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" The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 105
by Euclides - 1816 - 528 pages
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 516 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the scoond, which the third has to the fourth, when any equimultiples whatsoever of the first and third...
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A Treatise on Algebra

George Peacock - Algebra - 1830 - 685 pages
...be equal to that of the second, the multiple of the third will be equal to that of the fourth : and if the multiple of the first be less than that of the second, the multiple of the third will be less than that J of the fourth. It is this proposition which is deduced as a necessary consequence...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...having the same ratio to two others В and D, of the same kind with the former two respectively. Def. 7. The first of four magnitudes is said to have the same ratio to the se* By the word " corresponding" here used, it U RTy iat*nded to point out the fact of there...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...ought to be defined, is still a subject of controversy among geometers. Euclid defines them thus : The first of four magnitudes is said to have the same...equimultiples whatsoever of the second and fourth being taken, the equi-multiples of the first and third either together exceed, are equal to, or are...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same...taken, and any equimultiples whatsoever of the second arid rt fourth, if the multiple of the first be less than that of li T.* • * the second, the multiple...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...less, that is, ' when the ' greater contains the less a certain number of times ex' actly.' III. ' Ratio is a mutual relation of two magnitudes of the...magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...less, that is, ' when the ' greater contains the less a certain number of times ex' actly.' III. ' Ratio is a mutual relation of two magnitudes of the...magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...equal to, or less than the corresponding magnitude of the other ; and conversely (ax. 1, 2, 3, 4).* • "The first of four magnitudes is said to have the same ratio tu the second, which the third has to the fourth, when any equimultiples whatsoever of the first and...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...oft as there are units in the product of these two numbers. IV. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be tcriken of the first and third, and any whatever of the second...
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The Mechanical Euclid: Containing the Elements of Mechanics and Hydrostatics ...

William Whewell - Mechanics - 1837 - 182 pages
...GEOMETRY. ELEMENTS or GEOMETRY. EUCLID, Books *i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes is said to have the same...second which the third has to the fourth, when^ — any eq'wi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever of...
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