| 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 with... | |
| 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 with... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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.* 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 - 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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