| Euclid - 1833 - 183 Seiten
...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
...PROPOSITION XXIII. THBOR. — If there be any number of magnitudes, and as many See N. others, whifh, **taken two and two in a cross order, have the same ratio, the** Jirsl shall have to the last of the Jir si magnitudes, the same ratio which the Jirsl has to the last... | |
| Robert Simson - 1835 - 513 Seiten
...the number of magnitudes. Therefore, " if there be any number," &c. QED PROP. XXIII. THEOR. See N. **If there be any number of magnitudes, and as many...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... | |
| John Playfair - 1835 - 316 Seiten
...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...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... | |
| Euclid - 1835 - 513 Seiten
...D is less than F. Therefore, " if there be three," &c. QED PROP. XXII. THEOR. ABCABC DEFDEF See N. **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... | |
| James Ryan, Robert Adrain - 1835 - 361 Seiten
...XXII. THEOR. 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** ihe first rank of magnitudes, the same ratio which the first of the others has lo the last. NB This... | |
| John Playfair - 1836 - 471 Seiten
...: 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... | |
| John Playfair - 1836 - 114 Seiten
...and C : D : : E : F ; then A : D : : E : H. Because A, B, C, are three quantities, and F, G, H, three **others, which taken two and two in a cross order have the same ratio,** by the , first case, A : C : : F : H, but C : D : : E : F, wherefore again by the first case, A : D... | |
| 1836 - 472 Seiten
...third, the fourth is greater than the sixth ; if equal, equal; and if less, less. XXII. If there beany **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... | |
| Andrew Bell - 1837 - 240 Seiten
...E; therefore, by the first case, since C ^ A, F -^ D, that is, D *£. F. PROPOSITION XXn. THEOREM. **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... | |
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