| Robert Potts - Geometry, Plane - 1860 - 361 pages
...less, that is, ' when the greater contains the less a certain number of times exactly.' m. " 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... | |
| Eucleides - 1860
...they were said to be incommensurable, as in the case of the side and diagonal of a square. 3. Ratio **is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.** SCHOLIUM. This definition has been as severely criticised as perhaps any other portion of the Elements... | |
| Euclides - 1861
...mean ratio. None of these have a common measure, neither have they a common multiple. III. — Ratio **is a mutual relation of two magnitudes of the same kind to one another in respect of quantity.** A mistake in translating Euclid's хжт« mfaxornrtt. " in respect of quantity," has tended to confuse... | |
| George Sturton Ward - Geometry, Algebraic - 1862 - 79 pages
...equimultiples of them. If a = m Ъ and c = md, a and с are said to be equimultiples of Ъ and d. III. "Ratio **is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity."** If a and b express two magnitudes of the same kind in a common denomination, so that T is the fraction... | |
| Euclides - 1863
...two magnitudes of the same kind to one auotber, in respect of quantity, is called their ratio. IV. **Magnitudes are said to have a ratio to one another,...less can be multiplied so as to exceed the other.** V. The first of four magnitudes is said to have the same ratio to the second which the third has to... | |
| Euclides - 1864
...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... | |
| Euclides - 1865
...the less; that is, when the greater contains the less a certain number of times exactly. in. 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... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...by the less; that ia, 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... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 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...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... | |
| 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... | |
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