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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.... "
The Geometrical Companion, in which the Elements of Abstract Geometry are ... - Side 13
av George Darley - 1828 - 169 sider
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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volum 1

William Nicholson - 1809 - 716 sider
...fundamental propositions in elementary geometry. Thus it is proved, that two triangles, having two sides of the one equal respectively to two sides of the other, and the two included angles equal, are equal in all respects ; and two triangles, having one side and the....
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volum 1

William Nicholson - 1819 - 432 sider
...fundamental propositions in elementary geometry. Thus it is proved, that two triangles, having two sides of the one equal respectively to two sides of the other, and the two included angles equal, are equal in all respects ; and two triangles, having one side and the...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 172 sider
...BC, the sides AB and BC are together greater than AC. This, &c. ART. 44. If two triangles have two sides of the one equal respectively to two sides of the other, but the angle contained by each pair of these sides unequal,—the base of that triangle whose given...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 sider
...base. 40. To describe a triangle equal to a given quadrilateral figure. 41. If two triangles have two sides of the one equal respectively to two sides of the other, and have likewise the contained angles supplementary, the triangles are equal in area. 42. To bisect a...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - 1872 - 262 sider
...F the middle points of AB and CD. BF and DE trisect the diagonal A C. 50. If two triangles have two sides of the one equal respectively to two sides of the other, and the included angles supplementary, the triangles are equivalent. 51. The diagonals divide a parallelogram...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - 1872 - 216 sider
...prove the proposition by the help of the construction we must know, — 1. That if two AS have two sides of the one equal respectively to two sides of the other, and also the ^ included between the said sides in the first A equal to the ^ included between the said...
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An Elementary Geometry

William Frothingham Bradbury - 1872 - 124 sider
...F the middle points of AB and CD. BFand DE trisect the diagonal A C. 50. If two triangles have two sides of the one equal respectively to two sides of the other, and the included angles supplementary, the triangles are equivalent. 51. The diagonals divide a parallelogram...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873 - 588 sider
...less. IV. — If two triangles have two sides of the one equal to two sides of the other, each to each; and likewise the angles contained by those sides equal to one another; they shall likewise have theirbases, or third sides, equal; and the two triangles shall be equal; and...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 426 sider
...equiangular triangle is also equilateral. PROPOSITION XXXI. THEOREM, 115. lf two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of thefirst greater than the included angle of the second, then the third side...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 196 sider
..._f. DC< AB .f AC. Ex. 2. On the same sphere, or on equal spheres, if two spherical 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...
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