| 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 - 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 - Euclid's Elements - 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
...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
...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 - 544 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 - 199 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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