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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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Teacher's manual [&c.].

Robert Robinson (inspector of national sch, Ireland.) - 1867
...leads to the least misconception of what is really stated, and forms the best test of its accuracy. The product of the means is equal to the product of the extremes. Those who know that the expressions 3 : 4 : : 6 : 8 and are equivalent, and who understand some little...
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Practical Arithmetic, Embracing the Science of Numbers and the Art of ...

John Fair Stoddard - Arithmetic - 1868 - 380 pages
...: 2 :: 6 : 3 4 6 becomes s=o> multiplying each member by 2 and 3, we 2i o have 4x3=6x2. Hence, 382. In every proportion, the product of the means is equal to the product of the extremes. 1. Either extreme is equal to the product of the means divided by the other extreme. 2. Either mean...
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Stoddard's Complete Arithmetic: Being the New Practical Arithmetic of the ...

John Fair Stoddard - Arithmetic - 1888 - 456 pages
...: : 6 : 3 4 6 becomes 5=5. multiplying each member by 2 and 3, we jy *_) have 4x3=6x2. Hence, 382. In every proportion, the product of the means is equal to the product of the extremes. 1. Either extreme is equal to the product of the means divided by the other extreme. 2. Either mean...
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 252 pages
...fourth terms of a proportion are called the extremes, and the second and third the means. 106. In a proportion the product of the means is equal to the product of the extremes. Let ie a : b = c : d Clearing of fractions, ad = be A proportion is an equation ; and making the product...
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Practical Arithmetic, by Induction and Analysis

Joseph Ray - Arithmetic - 1857 - 336 pages
...Thus, in the proportion 2 : 3 : : 4 : 6, 2 and 6 are the extremes, and 3 and 4 the means. ART. 200. In every proportion, the product of the means is equal to the product of tJie extremes. ILLUSTRATIONS. — If we have 3 : 4 : : 6 : 8, the ratios of each couplet being equal...
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New Practical Arithmetic in which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1869 - 324 pages
...repeated between the other two. Thus, In 12 : 6 :: 6 : 3, 6 is a mean proportional. TOIIVCIIVLES. 328. 1. In every proportion the product of the means is equal to the product of the extremes. For, in the proportion 6 : 3 : : 4 : 2, since the ratios are equal (Art. 326), WB have $ = . Now,...
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THE GEOMETRY OF THE CIRCLE AND MATHEMATICS

JAMES SMITH - 1869
...: B : C. When A denotes ^-^ and B denotes i, then, C = 1-28 : that is, 78125 : i : : I : 1-28, and the product of the means is equal to the product of the extremes. Hence : -~I**A and —-^ are equivalent ratios, and it follows, that the product of any number multiplied...
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The geometry of the circle and mathematics as applied to geometry by ...

James Smith - 1869 - 470 pages
...or proportion, A : B : : B : C, when A denotes * ^* and B denotes I ; then, -8 : I : : I : -125, and the product of the means is equal to the product of the extremes. Now, if the radius of a circle = -125, then, (6 x -125) = 75 = the perimeter of a regular inscribed...
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The ratio between diameter and circumference in a circle demonstrated by ...

James Smith - 1870
...63 agreed. If I : 2 : : 2 : 4, the converse of this proportional holds good ; 4 : 2 : : 2 : I, and the product of the means is equal to the product of the extremes : mxn = xm, whatever values we may put upon m and , and in either way, works out to the same result...
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Elements of Algebra: For Colleges, Schools and Private Students

Joseph Ray - Algebra - 1866 - 406 pages
...other as 6 to 7? Let 3a:= the first, and 5x= the second number. Then, 3z-|-9 : 5.r+9 : : 6 : 7. But in every proportion, the product of the means is equal to the product of the extremes. (RAT'S ARTTH., 3d Book, Art. 200.) Hence, 6(5a;+9)=7(3a;+9). From which the answer is readily found....
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