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" If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ...
by John Mason Good - 1813
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...magnitude of the other ; and conversely (ax. 1, 2, 3, 4).* ' " The first of fonr magnitudes is enid to bare the same ratio to the second, wh'ich the third has...the fourth, when any equimultiples whatsoever of the fir>t aiid third being taken, ”ind any equimultiples whatsoever of the second and fourth ; if the...
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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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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...controversy among geometers. Euclid defines them thus : The first of four magnitudes is said to have the same ratio to the second, which the third has...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
...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 second, which the third has...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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...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...equimultiples whatsoever of the second and fourth ; if the inulliple of the first be less than that of the second, the multiple of the third is also less than...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...is to G, so is c F to H. Therefore, " if the first," &c. QED See N. Cou. Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples LFCDH whatever of the first and third have the same ratio to the second...
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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
...*i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes is said to have the same ratio to 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 of...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...of G, H : therefore (V. def. 5.) as E : G : : F : H. Therefore, &c. Cor. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any like multiples whatever of the first and third have the same ratio to the second and...
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The Elements of Algebra: Designed for the Use of Students in the University

John Hind - Algebra - 1837 - 539 pages
...there being taken any equimultiples whatever of the first and third, and any equimultiples whatever of the second and fourth : if the multiple of the first be greater than the multiple of the second, the multiple of the third will be greater than that of the...
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