 | Euclides - 1846 - 292 σελίδες
...Therefore, by composition (5. 18), BA is to AE as DC is to CF. Wherefore, If four magnitudes <Sfe. QED PROP. XX. THEOR. If there be three magnitudes, and...three, which, taken two and two, have the same ratio, then, if the first be greater than the third, the fourth shall be greater than the sixth, and if equal,... | |
 | Dennis M'Curdy - 1846 - 168 σελίδες
...magnitudes, &c. QED Recite (a) def. 10, 5 ; (4) p. 15, 5; (c) Note 3, page 32; (d) p. A of b. 5. 21 Th. If there be three magnitudes, and other three, which, taken two and two, out of order, have the same ratio; if the first be greater than the third, the fourth will be greater... | |
 | Euclides - 1848 - 52 σελίδες
...is to its excess above the second, as the third to its excess above the fourth. PROP. XX. THEOREM. If there be three magnitudes, and other three, which,...if the first be greater than the third, the fourth shall be greater than the sixth, and if equal, equal ; and if less, less. PROP. XXI. THEOREM. If there... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...Wherefore, by composition (18. v.), BA is to AE, as DC is to CF. If, therefore, four, etc. QED PROPOSITION XX. THEOR. If there be three magnitudes, and other...if the first be greater than the third, the fourth shall be greater than the sixth; and if equal, equal; and if less, less. Let A, B, C be three magnitudes,... | |
 | Euclides - 1853 - 176 σελίδες
...to ae as dc is to c f. If, therefore, four magnitudes, &c. QED bd a d PROPOSITION XX. — THEOREM. If there be three magnitudes, and other three, which, taken two and two, have the same ratio ; ifthefirst be greater than the third, the fourth shall be greater than the sixth, and if equal, equal... | |
 | Euclid, John Playfair - 1853 - 336 σελίδες
...composition (18. 5.), A : AB :: C : CD. COR. In the same way, it may be proved that A : A+B : : C : C+D. PROP. XX. THEOR. If there be three magnitudes, and other three, which taken two and two, hare the same ratio; if the first be greater than the third, the fourth is greater than the sixth ;... | |
 | Euclides - 1855 - 270 σελίδες
...the next proposition given in the original Greek, which he declares to be vitiated PROP. XX. THEOREM. If there be three magnitudes, and other three, which, taken two and two, have the same ratio i and if the first be greater than the third, the fourth is greater than the sixth ; if equal, equal;... | |
 | Euclides - 1855 - 230 σελίδες
...another. HYPOTHESES. V. 21. . . V. 7. V.8. . . . V. 10 V. 11 VF (p. 63). . VG (p. 64). . VH (p. 65). . If there be three magnitudes, and other three, which, taken two and two, have the same ratio, then if the first be greater than the third. If there be three magnitudes, and other three, whichhave... | |
 | Euclid - 1859 - 150 σελίδες
...y' Kai rо TÉrapTov TOV '¿KTOv pЛСоv larat' rаí íàv laov, laov' fai iàv i\aaaov, i\aaaov. If there be three magnitudes, and other three, which, taken two and two, have the same ratio; and if the first be greater than the third, the fourth is greater than the»ixth; if equal, equal;... | |
 | Eucleides - 1860 - 396 σελίδες
...therefore A ~ B _ ^ C ~DC A 0 and A ~E therefore A : A ~ B :.- C : C ~ D. PROPOSITION XX. THEOREM. — If there be three magnitudes, and other three, which, taken two and two, have the same ratio; then if the first be greater than the third, the fourth shall be greater than the sixth ; and if equal,... | |
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XX. THEOR. IF there be three magnitudes, and other three, which, taken two and two, have the same ratio ; if the first be greater than the third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less... 
