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" UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity... "
Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 12
by Euclides - 1842
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...them are also equal. COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base, and on the same side of it, there cannot be two triangles having their conterminous sides at both extremities of the base, equal to each other. PROP. VIII. THEOR. If two...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...— Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base (AB), and on the same side of it, there cannot be two triangles having their conterminous sides (AC and AD, BC and BD) at both extremities of the base, equal to each other. When...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...triangle DBC is equal* to the triangle ACB, the less to the greater, which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. QED COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base,...
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Chambers's information for the people, ed. by W. and R. Chambers, Volume 2

Chambers W. and R., ltd - 1842 - 744 pages
...triangle DBC is equal to the triangle ACB, the less to the greater, which is absurd. Therefore, AB is not unequal to AC ; that is, it is equal to it. The corollary or inference drawn from this is, that all triangles having equal angles have also equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...equal to that of the triangle (4. 1.) ACB, the less to the greater ; which is absurd. Therefore, AB is not unequal to AC, that is, it is equal to it. COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and...
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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volume 2

Church schools - 1844 - 456 pages
...of another, of which the solidity is three times that of the former ; 1841. GEOMETRY. 1 . Prove that upon the same base, and on the same side of it, there cannot be two triangles which have the sides terminated in one extremity of the base equal to one another, and likewise those...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...DBC is equal to the triangle || ACB, the less to the II 4. i. greater ; which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it....Hence every equiangular triangle is also equilateral. PROPOSITION VII. THEOR. — Upon the same base, and on the same side of it, there cannot be two triangles...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...triangles, &c. QED COB. Hence every equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...equal to the triangle ACB, the less to the greater ; which is absurd. Therefore AB is not un- E equal to AC, that is, it is equal to it. Wherefore, if two angles, &c. Cor. Hence every equiangular triangle is also equilateral. axiom, which ought not to be done without...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...triangle DBC is equal to the triangle ACB, the less to the greater — which is absurd: Therefore AB is not unequal to AC, that is, it is equal to it. Wherefore, If two angles %c. QED COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOK. Upon the same...
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