| Luke Hodgkin - 2005 - 302 pagina’s
...its interpretation. (Or look at the commentary in editions of Euclid, websites, etc.) Definition V.5. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth , when, if any equimultiples whatever be taken of the first and third,... | |
| Giandomenico Sica - 2006 - 270 pagina’s
...of Euclid's Elements, Sir Thomas L. Heath, Dover Publications Inc., New York, 1956, vol. II, p. 114. ({Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and... | |
| Richard Fitzpatrick - 2006 - 411 pagina’s
...ratio with respect to one another which, being multiplied, are capable of exceeding one another.4 5 Magnitudes are said to be in the same ratio, the first to the second, and the third to the fourth, when equal multiples of the first and the third either both exceed, are... | |
| 1874 - 1094 pagina’s
...definition of proportion runs thus : — " Four straight lines are said to be proportionals, that is, the same ratio the first to the second as the third to the fourth, when the rectangle contained by the first and fourth is equal to the rectangle contained by the second and... | |
| Euclid - 452 pagina’s
...said to have a ratio to one another which are capable, when multiplied, of exceeding one another. 5. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and... | |
| Peter M. Engelfriet - 1998 - 516 pagina’s
...equality of ratios, no matter whether they are between commensurable or incommensurable magnitudes: Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and... | |
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