| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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