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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, Conic Sections, and Plane Trigonometry - Page 27
by Elias Loomis - 1877 - 443 pages
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A concise system of mathematics

Alexander Ingram - Mathematics - 1830 - 462 pages
...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. PROP. VI. If two...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...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 ...

Mathematics - 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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...these results contradicts the hypothesis: therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one equal...the other, each to each, the three angles will also bę equal, each to each, and the triangles themselves will be equal. Let the side ED=BA, the side EF-BC,...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...Which was to be proved. COR. Hence, every equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the one equal...to the three sides of the other, each to each ; the angles opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three sides...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 pages
...results contradicts the hypothesis: therefore, BAC is greater• than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one equal...each, and the triangles themselves will be equal. 20 GEOMETRY. Let the side ED=BA, the side EF=BC, and the side DF=AC ; then will the angle D=A, the...
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 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. VH.) Secondly, let the triangles be situated on contrary sides of the centre...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...agree in having two sides, and the angle contained by those sides, equal (as in Prop. 4); or, in having the three sides of the one equal to the three sides of the other (as in Prop. 8) ; or, finally, in having two angles and a side, similarly placed with respect to the...
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A Treatise on Geometry and Its Application in the Arts

Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...different forms. This proposition is usually enounced thus : — If two triangles have the three sides of one equal to the three sides of the other each to each, then the three angles will le equal each to each, and their areas will be equal. (63.) When two sides...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 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 other, each to each, namely, AD common to both, AB = AC, by hypothesis, and BD = DC, by construction; therefore (43) the...
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