 | Robert Simson - 1762 - 488 sider
...Wherefore, by Compofitionc, BA is to AE, as DC is to CF. If therefore four, &c. D. D SceK. PROP. XX. THEOR. IF there be three magnitudes, and other three, 'which taken two and two have the fame ratio ; if the firft be greater than the third, the fourth fhall be greater thaq the lixili ;... | |
 | Euclid - 1765 - 492 sider
...and L, N equimultiples of c, F : Therefore as A is to c, fo will [by 5. def. 5.] D be to F. Wherefore if there be three magnitudes, and other three, which taken two and two in a crofs order, are in the fame ratio, the firft fhall have to the laft of the firft magnitudes,... | |
 | Robert Simson - 1775 - 534 sider
...compofition *, BA is to AE, as DC is to CF : If, therefore, four, &c. Q._E. D. BD PR 0 P. XX. THEO R. IF there be three magnitudes, and other three, which taken two and two have the lame ratio ; if the firfl be greater than the third, the fourth fhall be greater than (he fuUi : and... | |
 | Euclid - 1781 - 552 sider
...compofitionc, BA is to AE, as DC is to CF : If, therefore, four, &c. Q;_E. D. PRO P. XX. THEO R. BD SceN. IF there be three magnitudes, and other three, which, taken two and two, have the fame ratio ; if the firft be greater than the third, the fourth fhall be greater than the fixth ; and... | |
 | Euclid, John Playfair - 1795 - 462 sider
...18 ? b7 compofition c, A : A — B : : C : C— D. Therefore, &c. QED, PROP. PROP. XX. THEO R. t . t IF there be three magnitudes, and other three, which, taken two and two, have the fame ratio ; If the firlt be greater than the third, the fourth Ihall be greater than the iixth; and... | |
 | Nicolas Vilant - 1798 - 196 sider
...A=D : C, Prop. B. Jointly, A + B : A=-.C+P : C, Prop. XVIII. PROPOSITION PROPOSITION XX— THEOREM. If there be three magnitudes, and other three, which taken two and two ordinately (Def. XVIII, XIX.), have the fame ratio; if the firft be greater than the third, the fourth... | |
 | Robert Simson - 1806 - 546 sider
...Wherefore, by composition c, BA is to AE, as DC is to CF. If, therefore, four, &c. QED EF PROP. XX. THLOR. 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,... | |
 | John Playfair - 1806 - 320 sider
...Therefore, &c. QED COR. In the same way it may be proved that A : A+B : : C : C+D. PROP. XX. THEOR. Bookv. 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 is greater than the sixth ; if equal, equal; and... | |
 | John Mason Good - 1813 - 714 sider
...exciss above the second, as the third to its excess above the fourth. Prop. XX. Theor. If there he 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;... | |
 | Euclides - 1816 - 588 sider
...composition c, BA is to AE, as DC is to CF : If, therefore, four, &c. QED A C F B 35 PROP. 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,... | |
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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, equal; and if less, less. 
