 | Robert Simson - Trigonometry - 1762 - 488 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... | |
 | Robert Simson - Trigonometry - 1775 - 534 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;... | |
 | Euclid - 1781 - 552 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 ;... | |
 | Robert Simson - Trigonometry - 1781 - 534 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1795 - 462 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... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 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.... | |
 | John Playfair, Euclid - Circle-squaring - 1804 - 468 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.... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...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 ;... | |
 | John Playfair - Mathematics - 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, s«e N. there cannot be two triangles, that have their sides which are terminated in one extremity... | |
 | Robert Simson - Trigonometry - 1806 - 546 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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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... 
