 | Robert Simson - 1838 - 434 σελίδες
...FC. Wherefore, by composition (18. 5.), BA is to AE, as DC is to CF. If, therefore, four, &c. QED BD 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,... | |
 | Euclid - 1838 - 470 σελίδες
...FC. Wherefore, by composition (18. 5.), BA is to AE, as DC is to CF. If, therefore, four, &c. QED BD PROP. XX. THEOR. IF there be three magnitudes, and other three, which, takeq two and two, have the same ratio ; if the first be greater than the third, the fourth shall be... | |
 | Euclides - 1840 - 192 σελίδες
...'. C : C — D (v. Prop. i3). 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 in the same order, have the same ratio; if the first be greater than the third, the fourth is greater... | |
 | Oliver Byrne - 1841 - 144 σελίδες
...ex sequali in proportione pertúrbala seu inordinatâ " infers that A : F ;: L : Q. PROP. XX. THEO. 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... | |
 | Euclides - 1841 - 378 σελίδες
...as DF to FC; therefore, by composition,* BA is to AE, as DC is to CF. If, therefore, four, SEC. QED PROP. XX. THEOR. If there be three magnitudes, and other three, which, taken two ai'd two, have the same ratio; then if the first *3. 5. * Hyp * 13. 5. * B. 5. * Cor. 13 5. * 10. 5.... | |
 | John Playfair - 1842 - 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 - 1845 - 382 σελίδες
...that the first is to the sum of the first and second, as the third to the sum of the third and fourth. PROP. XX. THEOR. — If there be three magnitudes,...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... | |
 | Euclid - 1845 - 218 σελίδες
...Wherefore, by composition J, BA is to AE, as DC is to CF. If, therefore, four, &c. QBD PROPOSITION XX. THEOR. — If there be three magnitudes, and other...same ratio ; if the first be greater than the third, t!ie fourth shall be greater than t!ie sixth; and if equal, equal; and if less, less. Let A, B, C be... | |
 | Euclides - 1845 - 546 σελίδες
...composition, BA is to AE,'as DC is to CF. (v. 18.) If therefore four, &c. QED 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... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...composition (18. 5.), A: AB ::C: CD. COR. In the same way, it may be proved that A : A+B : : C : CfD. 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,... | |
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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... 
