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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... "
Euclidian Geometry - Page 157
by Francis Cuthbertson - 1874 - 349 pages
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...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 - 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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 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...the second, which the third has to the fourth, when any equi-multiples whatsoever of the first and third being taken, and any equimultiples whatsoever...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...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 ...

Euclid - 1835 - 540 pages
...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 Pierce ...

Mathematics - 1835 - 684 pages
...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 - 1837 - 226 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...the 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...the sixth, is of the fourth D. If, therefore, &c. PROP. IV. THEOR. IF the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then any like multiples whatever of the first and third have the same ratio to any like multiples...
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