 | John Playfair - 1842 - 332 σελίδες
...certain number of times, exactly, in the greater. 2. A greater magnitude is said to be a multiple o£ a less, when the greater is measured by the less,...contains the less a certain number of times exactly. 3. Ratio is a mutual relation of two magnitudes, of the same kind, to one another, in respect of quantity.... | |
 | Euclides - 1842 - 316 σελίδες
...another. II. A greater magnitude, or number, is said to be a multiple of a less magnitude, or number, when the greater is measured by the less, that is,...contains the less a certain number of times exactly. III. A less magnitude, or number, is said to be a part, or a submultiple, of a greater magnitude, or number,... | |
 | George Peacock - 1842 - 426 σελίδες
...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 σελίδες
...is free 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 of... | |
 | Euclid - 1845 - 218 σελίδες
...circumscribed about it. BOOK V. DEFINITIONS. I. A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when...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... | |
 | Euclides - 1845 - 546 σελίδες
...greater; that is, 'when the less is contained a certain number of times exactly in the greater.' II. A greater magnitude is said to be a multiple of a...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... | |
 | Nathan Scholfield - 1845 - 894 σελίδες
...magnitude. 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... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...greater, that is, when the less is contained a certain number of times, exactly, in the greater. 2. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly. 4. Magnitudes are said to be of the same kind, when the less can be multiplied so as to exceed the... | |
 | Euclides - 1846 - 292 σελίδες
...greater, that is, when the less is contained a certain number of times exactly in the greater. II. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly. in. Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity.... | |
 | Euclides - 1846 - 272 σελίδες
...aliquot part, or a submultiple of a greater, when the less measures the greater. 2. A greater is called a multiple of a less, when the 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... | |
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A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times 
