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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: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 346 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 Bide of the other, needs no demonstration. Therefore, upon the same base, and on the same side of it,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...triangle is also equilateral. PROPOSITION VII. See N. THEOR. — Upon the same base, and on the mine side of it, there cannot be two triangles that have their sides which arc terminated in one extremity of the base, equal to one a not her, and likewise those which are terminated...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...a 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...base, and on the same side of it, there cannot be two trianyles that have tfieir sides which are terminated in one extremity of the base equal to one another,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
..." 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...demonstration. Therefore, upon the same base, and on thf* same side of it, there cannot be two triangles that have their sides which are terminated in one...
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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
...equal (I. 5.) to 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...side of the other, needs no demonstration. Therefore on the same base, and on the same side of it, there cannot be two triangles that have their sides which...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...equal 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. PROPOSITION VIII. THEOREM. If two triangles have two sides of the one equal to two sides of the other,...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...2. that .'. Aflisnot =/= AC, ie, that AB = AC. PROPOSITION VII. (Argument ad Absurdum.) Theorem. On the same base, and on the same side of it, there cannot be two triangles that have their sides terminated in one extremity of the base equal to each other, and likewise those terminated in the other...
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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....
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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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...two angles, &c. QED COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there cannot be two triangles thai have their sides which are terminated in one extremity of the base equal to one another, and likewise...
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