 II. 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.' III. " Ratio is a mutual relation of two magnitudes of the same kind...  Proceedings of the Edinburgh Mathematical Society - Page 100by Edinburgh Mathematical Society - 1897Full view - About this book
 | Euclides - Geometry - 1853 - 334 pages
...times exactly, the former magnitudes are called " equimultiples " of the latter. III. Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity. OBS. It appears that for one magnitude to have a ratio to another, they must both be of the... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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 one another, in respect of quantity.' 4. Magnitudes are said to have a ratio to one another, when the less can be multiplied so... | |
 | Euclides - Geometry - 1853 - 176 pages
...that is, when the greater contains the less a certain number of times exactly. III. Batió 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... | |
 | Euclides - 1855 - 230 pages
...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... | |
 | Euclides - 1855 - 270 pages
...called the multiple öS the smaller ; and the smaller, the subimcltiple of the greater. III. The mutual relation of two magnitudes of the same kind to one another, in respect of quantity, is called their,ratio. The term ratio is employed to express the relation of two like magnitudes... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...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... | |
 | Eucleides - 1860 - 396 pages
...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... | |
 | Euclides - 1861 - 464 pages
...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... | |
 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...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... | |
 | Euclides - 1864 - 448 pages
...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... | |
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