 | William Harding Girdlestone - 1867 - 368 pages
...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... | |
 | William Thomas Brande, George William Cox - Encyclopedias and dictionaries - 1867 - 1090 pages
...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... | |
 | Robert Potts - 1868 - 434 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... | |
 | Literary and Philosophical Society of Liverpool - 1870 - 312 pages
...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... | |
 | Edward Wyndham Tarn - Curves, Plane - 1871 - 244 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,... | |
 | Euclid - Geometry - 1872 - 284 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... | |
 | 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... | |
 | Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 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,'... | |
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...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,'... | |
 | William Alexander Willock - Circle - 1875 - 196 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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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... 
