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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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 466 pages
...equal to the triangle b ACB, the o / \ r* b. 4- 1• kfs to the greater; which is abfurd. Therefore AB is not unequal to AC, that is, it is equal to it....&c. Q^ED COR. Hence every equiangular triangle is alfo equilateral. PROP. VII. THEOR. UPON the fame bafe, and on the fame fide of it,seeN. there cannot...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 520 pages
...further from the ftraight line AB, and then comes nearer to it, which is alfo impoflible. Therefore FE is not unequal to AC, that is, it is equal to it. PRO P. i. If two equal ftraight lines rtC, BD be each at right angles to the fame ftraight line AB;...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 550 pages
...further from the ftraight line AB, and then comes nearer to it; which is alfo impoffible. Therefore FE is not unequal to AC, that is, it is equal to it. PROP. 2. If two equal ftraight lines AC, BD be each at right angles to the fame ftraight line AB ;...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 466 pages
...impofllble. and the fame thing will follow, if FE be faid to be greater than CA, or DI3. therefore FE is not unequal to AC, that is, it is equal to it. PROP. 2. If two equ.il ftraight lines AC, BD be each at right angles to lj-c fame ftraight line AB...
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Elements of Geometry: Containing the First Six Books of Euclid, with Two ...

John Playfair - Trigonometry - 1795 - 444 pages
...DBC is equal to the U 4, i, triangle b ACB, the lefe to the greater ; which is abfurd. Therefore AB is not unequal to AC, that is, it is equal to it....&c. Q'.ED CoR. Hence every equiangular triangle is alfo equilateral. PROP. PROP. VII. THEOR. Book i. UPON the fame bafe, and on the fame fide of it, there...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 351 pages
...to BooK I. to the triangle b ACB, the lefs to the greater ; which is abfurd. *— ^VsJ Therefore AB is not unequal to AC, that is, it is equal to it. b. 4. i. Wherefore, if two angles, &c. Q^ED CoR. Hence every equiangular triangle is alfo equilateral....
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1804 - 470 pages
...equal to the b 4. i. triangle b ACB, the lefs -to the greater ; which is abfurd. Therefore, AB is net unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. (XE.D. CoR. Hence every equiangular triangle is alfo equilateral. PROP. PROP. VII. THEO R. Book I....
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...impoflible. and the fame thing will follow, if FE be <"aid to be greater than CA, or DB. therefore FE is not unequal to AC, that is, it is equal to it. PROP. 2. If two equal ftraight lines AC, BD be each at right angles to the fame ftraight line AB ;...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...less to the greater, whichfis absurd. Therefore AB is not unequal to AC, that is, it is equal to 5t.jf Wherefore, if two angles, &c. QED COR. Hence every...THEOR. UPON the same base, and on the same side of it, se N. there cannot be two triangles, that have their sides which are terminated in one extremity...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...equal to the triangle b ACB, the less to the great- / \\ b4. 1. er ; which is absurd. Therefore AB is / ^\ not unequal to AC, that is, it is equal to *• * it. Wherefore, if two angles, &c. QED B CoR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. UPON the same base,...
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