| James Ryan, Robert Adrain - 1824 - 516 Seiten
...greater than C, D will be greater than F ; if equal, equal ; and if less, less. tt. PROI'. XXII. THEOB. **If there be any number of magnitudes, and as many others, which, taken two and two in** order, have the same ratio ; the first shall have to the last of the first rank of magnitudes, the... | |
| Peter Nicholson - 1825 - 372 Seiten
...to F: A is to D. as E to H. Because А, В, С, яге three magnitudes, and F, G, H, other three, **which, taken two and two in a cross order, have the same ratio** ; by the first case, A is to C, as F to H: But с is to D, as E to F ; wheretbre again. by the first... | |
| James Ryan - 1826 - 383 Seiten
...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... | |
| Robert Simson - 1827 - 513 Seiten
...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 others, which taken two and two in** order have the same ratio ; theJirst shall have to the last of the Jirst magnitudes the same ratio... | |
| Euclid, Dionysius Lardner - 1828 - 324 Seiten
...greater than A' (by the first case) ; that is A' is less than C'. PROPOSITION XXII. THEOREM. (501) **If there be any number of magnitudes, and as many others, which taken two and two in** order have the same ratio ; the first has to the last of the first magnitudes the same ratio which... | |
| George Peacock - 1830 - 685 Seiten
...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, as the last... | |
| John Playfair - 1832 - 333 Seiten
...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... | |
| Perry Fairfax Nursey - 1833
...ist propositions. Solution by l In- Hon. Lionel Smytke, the Proposer. I. The 22d Proportion, Book V. **If there be any number of magnitudes, and as many others, which, taken two and two in** order, have the same ratio, the first will have to the last of the first magnitudes the same ratio... | |
| 1833
...2ist propositions. Solution ty the Hon. Lionel Smythe, the Proposer. I. The 22d Proposition, Book V. **If there be any number of magnitudes, and as many others, which, taken two and two in** order, have the same ratio, the first will have to the last of the first magnitudes the same ratio... | |
| John Playfair - 1833 - 333 Seiten
...ex sequo," PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, — „.., **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 ratio which the first of the others has to the... | |
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