| Euclides - 1846
...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 - 246 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
...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
...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
...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 - 147 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
...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
...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
...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 - 318 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... | |
| |