| Euclid - 1833 - 183 sider
...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... | |
| Euclides - 1834
...less than F. Therefore, if there be three, &c. Q. E, D. AB DE Ill PROPOSITION XXII. See N. 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 the Jirsl has to Ihe... | |
| James Ryan, Robert Adrain - 1835 - 361 sider
...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...the same ratio ; the first shall have to the last of** ihe first rank of magnitudes, the same ratio which the first of the others has lo the last. NB This... | |
| Robert Simson - 1835 - 513 sider
...first; consequently D is less than F. Therefore, " if there be three" &c. QED PROP. XXII. THEOR. See N. **If there be any number of magnitudes, and as many...and two in 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... | |
| John Playfair - 1835 - 316 sider
...H. In the same manner is the demonstration extended to any number of magnitudes. 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 first will have to the last of the first magnitudes the same... | |
| Euclid - 1835 - 513 sider
...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... | |
| John Playfair - 1836 - 114 sider
...therefore ^=^ , or A : B : : E : F. JJ r D r PROP. XVI. THEOR. If there be any number of quantities, **and as many others, which taken two and two in order have the same ratio, the first shall have to the** laist of the first quantities the same ratio which the first of the others has to the last. This is... | |
| 1836 - 472 sider
...last of the first magnitudes, the same ratio which the first of the others has to the last. XXIII. **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... | |
| John Playfair - 1836 - 471 sider
...: E, therefore, by the first case, since C^A, F^^D, that is, Therefore, &c. QED PROP. XXII. THEOR. **If there be any number of magnitudes, and as many others, which, taken two and** tico in order, have the same ratio ; the first will have to the last of tlie jirst magnitudes, the... | |
| Euclid, James Thomson - 1837 - 390 sider
...the number of magnitudes. Therefore, if there be any number of magnitudes, &c. 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 first has to the last of the first magnitudes the same ratio... | |
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