 | John Farrar - Trigonometry - 1833 - 155 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... | |
 | 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. Since... | |
 | Euclid - Euclid's Elements - 1833 - 183 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... | |
 | John Farrar - Trigonometry - 1833 - 272 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Euclid - 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.*... | |
 | Euclides - 1840 - 82 pages
...greater of two given straight lines, to cut off a part equal to the less. PROP. IV. THEOREM. If two triangles have two sides of the one respectively equal to two sides of the other, and the angles contained by those equal sides also equal; then their bases or third sides are also... | |
 | Euclides - 1840 - 194 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... | |
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If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. 
