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" If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ratio which the first of the others has to the last. NB This is usually... "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 217
von Euclides - 1861
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 Seiten
...: A : : F : E, therefore, by this first case, since C 7 A, F 7 D, that is, D/F. PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, which, taken two ana two in order, have the same ratio ; the first will have to the last of the first magnitudes, the...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 Seiten
...demonstrated in the 22d proposition of this book. 20. Ex tequo, inversely ; when there are three or more magnitudes, and as many others, which taken two and two in a rro.ii order, have the same ratio; that is, when the first magnitude is to the second in the first...
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The Elements of Euclid

Euclid - 1838 - 416 Seiten
...whatever be the number of magnitudes. Therefore, if there be any number, &c» QED PROP. XXIII. THEOR. IF there be any number of magnitudes, and as many...have to the last of the first magnitudes the same jatio which the first of the others has to the last. NB This is usually cited by the words " ex sequali...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...H. In the same manner is the demonstration extended to any number of magnitudes. PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two, irregularly, have the same ratio ; the first will have to the last of the first series of magnitudes...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 Seiten
...greater than D, that is, D is less than F. Therefore, if there be three, &c. QED PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio; the first shall have to the last of the first magnitudes, the same ratio...
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 98 Seiten
...shown that : ! ^ .-. by the first case Q is that is, 0 "^ OIf there be three, &c. PROP. XXII. THEO. If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes the same ratio...
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 98 Seiten
...<?> :; (¿) : /\ For, because Гу, i^=J, |з) are three magnitudes, and @, ПП, /N. other three, which, taken two and two in a cross order, have the same ratio, therefore, by the first case, [^ 0 :: 0 : /^> therefore again, by the first case, ГП : o) :; and...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...(Schol. C.) a + c 4 e : a :: b + d + /, which represents the proportion AB :: A+C + E:B + D + F. PROP. X. IF there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio : the first of the one rank of magnitudes will have to the last, the same...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 Seiten
...: A : : F : E, therefore, by this first case, since Cy A, F "7 D, that is, D/F. PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, which, taken two ana two in order, have the same ratio ; the first will have to the last of the first magnitudes, the...
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A Treatise on Algebra: Arithmetical algebra

George Peacock - 1842
...magnitudes in each set. Ex iequali 298. " If there be any number of magnitudes and as many in proper- otners which, taken two and two in a cross order, have the same tione perturbati. ratio; namely, if the first be to the second of the first set of magnitudes as the...
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