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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 Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...less, that is, ' when the greater contains the less a certain number of times exactly.' m. " 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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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...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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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...mean ratio. None of these have a common measure, neither have they a common multiple. III. — Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity. A mistake in translating Euclid's хжт« mfaxornrtt. " in respect of quantity," has tended to confuse...
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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - Geometry, Algebraic - 1862 - 79 pages
...equimultiples of them. If a = m Ъ and c = md, a and с are said to be equimultiples of Ъ and d. III. "Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity." If a and b express two magnitudes of the same kind in a common denomination, so that T is the fraction...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...two magnitudes of the same kind to one auotber, in respect of quantity, is called their ratio. IV. Magnitudes are said to have a ratio to one another,...less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second which the third has to...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...by the less; that ia, 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, that the third has to the fourth, when any equimultiples...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 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...exceed the other. 5. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples...
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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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