 | Sir Thomas Little Heath - Mathematics - 1921 - 474 pages
...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 any equimultiples whatever of the... | |
 | Sir Thomas Little Heath - Mathematics - 1921 - 474 pages
...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 any equimultiples whatever of the... | |
 | Sir Thomas Little Heath - Mathematics - 1921 - 482 pages
...definition (5) of magnitudes which are in the same ratio : ' Magnitudes are said to be in the same ~T 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... | |
 | Cambridge Philosophical Society - Philosophy - 1923 - 676 pages
...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 equimultiples whatever of the... | |
 | Mathematicians - 1927 - 578 pages
...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 any equimultiples whatever of the... | |
 | Robert S. Cohen, J.J. Stachel, Marx W. Wartofsky - Biography & Autobiography - 1974 - 702 pages
...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 any equimultiples whatever of the... | |
 | Edward Grant - History - 1974 - 890 pages
...proportional. Furthermore, that he says in the sixth definition that "quantities said to be in one [and the same] ratio, the first to the second and the third to the fourth," and so on, is as if he were to say that I call all four quantities discontinuously proportional and... | |
 | David C. Lindberg - Science - 1978 - 566 pages
...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 any equimultiples whatever of the... | |
 | Howard Whitley Eves - History - 1983 - 292 pages
...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 any equimultiples whatever of the... | |
 | W. R. Shea - Gardening - 1983 - 346 pages
...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 any equimultiples whatever of the... | |
| |
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... 
