| James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...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 - Algebra - 1826 - 383 pages
...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 - Trigonometry - 1827 - 513 pages
...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 - Euclid's Elements - 1828 - 544 pages
...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 - Algebra - 1830 - 732 pages
...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 - Euclid's Elements - 1832 - 333 pages
...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... | |
| Industrial arts - 1833 - 496 pages
...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... | |
| Perry Fairfax Nursey - Industrial arts - 1833 - 488 pages
...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... | |
| Euclid - Euclid's Elements - 1833 - 183 pages
...of A is contained in B; (ii)Def.5. therefore A is to C as B to DO (11). PROP. XXXIV. THEOR. Fig. 29. **If there be any number of magnitudes, and as many others which taken two** by two are in the same ratio, and if their proportion be ordinate ; they are ex aequali in the same... | |
| Euclid - 1835 - 540 pages
...the number of magnitudes. Therefore, " if there be any number," &c. QED PROP. XXIII. THEOR. s«e N. **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 t/ie same... | |
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