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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
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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 ;...
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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,...
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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...
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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...
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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...
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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...
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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,...
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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,...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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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