 | Robert Potts - Geometry, Plane - 1860 - 380 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 - 396 pages
...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 - 464 pages
...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 - 104 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 - 122 pages
...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 - 448 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... | |
 | Euclides - 1865 - 402 pages
...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... | |
 | Robert Potts - 1865 - 528 pages
...less, that is, ' when the greater contains the less a certaia 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 - 426 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 - 424 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... | |
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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... 
