 | Alexander Jamieson - Logic - 1837 - 312 pages
...applied to ratio ; yet it seems that no plainer word could be found. " Ratio," says Simpson, " is the mutual relation of two magnitudes, of the same kind, to one another, in respect of quantity." (See II! an. 3. Art. 304.) Example 8. MOTION is another simple Idea, on which ARISTOTLE, and the SCHOOLMEN... | |
 | Euclides - 1840 - 192 pages
...exactly in the greater ; and in this case the less is said to be a SUBMULTIPLE of the greater). 2. A greater magnitude is said to be a MULTIPLE of a...contains the less a certain number of times exactly ; and when two magnitudes contain two others respectively the same number of times, they are said to... | |
 | Oliver Byrne - Mathematics - 1841 - 140 pages
...contained in 20 four times exactly ; the same may be said with respect to other numbers and magnitudes. II. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly. Let the line A be 6 feet, and B one foot in length ; . . * . . , A is said to be a multiple of B, because... | |
 | Euclides - Geometry - 1841 - 378 pages
...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...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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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 pages
...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 - 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
...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... | |
 | Nathan Scholfield - 1845 - 894 pages
...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 - Euclid's Elements - 1846 - 334 pages
...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... | |
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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 
