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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... "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 149
von Euclides - 1861
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 Seiten
...Propositions are introduced by SIMSON. PROPOSITION A. THEOREM. (480) If the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then, if the first be greater than the second, the third is also greater than the fourth ; and if...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 Seiten
...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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 Seiten
...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 R«TÍy 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 - 1833 - 183 Seiten
...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 Seiten
...said to have a ratio to one another, when the 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 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 - 1835 - 513 Seiten
...said to have a ratio to one another, when the 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 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 ...

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 ...

1836 - 472 Seiten
...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 - 1837 - 182 Seiten
...rs-s=(rl)s, ar" — a whence = s. r - I GEOMETRY. ELEMENTS or GEOMETRY. EUCLID, Books *i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes...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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