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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... "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ... - Page 89
by John Mason Good - 1813
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 333 pages
...equal ratios, DBF. IV. This definition is a little altered in the expression; Euclid has it, that " magnitudes are said to have a ratio to one another, when the " less can oe multiplied so as to exceed the greater." DEF. V. One of the chief obstacles to the ready understanding...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...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, tclum they are such that the less can be multiplied so as to exceed the greater. Note. All commensurable*...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...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, that the third has to...
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A Grammar of Logic and Intellectual Philosophy: On Didactic Principles ...

Alexander Jamieson - Logic - 1835 - 304 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 Illus. 3. An. 304.) Example 8. MOTION is another simple Idea, on which ARISTOTLE, and the SCHOOLMEN...
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A Dictionary of General Knowledge, Or, An Explanation of Words and Things ...

George Crabb - Industrial arts - 1835 - 368 pages
...with a cone form the subject of conic sections, which is a branch of sublime geometry. Ratio is the mutual relation of two magnitudes of the same kind to one another, in respect to quantity, as 2 to 1, which is double ; the former of these is called the antecedent and the latter...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 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...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...Equimultiples of magnitudes are multiples that contain them, respectively, the same number of times. 6. Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity. 7. Magnitudes are .said to \ie homogeneous, or of the same kind, when the less can be multiplied so...
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A Grammar of Logic and Intellectual Philosophy: On Didactic Principles ...

Alexander Jamieson (LL.D.) - Logic - 1837 - 304 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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - Geometry - 1838 - 416 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...
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