| Andrew Bell - 1837 - 240 sider
...same manner is the demonstration extended to any number of magnitudes. 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 first shall have to the last of the first magnitudes the same... | |
| John Playfair - 1837 - 318 sider
...: 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 - 1838 - 416 sider
...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 same** jatio which the first of the others has to the last. NB This is usually cited by the words " ex sequali... | |
| Euclid, Robert Simson - 1838 - 416 sider
...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 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 - 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 sider
...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...of the first magnitudes, the same ratio which the** fi'..*t has to th . last of the others. N. 13. This is usually cited by the words " ex aequali," or... | |
| Oliver Byrne - 1841 - 98 sider
...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...the first magnitudes the same ratio which the first** of the others has to the last of the same. NB — This is usually cited by the words "ex œquali in... | |
| Oliver Byrne - 1841 - 98 sider
...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
...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 - 1842 - 317 sider
...: 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... | |
| |