 | Jules Vuillemin - 1986 - 184 pagina’s
...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,... | |
 | John N. Crossley - 1987 - 240 pagina’s
...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... | |
 | Heinz-Dieter Ebbinghaus - 1991 - 424 pagina’s
...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... | |
 | Morris Kline - 1990 - 434 pagina’s
...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... | |
 | Douglas M. Jesseph - 1993 - 335 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... | |
 | Richard W. Hadden - 1994 - 214 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 of the second and fourth, the former... | |
 | Paolo Mancosu - 1999 - 290 pagina’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,... | |
 | John J. Roche - 1998 - 364 pagina’s
...to the Athenian mathematician Theatetus (c BC 417-369)85 and to Eudoxus of Cnidus (c. BC 400347)86: 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... | |
 | Emily Grosholz, Elhanan Yakira - 1998 - 118 pagina’s
...kind". The next definition, that which according to Leibniz is the one Euclid actually uses, says that 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,... | |
 | Douglas M. Jesseph - 1999 - 440 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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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... 
