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" 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, equal ; and if less, less... "
An Elementary Treatise on Algebra: Theoretical and Practical ... - Σελίδα 341
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...DF to FC. 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

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...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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...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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...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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...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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...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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...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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...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,...if the first be greater than the 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...

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...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...if the first be greater than the third, the fourth shall be greater than the sixth; and if equal, equal; and if less, 1res. Prop. XXI. Theor. II' there...

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...is. 5. fore, by 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...if the first be greater than the 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...




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