| James Ryan - 1824 - 550 σελίδες
...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 - 542 σελίδες
...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 - 430 σελίδες
...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 - 326 σελίδες
...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 - 546 σελίδες
...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 - 542 σελίδες
...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 - 732 σελίδες
...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 - 358 σελίδες
...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 - 488 σελίδες
...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 - 496 σελίδες
...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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