 | Euclides - 1840 - 192 pages
...within or without the circle. APPENDIX (E). FIFTH AND SIXTH BOOKS. X. EUCLID defines Ratio to be the relation of two magnitudes of the same kind to one another in respect of quantity, and he defines Proportion to be the sameness of ratios. Yet this is not enough, for he has recourse... | |
 | Euclides - Geometry - 1841 - 378 pages
...less, that is, ' when the greater contains the less a certain num' ber of times exactly.' III. " Ratio is a mutual relation of two magnitudes of the " same kind to one another, in respect of quantity." IV. V. The first of four magnitudes is said to have the same ratio to the second, which the third has... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...term " ratio ;" the following are quoted from some of the best writers on proportion : — " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity." — Simson'a Euclid. " Ratio is the relation which one quantity bears to another in respect of magnitude,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 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... | |
 | George Peacock - Algebra - 1842 - 426 pages
...ascertained as necessary consequences of it : for ratio is said to be (Euclid, Book V. Def. 3.) the mutual relation of two magnitudes of the same kind to one another, with respect to quantity, a description of its meaning much too vague and general to be considered... | |
 | Downside sch - 1844 - 384 pages
...from two serious objections to which the latter is obnoxious. In most books it runs thus : " Ratio is a MUTUAL relation of two magnitudes of the same kind, to one another, in respect to QUANTITY." Our first objection is to the term 'mutual.' It seems to be, we humbly suggest a misapprehension... | |
 | Euclides - 1845 - 546 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... | |
 | Euclid - Geometry - 1845 - 218 pages
...; 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... | |
 | Nathan Scholfield - 1845 - 894 pages
...Magnitudes so represented by numbers may be compared with each ofher, and hence results ratio. 2. Ratio is a mutual relation of two magnitudes of the same kind to each other in respect of quantity. Or it is the quotient arising from dividing one quantity by another... | |
 | Euclides - 1846 - 272 pages
...greater is measured by the less. 3. Ratio is a mutual relation of two magnitudes of the same kind, in respect of quantity. 4. Magnitudes are said to...when the less can be multiplied so as to exceed the greater. 5. Magnitudes are said to be in the same ratio, the first to the second, and the third 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... 
