles contained by those sides unequal; the third side of that triangle which has the greater... | |
 | Education - 1836 - 502 pages
...given by Euclid, as also to prove simple derivative propositions of such a form as this — " If two triangles have two sides of the one respectively equal to two sides of the other, but the included Angles unequal, the remaining sides will be unequal, &c." On the question whether... | |
 | Schoolmaster - 1836 - 926 pages
...given by Euclid, as also to prove simple derivative propositions of such a form as this — " If two triangles have two sides of the one respectively equal to two sides of the other, but the included angles unequal, the remaining sides will be unequal, &c." On the question whether... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...from the vertex of a triangle to the point of bisection of the base, bisects the triangle : and 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. PROB. XXXIX. THEOR.* EQUAL triangles... | |
 | Euclides - 1840 - 82 pages
...be unequal; and that is the greater base which subtends the greater angle. PROP. XXV. THEOR. If two triangles have two sides of the one respectively equal to two sides of the other, but their bases unequal, the angle subtended by the greater base of the one, must be greater than the... | |
 | Euclides - 1840 - 192 pages
...greater line AB, is equal to the less C (Ax. i). PROP. IV. THEOREM. If two triangles (ACB and DFE) have two sides of the one respectively equal to two sides of the other, (CA to FD and CB to FE), and the angles (c and F) contained by those equal sides also equal ; then... | |
 | Benjamin Peirce - Geometry - 1841 - 186 pages
...AB would by § J5J_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 the included angle of the first triangle is greater than the included angle of the second triangle,... | |
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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. 
