| Euclides - 1885
...greater. in. 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 . m., . which has the fault of conveying... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...part* or 'measure' of the greater ; (2) the greater is called a ' multiple' of the less. 3. ' Ratio ' **is a mutual relation of two magnitudes of the same kind to one another in respect of quantity.** We have given the definition in its usual form ; but the word ' quantity ' is misleading. De Morgan... | |
| Charles William Leverett Johnson - Music theory - 1896 - 76 pages
...notes. 'Katio is defined by Euclid in the following words (Euclid, Elements, v. def. 3) : " Batió **is a mutual relation of two magnitudes of the same kind to one another in respect of quantity,"** or rather of " quantnplicity." It is immaterial which of the two magnitudes first receives the attention... | |
| Edinburgh Mathematical Society - Electronic journals - 1897
...text of Euclid there may be said to be two definitions, of which the first is " ratio is the (or a) **relation of two magnitudes of the same kind to one another in respect of** quantuplicity." It may be remarked that this definition has a rather curious history. Barrow, a most... | |
| Education - 1901
...compass is incomplete, and on p. 290 we have the remarkable statement that "Euclid's definition that **'magnitudes are said to have a ratio to one another...when the less can be multiplied so as to exceed the** greater' is only an indirect way of stating that two magnitudes have a ratio when, and only when, they... | |
| Joseph Battell - Force and energy - 1903
...denominator or standard of measure. But it is done both ways. " In the first definition, that ratio **is a mutual relation of two magnitudes of the same kind, to one another, in respect of quantity,** the ratio between the same two quantities or other equally proportional quantities cannot vary ; and... | |
| Education - 1908
...Vol. XIII, 1907. p. 392. Archimedean postulate is hidden in one of the definitions (Def. 4, Bk. V.)- **"Magnitudes are said to have a ratio to one another,...less can be multiplied so as to exceed the other."** As long as an argument involves assumptions which are not explicitly set forth in the mind, the logic... | |
| John James Roche, ROCHE - Mathematics - 1998 - 330 pages
...ratio as a relationship between two quantitative terms and expressed it as such. For Euclid108, 'Ratio **is a mutual relation of two magnitudes of the same kind to one another in respect of quantity'.** Ratio belonged, therefore, to the category of relation and was not a simple quantity or a single number.... | |
| Mathematicians - 1915
...exceeded." Euclid in his Elements (Bk. V, Def. 4) gives the postulate in the form of a definition: **"Magnitudes are said to have a ratio to one another,...less can be multiplied so as to exceed the other."** The Method of Archimedes, a book formerly thought to be irretrievably lost, but fortunately discovered... | |
| Manchester univ - 1877
...a given line in a given point and bisecting the circumference of a given circle. 9. Magnitudes arc **said to have a ratio to one another when the less can be multiplied so as to exceed the** greater. Explain this. Prove that equal magnitudes have the same ratio to the same magnitude and conversely.... | |
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