| Euclides - 1884 - 434 pages
...BV 13 Now C:B = E:D; .-. E: F is less than E:D; F. 13 D is less than FF 10 PROPOSITION 22. THEOREM. **If there be any number of magnitudes, and as many others, which taken two and two in** direct order, have the same ratio ; tJie first shall have to the last of the first magnitudes the same... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...[IST PART. and the theorem can be easily extended to any number of magnitudes. Hence generally : — **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... | |
| Joseph Battell - Force and energy - 1903 - 722 pages
...which the first of the others has to the last.' " See Proposition XX. PROPOSITION XXIII. ' If there are **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 - Mathematics, Greek - 1908 - 456 pages
...P." He also gives the extension of the proposition to any number of magnitudes, enunciating it thus : **"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 - 452 pages
...He also gives the extension of the proposition to any number of magnitudes, enunciating it thus : " **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... | |
| Oxford univ, exam. papers, 2nd publ. exam - 1884 - 594 pages
...rectilineal figure and equal to another given rectilineal figure. 8. Inscribe a square in a given circle. 9. **If there be any number of magnitudes, and as many others, which** have the same ratio, taken two and two in a cross order, the first shall have to the last of the first... | |
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