| James Ryan, Robert Adrain - 1824 - 516 sider
...of the proposition may be shown, whatever be the number of magnitudes. QED 3«J 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 6rst shall have to the last of the first magnitudes the same... | |
| James Ryan, Robert Adrain - 1824 - 516 sider
...truth of the proposition may be shown, whatever be the number of magnitudes. 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 6rst shall have to the last of the first magnitudes the... | |
| James Ryan - 1826 - 383 sider
...greater than C, D will be greater than F ; if equal, equal ; and if less, less. PROP. XXII. THEOR. **If there be any number of magnitudes, and as many others, •which,** take two and two in order, have the same ratio ; the first shall have to the last of the first rank... | |
| Euclid, John Playfair - 1826 - 320 sider
...Therefore, &e. QED PROP. XXII. THEOR: If there be any number of magnitudes, and as many Others, whieh, **taken two and two in order, have the same ratio ; the first** will have to the last of the first magnitudes, the same ratio whieh the first of the others has to... | |
| Robert Simson - 1827 - 513 sider
...Therefore, if there be three, &c.. SeeN. * 4.'5. * 20. 5. •f- Constr. *5Def. 5. PROP. XXII. THEOR. **If there be any number of magnitudes, and as many...which taken two and two in order have the same ratio** ; theJirst shall have to the last of the Jirst magnitudes the same ratio which theJirst has to the... | |
| Euclid, Dionysius Lardner - 1828 - 324 sider
...may be extended to series consisting of any number of magnitudes. PROPOSITION XXIII. THEOREM. (502) **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... | |
| George Peacock - 1830 - 685 sider
...perturbatfi. A similar demonstration will apply when there are more than three magnitudes in each set. 413. " **If there be any number of magnitudes and as many others, which, taken two and two in** a cross order, jlaye ^ same rati0; namely, if the first be to the second of the first set of magnitudes,... | |
| John Playfair - 1832 - 333 sider
...therefore, by the first case, since C> A, F>D, that is, D^_F. Therefore, &c. QED PROP. XXII. THEOR. Jf **there be any number of magnitudes, and as many others, which, taken two and two in order, have** (he same ratio; the Jirst will have to the lust of the first magnitudes, the same ratio which the first... | |
| Perry Fairfax Nursey - 1833
...1st case ; but it seems tome impossible to make it shorter than in Euclid. II. The 23d Proposition. **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 will have to the last of the first magnitudes the same... | |
| 1833
...1st case; but it seems tome impossible to make it shorter than in Euclid. II. The 23d Proposition. **If there be any number of magnitudes, and as many others, which, taken two and two in** a cross order, Lave the same ratio, the first will have to the last of the first magnitudes the same... | |
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