 | Euclides - 1846 - 292 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... | |
 | Henry McMurtrie - Encyclopedias and dictionaries - 1847 - 268 pages
...scratch the earth in search of food. RA'TIO, Geom., Lat., ratio, proportion. Defined by Euclid as " a mutual relation of two magnitudes of the same kind to one another in respect of quantity," and by Leslie as " a certain mutual habitude of two homogeneous magnitudes with respect to quantity... | |
 | Euclides - 1848 - 52 pages
...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 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... | |
 | Henry McMurtrie - 1851 - 272 pages
...scratch the earth in search of food. RA'TIO, Geom., Lat., ratio, proportion. Defined by Euclid as " a mutual relation of two magnitudes of the same kind to one another in respect of quantity," and by Leslie as " a certain mutual habitude of two homogeneous magnitudes with respect to quantity... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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 which the third has to the fourth, when any equimultiples... | |
 | Euclides - Geometry - 1853 - 176 pages
...the less ; 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 as to exceed... | |
 | Euclides - Geometry - 1853 - 334 pages
...number of 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 same kind.... | |
 | Euclides - 1855 - 230 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 - 1855 - 270 pages
...is 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 to... | |
 | John Playfair - Euclid's Elements - 1855 - 340 pages
...equal ratios. DEF. IV. This definition is a little altered in the expression; Euclid has it, tha. ' magnitudes are said to have a ratio to one another, when the loss can be " multiplied so as to exceed the greater." DEF. V. One of the chief obstacles to the ready... | |
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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... 
