 | Robert Simson - Trigonometry - 1762 - 488 pages
...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 - Geometry - 1765 - 492 pages
...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 - Trigonometry - 1775 - 534 pages
...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 - 550 pages
...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 - Euclid's Elements - 1795 - 462 pages
...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 - Algebra - 1798 - 196 pages
...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 - Trigonometry - 1806 - 546 pages
...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,...third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less. A D B E c F -Let A, B, C be three magnitudes, and D, E,... | |
 | John Playfair - Euclid's Elements - 1806 - 320 pages
...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,...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,... | |
 | John Mason Good - 1813 - 722 pages
...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...third, the fourth shall be greater than the sixth; and if equal, equal; and if less, 1res. Prop. XXI. Theor. II' there be three magnitudes, and other... | |
 | Euclides - 1816 - 588 pages
...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,...third, the fourth shall be greater than the sixth, and if equal, equal ; and if less, less. C F Lat A, B, C, be three magnitudes, and D, E, F other three,... | |
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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... 
