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" If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.... "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 28
by George Roberts Perkins - 1856 - 235 pages
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An Elementary Treatise on the Application of Trigonomentry to Orthographic ...

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...
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An Elementary Treatise on the Application of Trigonomentry to Orthographic ...

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...
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The First Six Books of the Elements of Euclid: With Notes

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...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

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....
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The schoolmaster: essays on practical education, selected from the works of ...

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...
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Elements of Geometry, Theoretical and Practical: Including Constructions of ...

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...
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The Schoolmaster: Essays on Practical Education, Selected from the ..., Volume 1

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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

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...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

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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