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Books Books 31 - 40 of 96 on The first of four magnitudes is said to have the same ratio to the second, which....
" 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... "
A system of practical mathematics; being no.xvi. of a new series of school-books - Page 111
1845
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 second, which the third has to the fourth, when, any equimultiples whatever of the first and third being taken,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 317 pages
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the first has the same ratio to the second that the third has to the fourth. We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,...
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Arithmetic, in Two Parts

Frederic A. Adams - Arithmetic - 1846 - 212 pages
...tho value is not altered ; it is still 2. PROPORTION. If there are four numbers, and the first has the same ratio to the second that the third has to the fourth, the four numbers are said to be in proportion. Thus the numbers 2:1:: 12 : 6, are in proportion. The...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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 second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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A manual of explanatory arithmetic

Edward Hughes - 1849
...9. 18. 12. 12. 18. 4. 48. Suppose any four terms to be proportional, that is, the first term shall have the same ratio to the second that the third has to the fourth ; for example : 8 : 12: : 10 : 15. Let us multiply the two means together 1 2 X 10=1 20, and also the...
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Putnam's Arithmetic

Rufus Putnam - Arithmetic - 1849 - 264 pages
...proportion consists of two equal ratios. When four numbers are so related to each other, that the first has the same ratio to the second that the third has to the fourth, they constitute a proportion. Thus the numbers 4, 5, 2, 15, form a proportioH, because the ratio...
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An Elementary and Practical Arithmetic

James B. Dodd - 1850
...PROPORTION consists in an equality of ratios. Four quantities are in proportion, when the first has the same ratio to the second, that the third has to the fourth. Thus, the numbers 6, 3, 8, 4, are in proportion; since the ratio of 6 to 3 is =2, and the ratio of...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - Mathematics - 1853
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. 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,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 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 second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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High school arithmetic

James B. Dodd - 1853
...PROPORTION consists in an equality of ratios. Four quantities are in proportion, when the first has the same ratio to the second, that the third has to the fourth. Thus, the numbers 6, 3, 8, 4, are in proportion; since the ratio of 6 to 3 is f=2, and the ratio of...
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