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" If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. "
Principles of Plane Geometry - Page 13
by James Wallace MacDonald - 1889 - 63 pages
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An essay on mechanical geometry, explanatory of a set of models

Benjamin Donne - 1796 - 120 pages
...on the other ; the line DF will coincide with AC, and EF with BC. THEOREM 16. If two triangles have three sides of one equal to the three sides of the other, each to each, thefe triangles are equal in every rcfpeft. — 8 E. 1, or 17 D. 1. Ciť For if the triangle DEF be...
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An Introduction to the Theory and Practice of Plane and Spherical ...

Thomas Keith - Navigation - 1810 - 478 pages
...construetion, also AB is common to the two triangles ABC and ADB, therefore the three sides of the one are equal to the three sides of the other, each to each. The angles -which are opposite to the equal sides in each triangle are equal. For, Produce the sides BC...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...Theorem. If two spherical triangles * on the same sphere, or on equal spheres, have the three sides of the one equal to the three sides of the other, each to each, the angles also of the one shall be equal to the angles of the other, each to each, to which thevequal...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...thus two circles having the same radius arc equal ; and two triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...BC : EF : : AC : DF; consequently FG = DF; hence the triangles EOF, DEF, have the three sides of the one equal to the three sides of the other, each to each ; they are therefore equal (43). But, by constr .ction, the triangle EGF is equiangular with the triangle...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...thus two circles having the same radius are equal ; and two triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 504 pages
...equally obtuse. PROPOSITION Til. (B) In any two spherical triangles, if the three sides of the one be equal to the three sides of the other, each to each, the angles which are opposite to the equal sides will be equal. Let ABC be any triangle on the surface...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, have the three sides of the one equal to the three sides of the other, each to each, viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let AB be that side...
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A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...circle, meet in the poles of that circle. PROP. V. If two spherical triangles have the three sides of the one equal to the three sides of the other, each to each, the angles which are opposite to the equal sides are likewise equal ; and conversely. PROP. VI. If two...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...each. For, if the polar triangles A' B' C', D' E' F be described, they will have the three sides of the one equal to the three sides of the other, each to each, because every two corresponding sides, as A' B' and D' E' are (7.) supplements of the measures of equal...
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