 | 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 - 430 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 - 546 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 - 542 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 - 358 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 - 216 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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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 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... 
