 | Jules Vuillemin - Philosophy - 1986 - 184 pages
...those contained by straight lines' (Euclid's Elements, p. 411). 26 airr/fiora / Koival evvoiai. 2 7 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 the third, and any equimultiples whatever of... | |
 | John N. Crossley - Mathematics - 1987 - 240 pages
...approximation to another length by applying the strategy of the Eudoxian definition 5 of Euclid Book V: 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, any equimultiples whatever of the second... | |
 | Dirk Jan Struik - Mathematics - 1967 - 260 pages
...incommensurable or commensurable magnitudes superfluous. Typical is Definition 5, Book V, of Euclid's Elements; Magnitudes are said to be in the same ratio, the first to the second and third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples... | |
 | Morris Kline - Mathematics - 1990 - 434 pages
...multiple of the smaller one will exceed the larger. The next definition is the key one. Definition 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 any equimultiples whatever of the... | |
 | Heinz-Dieter Ebbinghaus - Mathematics - 1991 - 424 pages
...another, the following is given (Definition 5 in Book V of EUCLID'S Elements in Heath's translation): "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... | |
 | Douglas M. Jesseph - Mathematics - 1993 - 344 pages
...are 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 any multiples whatever of the second... | |
 | Richard W. Hadden - Social Science - 1994 - 214 pages
...are 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 of the second and fourth, the former equimultiples alike exceed, are... | |
 | Paolo Mancosu - Philosophy - 1996 - 286 pages
...Euclid's Elements. Later on I will also refer to the definition of equality of ratio given in definition 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 the third, and any equimultiples whatever of... | |
 | Howard Whitley Eves - Mathematics - 1997 - 370 pages
...6Material in this section has been adapted from H. Eves [1]. and runs as follows: Magnitudes are said io 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... | |
 | Patrick Hugh Byrne - Philosophy - 1997 - 330 pages
...Eudoxus defined "proportionality" as follows: 5. Magnitudes are said to be in the same ratio [logoi], the first to the second and the third to the fourth, when, if any equimultiples whatever being taken of the first and third, and any equimultiples of the second... | |
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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... 
