| Euclides - 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 - Euclid's Elements - 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 - 320 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 - 380 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 - 544 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 - 332 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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