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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. "
Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ... - Página 155
por Euclides - 1840
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - 1816 - 352 páginas
...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 - 1819 - 574 páginas
...the other, coincide entirely ; 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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 280 páginas
...however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. .fc 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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 294 páginas
...equivalent, however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. 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...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 276 páginas
...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 - 276 páginas
...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...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - 1829 - 228 páginas
...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 - 1830 - 458 páginas
...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....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 páginas
...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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 páginas
...describe (42.) the equilateral triangle BDC, and join A D. Then, because the triangles AB D, А С D have the three sides of the one equal to the three sides of the other, each to each, (7.) the angle BAD is equal to the angle CAD, Therefore, &c. Cer. By repeating this process...
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