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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 of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...within or without the circle. APPENDIX (E). FIFTH AND SIXTH BOOKS. X. EUCLID defines Ratio to be the relation of two magnitudes of the same kind to one another in respect of quantity, and he defines Proportion to be the sameness of ratios. Yet this is not enough, for he has recourse...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...less, that is, ' when the greater contains the less a certain num' ber of times exactly.' III. " Ratio is a mutual relation of two magnitudes of the " same kind to one another, in respect of quantity." IV. V. The first of four magnitudes is said to have the same ratio to the second, which the third has...
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Euclid's Elements - 1841 - 98 pages
...term " ratio ;" the following are quoted from some of the best writers on proportion : — " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity." — Simson'a Euclid. " Ratio is the relation which one quantity bears to another in respect of magnitude,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...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...in respect of quantity. 4. Magnitudes are said to be of the same kind, when the less can be multiplied so as to exceed the greater ; and it is only such...
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A Treatise on Algebra: Arithmetical algebra

George Peacock - Algebra - 1842
...ascertained as necessary consequences of it : for ratio is said to be (Euclid, Book V. Def. 3.) the mutual relation of two magnitudes of the same kind to one another, with respect to quantity, a description of its meaning much too vague and general to be considered...
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The Downside magazine and monthly miscellany

Downside sch - 1844
...from two serious objections to which the latter is obnoxious. In most books it runs thus : " Ratio is a MUTUAL relation of two magnitudes of the same kind, to one another, in respect to QUANTITY." Our first objection is to the term 'mutual.' It seems to be, we humbly suggest a misapprehension...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...; 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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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...Magnitudes so represented by numbers may be compared with each ofher, and hence results ratio. 2. Ratio is a mutual relation of two magnitudes of the same kind to each other in respect of quantity. Or it is the quotient arising from dividing one quantity by another...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...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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