 | Robert Simson - 1806 - Počet stránok 546
...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 - 1806 - Počet stránok 320
...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 - 1807 - Počet stránok 476
...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 - 1809 - Počet stránok 542
...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 - Počet stránok 588
...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 - Počet stránok 354
...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 - 1819 - Počet stránok 350
...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 - 1821 - Počet stránok 514
...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 - Počet stránok 294
...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 - 1822 - Počet stránok 312
...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... 
