 | Euclides - Geometry - 1841 - 378 pages
...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...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 fi'..*t has to th... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...d' e' f a' V U * c' 1/ 7' > a ' 7 * ? ' d' a' ( r У Of Ь edefg Ь' tí ОГ y g PROP. XXIII. THEO. If there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio ; the first shall have to the last of the first magnitudes the same... | |
 | Euclides - 1842 - 316 pages
...proportion. The proposition is usually cited by the words, ex cequali (sc. distantia), or ex &quo. PROP. XI. IF there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio : the first of the one set of magnitudes will have to the last,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...: 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... | |
 | Euclid - Geometry - 1845 - 218 pages
...number of magnitudes. Therefore, if there be any number, &c. QED ABCD EFGH PROPOSITION XXIII. THEOR. — If there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio ; the first shall have to the last of the first magnitudes, the... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...the number of magnitudes. Therefore, if there be any numberof magnitudes, &c. PROP. XXIII. THEOR. — If there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio ; the first has to the last of the first magnitudes the same ratio... | |
 | Euclides - 1845 - 546 pages
...be the number of magnitudes. Therefore, if there be any number, &c. QED PROPOSITION XXIII. THEOREM. If there be any number of magnitudes, and as many others, which taken two and two in a cross order, have the same ratio ; the Jirsl shall have to the last of the first magnitudes the same... | |
 | Euclides - 1846 - 292 pages
...greater than D, that is, D is less than F. Wherefore, If there be three %c. QED PROP. XXII. THEOS. If there be any number of magnitudes, and as many...two in order, have the same ratio, then the first shall have to the last of the first magnitudes the same ratio which the first of the others has to... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...the same manner is the demonstration extended to any number of magnitudes. PROP. XXIII. THEOR. iff there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio ; thefirst will have to the last of the first magnitudes the same... | |
 | Euclides - 1848 - 52 pages
...others. • NB This is usually cited by the words "ex tequali," or "ex aguo." PROP. XXIII. THEOREM. If there be any number of magnitudes, and as many others, which taken two and two, in a cross order, have the same ratio ; the first shall have to the last of the first magnitudes the same... | |
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IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross 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... 
