 | Robert Simson - Trigonometry - 1806 - 546 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 - Mathematics - 1806 - 320 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 - 476 pages
...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 - 542 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 - 588 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 - 354 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 - 350 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 - 514 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 - 294 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, •when they are such that the less can be multiplied so as to exceed the greater. Note. All commensurable... | |
 | Alexander Jamieson - Logic - 1822 - 312 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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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... 
