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" In any proportion, the product of the means is equal to the product of the extremes. "
The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ... - Page 67
by Zadock Thompson - 1848 - 168 pages
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Encyclopędia Americana: A Popular Dictionary of Arts, Sciences ..., Volume 10

Francis Lieber, Edward Wigglesworth, Thomas Gamaliel Bradford - Encyclopedias and dictionaries - 1835
...proportion, the sum of the extremes is equal to that of the means, and, in geometrical proportions, the product of the means is equal to the product of the extremes, either extreme (or mean) may be found in the former, by subtracting the given extreme (or mean) from...
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A New Introduction to the Science of Algebra...

Silas Totten - Algebra - 1836 - 304 pages
...progression 2, 5, 8, 11, &c. to 31 terms. Ans. 1457. GEOMETRICAL PROPORTIONS. (65.) In every geometrical proportion, the product of the means is equal to the product of the extremes. Take the proportion 12 : 4 = 18 : 6, or -T- = -»-. Now, if 12 18 we reduce the fractions -j- and -^...
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A New Introduction to the Science of Algebra...

Silas Totten - Algebra - 1836 - 304 pages
...— . Putting x in the place of the unknown term, the proportion becomes 12 : 4 = 18 : x ; and since the product of the means is equal to the product of the extremes (05), we have 12 xx = 18 x 4, or 12 x - 72 ; and as 1£ times x = 72, it ja 72 evident that x, the...
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A Treatise on the Elements of Algebra

James Bryce - Algebra - 1837 - 80 pages
...72— 4я+8; whence we easily find 4. Given, — £— : — ^ — : : 7 : 4, to find ». Since, in a proportion, the product of the means is equal to the product of the extremes (Eue. VI. 16), it follows that 126—7х 10х+8= - 4 - O2 By multiplication, 40 x +32 =126— 7x. whence,...
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A Practical and Theoretical System of Arithmetic: Containing a New System of ...

George Willson - Arithmetic - 1838 - 192 pages
...geometrical proportion consisting of four terms, have been explained on page 92, and the reason assigned why the product of the means is equal to the product of the extremes. This equality between their products suggests an obvious method of finding any term of a proportion,...
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The Western Practical Arithmetic: Wherein the Rules are Illustrated, and ...

Arithmetic - 1838 - 204 pages
...rule of three is derived.. In the following proportions the pupil will perceive that in every case the product of the means is equal to the product of the extremes. As 2 : 4 :: 6 : 12 2 : 8 :: 5 : 20 3 : 5 :: 6 : 10 7 : 11 :: 14 : 22 , Now suppose that we had the...
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A Practical and Theoretical System of Arithmetic: Containing Several New ...

George Willson - Arithmetic - 1838 - 192 pages
...geometrical proportion consisting of four terms, have been explained on page 92, and the reason assigned why the product of the means is equal to the product of the extremes. This equality between their products suggests an obvious method of rinding any term of a proportion,...
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The Teacher's Manual: Being an Exposition of an Efficient and Economical ...

Thomas H. Palmer - Education - 1840 - 263 pages
...whatever. Now, as these equal products are those of the extremes and means, we thus have the rule of proportion : The product of the means is equal to the product of the extremes. [Let this be demonstrated, a few times, on the blackboard, till it has become familiar. It will be...
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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - Mechanics - 1841 - 184 pages
...by one of the inclined sides ; that is, P = — S TT By theorem 1, P ; R ; ; — ; S ; and because the product of the means is equal to the product of the extremes, PS=R|; and dividing each of these equals by S, K! From theorem 2 we derive the following rule for finding...
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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - Mechanics - 1841 - 184 pages
...= —•; one value of V. Solution 2.—By the third expression, v \ V ; ; - ; —. * i And because the product of the means is equal to the product of the extremes, and dividing by -, V = (4) "OT ; second value of V, by the third expression (which is here used for...
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