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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. "
Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ... - Page 281
by Charles Davies - 1872
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An essay on mechanical geometry, explanatory of a set of models

Benjamin Donne - 1796
...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. Ci 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 - 420 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, Spherical - 1816 - 294 pages
...triangles, which 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
...will 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...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...the 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...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...will be equal to the arc ENG. 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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...line AD 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
...base 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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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 442 pages
...through two given points on the surface of the sphere. Hence, the three sides of the one triangle being equal to the three sides of the other, each to each, the triangles are equal. (Prop, vu.) Secondly, let the triangles be situated on contrary sides of the centre...
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Elements of Geometry Upon the Inductive Method

James Hayward - Geometry - 1829 - 172 pages
...coincide in all their parts ; they are not different, therefore, but equal; and we 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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