| 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... | |
| 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 - 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... | |
| 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... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...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... | |
| John Playfair - Geometry - 1837 - 332 pages
...: A : : F : E, therefore, by this first case, since C 7 A, F 7 D, that is, D/F. PROP. XXII. THEOR. **If there be any number of magnitudes, and as many others, which, taken two** ana two in order, have the same ratio ; the first will have to the last of the first magnitudes, the... | |
| Euclid - Geometry - 1838 - 478 pages
...first ; and therefore D is less than F. Therefore, if there be three, &c. QED PROP. XXII. THEOR. Ir **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... | |
| Robert Simson - Geometry - 1838 - 434 pages
...whatever be the number of magnitudes. Therefore, if there be any number, &c. 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 first shall have to the last of the first magnitudes the same... | |
| Euclides - 1840 - 194 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,** irregularly, have the same ratio ; the first will have to the last of the first series of magnitudes... | |
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