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Books Books 1 - 10 of 58 on But it is commonly necessary that this first proportion should pass through a number....  
" But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect... "
An introduction to algebra: being the first part of a Course of mathematics ... - Page 190
by Jeremiah Day - 1827 - 332 pages
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 303 pages
...quantities are proportional. If the products are not equal, the quantities are not proportional. 379. In mathematical investigations, when the relations...products, will not destroy the proportion. Thus, if a : b : : c:d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1831 - 332 pages
...d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence, 379. In mathematical investigations, when the relations...of the means equal to the product of the extremes. 380. If four quantities are proportional, THE ORDER op THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS...
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An Introduction to Algebra ...

Jeremiah Day - 1832
...quantities are proportional. If the products are not equal, the quantities arc not proportional. 379. In mathematical investigations, when the relations...quantities may be varied, in any way which will leave adó be. Hence, 380. If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES,...
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A New Introduction to the Science of Algebra...

Silas Totten - Algebra - 1836 - 304 pages
...fractions being equal, and the denominators the same, the numerators must also be equal ; and hence, the product of the means equal to the product of the extremes. (66.) The property of geometrical proportions which has just been proved, is the fundamental principle...
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A practical and theoretical system of arithmetic: containing several new ...

George Willson - Education - 1838 - 192 pages
...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? ' What rule is founded on this equality ? Explain the common method of stating in the Single Rule...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1841 - 332 pages
...demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leasre the product of the means equal to the product of the...products, will not destroy the proportion. Thus, if a : 6 : : c : d, the order of these four quantities may be varied, in any way which will leave ad=bc....
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1842 - 332 pages
...proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of ihe ratios; or which will leave the product of the means...products, will not destroy the proportion. Thus, if o: 6:: c: d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

James Bates Thomson - Algebra - 1844 - 252 pages
...proportional. 343. It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the ratios ; or which will leave the...of the means equal to the product of the extremes. These changes are numerous, but they may be reduced to a few general principles. CASE I. Changes in...
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A New Practical and Theoretical Arithemtic: In Which, in Addition to the ...

Horatio Nelson Robinson - Arithmetic - 1845 - 288 pages
...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? What rule is founded on this equality ? Explain the common method of stating in the Single Rule of...
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 294 pages
...:: D : C; B : D : : A : C, &c. &c. From each of which we may readily derive the equation AD= CB, or the product of the means equal to the product of the extremes. Many other properties might be presented, but we limit ourselves to this short discussion, and proceed...
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