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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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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...the less, that is, when the greater contains the less a certain number of times exactly. in. 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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Lexicon Scientiarum: A Dictionary of Terms Used in the Various Branches of ...

Henry McMurtrie - Encyclopedias and dictionaries - 1847 - 246 pages
...scratch the earth in search of food. RA'TIO, Geom., Lat., ratio, proportion. Defined by Euclid as " a mutual relation of two magnitudes of the same kind to one another in respect of quantity," and by Leslie as " a certain mutual habitude of two homogeneous magnitudes with respect to quantity...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...the 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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Lexicon Scientiarum: A Dictionary of Terms, Etc

Henry McMurtrie - 1851
...scratch the earth in search of food. RA'TIO, Geom., Lat., ratio, proportion. Defined by Euclid as " a mutual relation of two magnitudes of the same kind to one another in respect of quantity," and by Leslie as " a certain mutual habitude of two homogeneous magnitudes with respect to quantity...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...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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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...the less ; that is, when the greater contains the less a certain number of times exactly. III. Batió 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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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...number of times exactly, the former magnitudes are called " equimultiples " of the latter. III. Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity. OBS. It appears that for one magnitude to have a ratio to another, they must both be of the same kind....
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...they were said to be incommensurable, as in the case of the side and diagonal of a square. 3. Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity. SCHOLIUM. This definition has been as severely criticised as perhaps any other portion of the Elements;...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...is called the multiple öS the smaller ; and the smaller, the subimcltiple of the greater. III. The mutual relation of two magnitudes of the same kind to one another, in respect of quantity, is called their,ratio. The term ratio is employed to express the relation of two like magnitudes to...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1855 - 318 pages
...equal ratios. DEF. IV. This definition is a little altered in the expression; Euclid has it, tha. ' magnitudes are said to have a ratio to one another, when the loss can be " multiplied so as to exceed the greater." DEF. V. One of the chief obstacles to the ready...
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