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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...
The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ... - Page 57
by George Sturton Ward - 1862 - 79 pages

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

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,...

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

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...

The First Six Books: Together with the Eleventh and Twelfth

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...

Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

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...

The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

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...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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,...