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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. "
An essay on mechanical geometry, explanatory of a set of models - Page 26
by Benjamin Donne - 1796
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 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 - 208 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 - 280 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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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 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 - 462 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...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...equilateral triangles. JoinBD; then because the triangles В FD, В С D have the three sides of the one equal to the three sides of the other, each to each, the angle В FD is equal to the angle В С D (I. 7.), that is, to the angle of a regular pentagon...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...last circle in F ; and join FA, F В. Then, because the triangles ECD, FAB have the three sides of the one equal to the three sides of the other, each to each, (7.) they are equal in every respect, and the angle at A is equal to the angle at C. Therefore, &c....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also bę equal, each to each, and the triangles themselves will be equal. Let...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the one equal to the three sides of the other, each to each ; the angles opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three...
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