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" ... If there be three magnitudes, and other three, which have the same ratio taken two and two, but in a cross order; then if the first magnitude be greater than the third, the fourth shall be greater than the sixth: and if equal, equal; and if less,... "
The First Six Books of the Elements of Euclid, with a Commentary and ... - Σελίδα 107
των Euclid, Dionysius Lardner - 1828 - 324 σελίδες
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1804 - 440 σελίδες
...and other three, which ^ have the fame ratio taken two and two, but in a crofs order ; if the firft magnitude be greater than the third, the fourth is greater than the fixth ; if equal, equal ; and if lefs, lefs. If there be three magnitudes, A, B, C, and other three,...

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

John Playfair - 1806 - 311 σελίδες
...first case, if C>A, F>D, that is, if A<C, D<F. Therefore, &c. QED A, B, C, D, E, F. PROP. XXI. THEOR. IF there be three magnitudes, and other three, which...same ratio taken two and two, but in a cross order ; if the first magnitude be greater than the third, the fourth is greater than the sixth; if equal,...

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

Robert Simson - 1806 - 518 σελίδες
...5. . c Cor. 13. sd 10. 5. e 7. 5. f 11. 5. 9 5A D c F Let A, B, C be three magnitudes, and D, E, F other three, which have the same ratio, taken two and two, but in a cross order, viz. as A is to B, so is E to F, and as B is to C, so is D to E. If A be greater than C, D shall be...

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

John Mason Good - 1813
...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 three, which have the same ratio taken two aud two, but in a cross order; if the first magnitude be greater than the third, the fourth shall be...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...wherefore D is to E, asF tc E f ; and therefore D is equal to Fs. A. PROP. XXI. THEOR. Therefore, it IF there be three magnitudes, and other three, which have the same ratio taken two and t\vo, but in a cross order; if the first magnitude be greater than the .third, the fourth shall be...

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

Euclides - 1816 - 528 σελίδες
...8.5, k 13.5. Cor. 15.5. .* 10. S. p7. 5. * 11. 5. «9. 5. Let A, B, C be three magnitudes, and D, E, F other three, which have the same ratio, taken two and two, but in a cross order, viz. as A is to B, so is E to F, and as B is to C, so is D to E. If A be greater than C, D shall be...

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

John Playfair - 1819 - 333 σελίδες
...therefore, by the first case, if C-/A; FyD, that is, if A^C, D^.F. . Therefore, &c. QED x PROP. XXI. THEOR. If there be three magnitudes, and other three, which...same ratio taken two and two, but in a cross order ; if the first magnitude, be greater than the third, the fourth is greater than the sixth ; if equal,...

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

John Mason Good - 1819
...sixth ; nivl if equal, equal ; and if lets, less. Prop. XXI.Theor. If there be three magnitudes, •nd other three, which have the same ratio taken two and two, but in a cross order ; if the first magnitude be greater than the third, the fourth shall be greater than the sixth ; and...

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

Euclid, Robert Simson - 1821 - 516 σελίδες
...first case; and therefore D is less than F Therefore, if there be three, &c. QED PROP. XXI. THEOR. IP there be three magnitudes, and other three, which...same ratio taken two and two, but in a cross order, if the first magnitude be greater than the third, the fourth shall be greater than the sixth; and if...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...it is shown that when A is equal to C, D is equal to F ; and if less, less. QED I/ PROP. XXI. THEOR. If there be three magnitudes, and other three, which...same ratio taken two and two, but in a cross order ; if the first be greater than the third, the fourth shall also be greater than the sixth; if equal,...




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