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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. "
Elementary Geometry: With Applications in Mensuration - Page 112
by Charles Davies - 1850 - 216 pages
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...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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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 382 pages
...contradicts the hypothesis: therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also b« equal, each to each, and the triangles themselves will be equal. Let...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...two sides and the contained angle of the other : in the eighth, when the three sides of the one are equal to the three sides of the other, each to each ; and in the twentysixth, when two angles and a side of the one are respectively equal to two angles and...
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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 - 288 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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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...are equal (Def. 4), therefore AD=DB (BI Prop. 19, Cor. 2); hence the two triangles ACD, BCD, having the three sides of the one equal to the three sides of the other, are equal, (B. I. Prop. 22), and the angles ACD, BCD, are equal ; and therefore the arcs AE, EB,are...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - Geometry - 1845 - 382 pages
...two sides and the contained angle of the other: in the eighth, when the three sides of the one are equal to the three sides of the other, each to each: and in the twenty-sixth, when two angles and a side of the one are respectively equal to two angles and...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...AP, since PB = PC, the oblique line AB = AC (B. VI, Prop, v) ; therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other ; consequently they are equal (BI, Prop, vm), and the angle ADB is equal to ADC ; therefore each is...
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