 | Sir Thomas Little Heath - 1921 - 474 pagina’s
...Most important of all is the fundamental definition (5) of magnitudes which are in the same ratio : ' 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... | |
 | Sir Thomas Little Heath - 1921 - 474 pagina’s
...Most important of all is the fundamental definition (5) of magnitudes which are in the same ratio : ' 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... | |
 | Cambridge Philosophical Society - 1923 - 678 pagina’s
...important results can be obtained by doing this. Sir TL Heath translates the Fifth Definition as follows : Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, if any equimultiples whatever be taken of the first and third, and any... | |
 | 1927 - 578 pagina’s
...does give, there is no explicit statement anywhere. Euclid's two definitions are: Book V, Definitions: 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... | |
 | Edward Grant - 1974 - 890 pagina’s
...definition must be taken as equivalent to Book V, Definition 5, of the Greek text (Heath, II, 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... | |
 | Robert S. Cohen, J.J. Stachel, Marx W. Wartofsky - 1974 - 702 pagina’s
...construction. (d) The fifth definition is of fundamental importance for the entire theory of ratios. '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... | |
 | 1871 - 592 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... | |
 | Howard Whitley Eves - 1983 - 292 pagina’s
...the magnitudes involved. This definition, which marks a GREAT MOMENT IN MATHEMATICS, runs as follows: 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... | |
 | David C. Lindberg - 1978 - 566 pagina’s
...determining equality of ratio would involve an endless search for a common measure: "(Elements, V. def. 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... | |
 | W. R. Shea - 1983 - 346 pagina’s
...present case. Definition 5 of Book V of the Elements gives a famous exposition of these conditions: 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... 
