| 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... | |
| William Thomas Brande, George William Cox - Encyclopedias and dictionaries - 1867
...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 - 410 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
...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 - 242 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 - 261 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 - 62 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
...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 - 172 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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