 | John Playfair - Euclid's Elements - 1832 - 358 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 - 304 pages
...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 - 336 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 - 540 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 - 312 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 - 378 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 - 488 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 - 290 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 - Logic - 1837 - 312 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... | |
 | Robert Simson - Geometry - 1838 - 434 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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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... 
