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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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A Military Dictionary: Comprising Terms, Scientific and Otherwise, Connected ...

George Elliot Voyle, G. de Saint-Clair-Stevenson - English language - 1876 - 581 pages
...property under their charge, if committed through carelessness, &c. Batió — In mathematics, the mutual relation of two magnitudes of the same kind to one another, in respect of quantity. Ratios are divided into arithmetical and geometrical. An arithmetical ratio consists in the difference...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...the less, that ia, when the greater contains the less a certain number of times exactly. XXIX. The mutual relation of two magnitudes of the same kind to one another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second,...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 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...ratio to one another, when the less can be multiplied go as to exceed the other. 5. The first of four magnitudes is said to hare the same ratio to the second,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...expressed, like many others, in commensurate terms; for their common measure, or common unit is unknown. IV. Magnitudes are said to have a ratio to one another, when the less can he multiplied so as to exceed the other. This definition is intended as a test of the likeness or similarity...
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The Elements of Euclid: For the Use of Schools and Colleges; Comprising the ...

Euclid - 1883
...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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Companion to algebra

Leonard Marshall - 1883
...circumference of each wheel? V.— RATIO, PROPORTION, AND VARIATION. 1. Ratio is defined by Euclid as the mutual relation of two magnitudes of the same kind to one another in respect of quantity (see Bk. V. Def. iii.). In Algebra the ratio of a : b is measured by the . , .. antecedent aj ., ....
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The Celtic magazine, conducted by A. Mackenzie and A. MacGregor, Volume 9

Alexander Mackenzie - 1884
...established between things which are not of the same kind. Euclid's definition is as follows : — " Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity." " Magnitudes which have the same ratio are called proportionals. When four magnitudes are proportionals...
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The Celtic Magazine, Volume 9

Alexander Mackenzie, Alexander Macgregor, Alexander Macbain - Clans - 1884
...established between things which are not of the same kind. Euclid's definition is as follows:—" Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity." " Magnitudes which have the same ratio are called proportionals. When four magnitudes are proportionals...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...are multiples that contain these magnitudes, respectively, the same number of times. 4. Ratio is a relation of two magnitudes of the same kind to one another, in respect of quantuplicity (a word which refers to the number of times or parts of a time that the one is contained...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - Euclid's Elements - 1885 - 312 pages
...greater. m. Eatio is the mutual relation of two magnitudes of the same kind with respect to quantity. Iv. Magnitudes are said to have a ratio to one another...when the less can be multiplied so as to exceed the greater. These definitions require explanation, especially Def. in., which has the fault of conveying...
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