| Robert Simson - Trigonometry - 1806 - 518 pages
...mutual relation of two magnitudes of the same kind Ste N ' 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.** V. The first of four magnitudes is said to have the same ratio to the second, which the third has to... | |
| John Playfair - Euclid's Elements - 1806 - 311 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.** Hook V. Magnitudes are said to be of the same kind, when the less can be multiplied so as to exceed... | |
| Isaac Dalby - Mathematics - 1807
...65. THE following Definition of Ratio it usually given in the 5th. Book of Euclid's Elements. " Ratio **is a mutual relation of two -magnitudes of the same kind to one another in respect of quantity."** This definition is frequently objected to as imperfect and obscure. And it seems difficult to acquire... | |
| Sir John Leslie - Geometry, Analytic - 1809 - 524 pages
...of the Elements has likewise given what Dr Barrow calls a metaphysical definition of ratio : " Ratio **is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity."** This sentence, as it now stands, appears either tautological, or altogether devoid of meaning ; and... | |
| Euclides - 1816 - 528 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, which the third has to... | |
| John Playfair - 1819 - 317 pages
...ratios. • DEF. IV. This definition is a little altered in the expression : Euclid has it, that " **magnitudes are said to have a ratio to one another,...the -" less can be multiplied so as to exceed the** greater." DEF. V. One of the chief obstacles to the ready understanding of the 5tU Book of Euclid,... | |
| John Playfair - Circle-squaring - 1819 - 333 pages
...the less, that is, when the greater contains the less a certain number of times exactly. HI. Ratio **is a mutual relation of two magnitudes, of the same kind, to one another, in respect of quantity.** IV. Magnitudes are said to be of the same kind, when the less can be multiplied so as to exceed the... | |
| Euclid, Robert Simson - Geometry - 1821 - 516 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 exceed... | |
| Euclides - 1821
...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, •when** they are such that the less can be multiplied so as to exceed the greater. Note. All commensurable... | |
| Alexander Jamieson - Logic - 1822 - 304 pages
...applied to ratio ; yet it seems that no plainer word could be found. "Katio," says Simpson, " is the **mutual relation of two magnitudes, of the same kind to one another, in respect of quantity."** (See Illus. 3. Art. 304.) Example 8. MOTION' is another simple Idea, on which ARISTOTLE, and the SCHOOLMEN... | |
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