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" A greater magnitude is said to be a multiple of a less, when the greater is measured by the less ; that is, ' when the greater contains the less a certain number of times exactly.' 3. ' Ratio is a mutual relation of two magnitudes of the same kind to... "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ...
by John Mason Good - 1813
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The Calendar of Owens college, Manchester

Manchester univ - 1877 - 544 pages
...a given line in a given point and bisecting the circumference of a given circle. 9. Magnitudes arc said to have a ratio to one another when the less can be multiplied so as to exceed the greater. Explain this. Prove that equal magnitudes have the same ratio to the same magnitude and conversely....
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 13

Perry Fairfax Nursey - Industrial arts - 1830 - 508 pages
...to another of the »ame kind, inrespect to magnitude or quantity." — Johnson's Dictionary. " Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity.'' — Euclid's Elements, book 5. "Byratio, is meant therelation which one quantity bears to another,...
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Proceedings of the Edinburgh Mathematical Society, Volume 16

Edinburgh Mathematical Society - Electronic journals - 1898 - 160 pages
...text of Euclid there may be said to be two definitions, of which the first is " ratio is the (or a) relation of two magnitudes of the same kind to one another in respect of quantuplicity." It may be remarked that this definition has a rather curious history. Barrow, a most...
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