| John Playfair - Euclid's Elements - 1832 - 333 pages
...equal ratios, DBF. IV. This definition is a little altered in the expression; Euclid has it, that " **magnitudes are said to have a ratio to one another, when the " less can** oe multiplied so as to exceed the greater." DEF. V. One of the chief obstacles to the ready understanding... | |
| Euclides - 1833
...less measures it. 3. Ratio is the mutual relation of two magnitudes of the same kind, with respect to **quantity. 4. Magnitudes are said to have a ratio to one another,** tclum they are such that the less can be multiplied so as to exceed the greater. Note. All commensurable*... | |
| John Playfair - Euclid's Elements - 1835 - 316 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...in respect of quantity. 4. Magnitudes are said to** be of the same kind, when the less can be multiplied so as to exceed the greater ; and it is only such... | |
| Euclid - 1835 - 513 pages
...mutual relation of two magnitudes of the same See N. ' kind to one another, in respect of quantity.' IV. **Magnitudes are said to have a ratio to one another,...less can be multiplied so as to exceed the other.** y. The first of four magnitudes is said to have the same ratio to the second, that the third has to... | |
| Alexander Jamieson - Logic - 1835 - 304 pages
...applied to ratio ; yet it seems that no plainer word could be found. " Ratio," says Simpson, " is the **mutual relation of two magnitudes, of the same kind, to one another, in respect of quantity."** (See Illus. 3. An. 304.) Example 8. MOTION is another simple Idea, on which ARISTOTLE, and the SCHOOLMEN... | |
| George Crabb - Industrial arts - 1835 - 368 pages
...with a cone form the subject of conic sections, which is a branch of sublime geometry. Ratio is the **mutual relation of two magnitudes of the same kind to one another, in respect** to quantity, as 2 to 1, which is double ; the former of these is called the antecedent and the latter... | |
| Mathematics - 1836 - 472 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...in respect of quantity. 4. Magnitudes are said to** be of the same kind, when the less can be multiplied so as to exceed the greater ; and it is only such... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...Equimultiples of magnitudes are multiples that contain them, respectively, the same number of times. 6. Ratio **is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.** 7. Magnitudes are .said to \ie homogeneous, or of the same kind, when the less can be multiplied so... | |
| Alexander Jamieson (LL.D.) - Logic - 1837 - 304 pages
...applied to ratio ; yet it seems that no plainer word could be found. " Ratio," says Simpson, " is the **mutual relation of two magnitudes, of the same kind, to one another, in respect of quantity."** (See II! an. 3. Art. 304.) Example 8. MOTION is another simple Idea, on which ARISTOTLE, and the SCHOOLMEN... | |
| Euclid, Robert Simson - Geometry - 1838 - 416 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... | |
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