 | James Ryan - 1824 - 550 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 - 1046 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 - 430 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 - 546 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 - 542 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 - 732 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 - 358 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 - 488 Seiten
...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 - 496 Seiten
...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 - 346 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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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 magnitudes, the same ratio which the first of the others has to the last. NB This is usually... 
