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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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Artithmetic theoretical and practical

William Harding Girdlestone - 1867
...attributed to the imperfect translation of Euclid's definition of Ratio, Book v., Definition 3. " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.„ Here we may ask what is the difference between the words magnitude and quantity ? Are they not in reality...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Volume 3

William Thomas Brande, George William Cox - Encyclopedias and dictionaries - 1867
...majority. Ratio (Lat.). In Geometry, this word is defined by Euclid (Elrmenis, book v. del'. 3) to be ' a mutual relation of two magnitudes of the same kind to one another in respect of quantity' This definition has been much criticised. Dr. Barrow (J.ectimies Math.), who calls it a metaphysical...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...less, that is, ' when the greater contains the less a certain number of times exactly.' III. " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity." IV. Magnitudes are said to have a ratio to one another, when the less can be multiplied so as to exceed...
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Proceedings, Volume 24

Literary and Philosophical Society of Liverpool - 1870
...bringing into account arithmetical notions. When Euclid, in Book V. def. 4, says that magnitudes " have a ratio to one another, when the less can be multiplied so as to exceed the * Lardner's Euclid, Appendix II., page 315. f Companion to British Almanack, 1849, page 13. J Cf. JM...
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Practical geometry for the architect, engineer, surveyor and mechanic

Edward Wyndham Tarn - Curves, Plane - 1871 - 242 pages
...equi-multiples of 2 and 3, 4 being twice 2, and 6 twice 3. Ratio, proportion, or relative magnitude, is a mutual relation of two magnitudes of the same kind to one another, with respect to the number of times that one is contained in the other. If there be four magnitudes,...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...greater is measured by the less. 3. Ratio is a mutual relation of two magnitudes of the same kind, in respect of quantity. 4. Magnitudes are said to...when the less can be multiplied so as to exceed the greater. 5. Magnitudes are said to be in the same ratio, the first to the second, and the third to...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...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...exceed the other. 5. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples...
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Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - Euclid's Elements - 1874 - 62 pages
...as a number, so that a magnitude is a multiple of itself, and also a part of itself. III. ' Batió is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity/ This is too vague to be of any practical use. Euclid explains more clearly what he means by ' ratio,'...
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Euclid, book v. proved algebraically, so far as it relates to commensurable ...

Charles Lutwidge Dodgson - 1874
...as a number, so that a magnitude is a multiple of itself, and also, a part of itself. III. ' Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.' This is too vague to be of any practical use. Euclid explains more clearly what he means by ' ratio,'...
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The Elementary Geometry of the Right Line and Circle ... With Exercises

William Alexander Willock - Circle - 1875 - 172 pages
...Proportion, which will be in constant use. RATIO. Ratio is Relative Magnitude ; or, as Euclid defines it, " A mutual relation of two magnitudes of the same kind to one another, in respect of quantity." The first of the two magnitudes in a ratio is termed the Antecedent, and the second the Consequent....
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