| 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 - 552 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 - 714 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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