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" And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth... "
A Supplement to the Elements of Euclid - Σελίδα 284
των Daniel Cresswell - 1819 - 410 σελίδες
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Elements of Geometry, Containing the First Six Books of Euclid

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...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second, than the third has to the fourth.f 8. Proportion is a similitude of ratios. 9. Proportion consists of three terms at least. 10....

An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - 1826 - 430 σελίδες
...by hypothesis-K=g-, CE and a\so— >•£-, U r therefore we have ^>|, ^£ D COR. And if the first have a greater ratio to the second than the third has to che fourth, but the third the same ratio to the fourth which the fifth has to the sixth^ it may be...

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

Robert Simson - 1827 - 546 σελίδες
...greater •7 Def. 5. ratio to B, than E has to F*. Wherefore, if the first, &c. QED COR. And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,...

The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...every ratie which is greater than the former is also greater than the latter. COR. — And if the first have a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth which the fifth has to the sixth ; it may be demonstrated,...

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

Euclid - 1835 - 540 σελίδες
...ratio to c 7. def. 5. B than E has to F c. Wherefore, " if the fast, &c. QED COR. And if the first have a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth which the fifth has to the sixth ; it may be demonstrated...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 488 σελίδες
...to a second that a third has to a fourth ? When are mag. nitudes proportionals ? When does the first have a greater ratio to the second than the third has to the fourth ? and when a less ? When are magnitudes continual proportionals ? When is a magnilüde a mean proportional...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 σελίδες
...def. 7.) A has a greater ratio to B, than E has to F. Wherefore, if the first, &c. Cor. If the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,...

The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 σελίδες
...(V.dei.7) A has a greater ratio to B, than E has to F. Wherefore, if the first, &c. Cor. If the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 σελίδες
...ratio to B, than E has to F. (v. def. 7•) Wherefore, if the first, &c. QED COR. And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,...

Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 σελίδες
...has a greater ratio to B, than E has to F§. Wherefore, if the first, &c. QED COR. And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,...




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