 | John Playfair - 1837 - 332 σελίδες
...: 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 - 410 σελίδες
...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 - 470 σελίδες
...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 - 192 σελίδες
...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 - 378 σελίδες
...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 - 144 σελίδες
...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 - 140 σελίδες
...<?> :; (¿) : /\ 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 - 316 σελίδες
...(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 - 332 σελίδες
...: 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 - 426 σελίδες
...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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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... 
