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" Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. "
Self-examinations in Euclid - Page 9
by John Martin Frederick Wright - 1829 - 188 pages
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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...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...97.), and the side CB to CA. Hence, in the two spherical triangles CAD, CDB, the three sides of the one are equal to the three sides of the other, each to each ; therefore, (Art. 86.) the angle CBD is equal to the angle CAD ; and the angle CBF has been shewn...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...shall have GC < BC, or EF< BC. THEOREM. 43. Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (Jig. 23), AC = DF,^g 23BC=EF ; then the angles will be equal,...
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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
...shall have GC <[ BC, or EF<BC. THEOREM. 43. 7V0o triangles are equal, when the three sides of the one are '< equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) JtC = DF, ^6- 23BC — EF ; then the angles will be...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...shall have GC < BC, or EF<BC. THEOREM. 43. 7\ťo triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) AC - DF, F'g.23BC = EF ; then the angles will be equal,...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 504 pages
...construction, also AB is common to the two triangles ABC and ABD, 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, If о be the centre...
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...also equal.* 4. The two angles at the basis of an isosceles triangle are equal to one another. 5. If the three sides of one triangle are equal to the three sides of another, each to each, the two triangles coincide with each other throughout ; that is, their angles...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...another: it shall be a parallelogram. For, in the triangles ABD, С DB, the three sides of the one are equal to the three sides of the other, each to each • therefore, the angle ABD is equal to С DB (7.), and (15.) AB is parallel to С D. And, for the...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 204 pages
...also equal.* 4. The two angles at the basis of an isosceles triangle are equal to one another. 5. If the three sides of one triangle are equal to the three sides of another, each to each, the two triangles coincide with each other throughout ; that is, their angles...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...one another: it shall be a parallelogram. For, in the triangles ABD, CDB, the three sides of the one are equal to the three sides of the other, each to each ; therefore, the angle ABD is equal to С DB (7.), and (15.) AB is parallel to С D. And, for the like...
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