| Euclid - Geometry - 1933 - 298 pages
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| 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.... | |
| 1800 - 834 pages
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| Perry Fairfax Nursey - Industrial arts - 1830
...to another of the »ame kind, inrespect to magnitude or quantity." — Johnson's Dictionary. " Ratio **is a mutual relation of two magnitudes of the same kind to one another in respect of quantity.''** — Euclid's Elements, book 5. "Byratio, is meant therelation which one quantity bears to another,... | |
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