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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. "
Elements of Geometry and Trigonometry: With Practical Applications - Page 57
by Benjamin Greenleaf - 1862 - 490 pages
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An essay on mechanical geometry, explanatory of a set of models

Benjamin Donne - 1796 - 118 pages
...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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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...are equal to them, are equal to one another. (2l6.) COR. 2. Hence, if two spherical triangles have the three sides of the one equal to the three sides of the other, or two sides and the included angle in the one, equal to two sides and the included angle, in the other,...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...be equal to the arc EJVG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will have the three sides of the one equal to the three sides of the other, each to each, namely, AC = EO, CD= OG and AD = EG; therefore these triangles are equal (43); hence the angle ACD...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...from the vertex A the arc AD be drawn to the middle of the base, the two triangles ABD, ADC, will have the three sides of the one equal to the three sides of the other, each to each, namely, AD common, J3D= DC, AB — AC; consequently, by the preceding theorem, the two trhngles will...
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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
...figure will be a parallelogram. Demonstration. Draw the diagonal BD ; the two triangles ABD, BDC, have the three sides of the one equal to the three sides of the other, each to each, they are therefore equal, and the angle ADB opposite to the side AB is equal to the angle DBC opposite...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...from the vertex A to the point D the middle of the base BC ; the two triangles ABD, ADC, will have the three sides of the one, equal to the three sides of the qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 272 pages
...at right angles. OF 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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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 172 pages
...parts ; they are not different, therefore, but equal; and \ve say, universally, When two triangles have the three sides of the one equal to the three sides of the other respectively, the angles will also be equal, respectively, and the two triangles will be equal in all...
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A concise system of mathematics

Alexander Ingram - Mathematics - 1830 - 120 pages
...and the same great 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
...three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the othrr, each to each, viz. those which are opposite to the equal angles.* Let the spherical triangles...
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