 | 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
...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 - Algebra - 1835 - 388 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...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 - Trigonometry - 1835 - 544 pages
...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 - 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 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 - 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... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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... | |
 | Mathematics - 1836 - 488 pages
...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 - 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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...same manner is the demonstration extended to any number of magnitudes. PROPOSITION XXIII. THEOREM. 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... | |
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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... 
