 | Robert Simson - 1827 - 546 σελίδες
...as DF to FC ; wherefore, by composition*, BA is to AE, as BD DC is to CF. If therefore four, &c. 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,... | |
 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...C : C - D. In a similar way it may be proved that A:A + B = C:C + D. PROPOSITION XX. THEOREM. (499) 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 is greater than the sixth ; and if equal,... | |
 | Euclid, Robert Simson - 1829 - 548 σελίδες
...to FC. Wherefore, by composition (18. 5.), BA is to AE, as DC is to CF. If, therefore, four, &c. QED PROP. XX. THEOR. IF there be three magnitudes, and...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,... | |
 | John Playfair - 1832 - 358 σελίδες
...A— B : : C : C— D. Therefore, &c. QED COB. In the same way, it may be proved that A: A+B::C: C+D. PROP. XX. THEOR. If there be three magnitudes, and...three, which taken two and two, have the same ratio; if I he first be greater than the third, the fourth is greater than the sixth; if equal, equal; and if... | |
 | Robert Simson - 1835 - 544 σελίδες
...to FC. Wherefore, by composition c, BA is to AE, as DC is to CF: « If, therefore, four," &c. QED BD PROP. XX. THEOR. If there be three magnitudes, and...than the sixth ; if equal, equal ; and if less, less. Let A, B, C be three magnitudes, and D, E, F other three, Book V. which, taken two and two, have the... | |
 | Euclid - 1835 - 540 σελίδες
...FC. Where- K fore, by composition c, BA is to AE, as DC is to CF: « Jf, therefore, four," &c. QED BD PROP. XX. THEOR. If there be three magnitudes, and...greater than the sixth ; if equal, equal ; and if less, lets. Let A, B, C be three magnitudes, and D, E, F other three, Book V. which, taken two and two, have... | |
 | 1836 - 488 σελίδες
...that is, the first is to its excess above the second, as the third to its excess above the fourth. XX. If there be three magnitudes, and other three, which...if the first be greater than the third, the fourth is greater than the sixth ; if equal, equal ; and if less, less. XXI. If there be three magnitudes,... | |
 | John Playfair - 1837 - 332 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...if the first be greater than the third, the fourth is greater than the sixth ; if equal, equal ; and if less, less. If there be three magnitudes, A, B,... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...that the first is to the sam of the first and second, as the third to the sum of the third and fourth. IF there be three magnitudes, and other three, which,...if the first be greater than the third, the fourth is greater than the sixth ; if equal, equal ; and if less, less. Let A, B, C be three magnitudes, and... | |
 | Andrew Bell - 1837 - 290 σελίδες
.... — • D ; therefore, by composition (V. 18), A : A — B : : C:C— D. PROPOSITION XX. THEOREM. If there be three magnitudes, and other three, which, taken two and two in order, have the same ratio ; if the first be greater than the third, the fourth shall be greater... | |
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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... 
