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" 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 any equimultiples whatever of the second and fourth, the former equimultiples alike... "
The Elements of Euclid with Many Additional Propositions and Explanatory Notes - Pagina 18
door Eucleides - 1860
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A History of Mathematics: From Mesopotamia to Modernity

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,...
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What is Geometry?

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...
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Euclid's Elements in Greek

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...
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The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science

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...
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The Thirteen Books of Euclid's Elements

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...
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

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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