 | 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... | |
 | Euclides - 1834 - 518 pages
...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 - Trigonometry - 1835 - 544 pages
...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 - Euclid's Elements - 1835 - 336 pages
...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 - 540 pages
...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 - Algebra - 1835 - 388 pages
...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 - Euclid's Elements - 1836 - 488 pages
...: 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 - Geometry - 1836 - 148 pages
...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... | |
 | Mathematics - 1836 - 488 pages
...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 - Euclid's Elements - 1837 - 290 pages
...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... | |
| |
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... 
