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" Therefore, 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 extretnity equal... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 14
by John Playfair - 1806 - 311 pages
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...1.) to the angle BCD; but BDC has been proved to be greaterthan the same BCD; which is impossible. The case in which the vertex of one triangle is upon a side of the other needs no demonstration. PROP. VIII. THEOR. IF two triangles have two sides of the one equal to two sides of the other, each...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...1.) to the angle BCD; but BDC has been proved to be greater than the same BCD; which is impossible. The case in which the vertex of one triangle is upon a side of the other, needs no demonstration. PROP. VIII. THEOR. //' two triangles have two sides of the one equal to two sides of the other, each...
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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's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...wherefore the angle BDC is both equal to, and greater than the angle BCD; which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore upon the same base and on the same side of it, &c. QED PROPOSITION VIII. THEOREM. If two triangles have two sides of the one equal to two sides of...
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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
...greater than the same BCD ; and therefore AC cannot be equal to AD, and at the same time BC to BD. The case in which the vertex of one triangle is upon...side of the other, needs no demonstration. Therefore on the same base, and on the same side of it, &c. equal in magnitude to ACB : but this being contrary...
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...the triangle possesses this property is evident from the theorem, (Euclid, 7, I.) which proves that, "Upon the same base, and on the same side of it, there...triangles that have their sides which are terminated at one extremity of the base equal to one another, and likewise those which are terminated in the other...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...If two angles %c. QED COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOK. Upon the same base, and on the same side of it, there cannot be two triangles which have their sides terminated in one extremity of the base equal to one another, and also those...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1847 - 340 pages
...is, it is equal to it. COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there...which are terminated in one extremity of the base equai to one another, and likewise those which are terminated in the other extremity, equal to one...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...been proved to be greater than the same BCD; which is impossible. The case in which the vertex of the triangle is upon a side of the other, needs no demonstration. Therefore, upon the same "base, and on the same sides of it, there cannot be two triangles, that have their sides which are terminated in one extremity...
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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...the triangle possesses this property is evident from the Theorem (Euclid 7. 1.) which proves that " Upon the same base, and on the same side of it, there...triangles that have their sides, which are terminated at one extremity of the base, equal to one another, and likewise those which are terminated in the...
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