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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. "
The elements of geometry, in eight books; or, First step in applied logic - Pagina 216
door L J V. Gerard - 1874
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - 1816 - 294 pagina’s
...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 - 1819 - 208 pagina’s
...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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 pagina’s
...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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 pagina’s
...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...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pagina’s
...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...
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ELEMENTS OF GEOMETRY UPON THE INDUCTIVE METHOD.

JAMES HAYWARD - 1829
...coincide in all their 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 - 120 pagina’s
...plane of one 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 - 272 pagina’s
...the 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 ...

1835
...and С с ; draw P О perpendicular to Ce; and join OQ. Then, because the triangles С P с, С Q с have the three sides of the one equal to the three sides scribe two circles, and kt them cut one another in P; and from P draw PM perpendicular to А В : then...
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