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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 ... - Page 89
by John Mason Good - 1813
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Euclid's Elements, Books 1-6; Book 11

Euclid - Geometry - 1933 - 298 pages
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Encyclopędia Britannica, Volume 10

Walter Yust - Encyclopedias and dictionaries - 1951 - 1146 pages
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Encyclopaedia Britannica: A New Survey of Universal Knowledge, Volume 10

Walter Yust - Encyclopedias and dictionaries - 1952 - 1150 pages
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The Bequest of the Greeks

Tobias Dantzig - Mathematics - 1955 - 200 pages
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Mathematics and Logic in History and in Contemporary Thought

Ettore Carruccio - Logic - 1964 - 398 pages
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The Mathematics of Measurement: A Critical History

John James Roche, ROCHE - Mathematics - 1998 - 330 pages
...ratio as a relationship between two quantitative terms and expressed it as such. For Euclid108, 'Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity'. Ratio belonged, therefore, to the category of relation and was not a simple quantity or a single number....
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The American Mathematical Monthly: The Official Journal of the ..., Volume 22

Mathematicians - 1915
...exceeded." Euclid in his Elements (Bk. V, Def. 4) gives the postulate in the form of a definition: "Magnitudes are said to have a ratio to one another,...less can be multiplied so as to exceed the other." The Method of Archimedes, a book formerly thought to be irretrievably lost, but fortunately discovered...
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The Calendar of Owens college, Manchester

Manchester univ - 1877
...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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Classical miscellany: Pamphlet vols.], Volume 42

1800 - 834 pages
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 13

Perry Fairfax Nursey - Industrial arts - 1830
...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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