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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 73
by Zadock Thompson - 1832 - 168 pages
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...the extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, the product of the means is equal to the product of the extremes. APPLICATION OF THE FORMULAS. 364. The two primitive equations, ,. ,given, the other two may be...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...the. extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, the product of the means is equal to the product of the extremes. APPLICATION OF THE FOKMULAS. 364. The two primitive equations, contain the five quantities, a, r, l,...
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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 252 pages
...thus : Let a;= one part ; then, 55 — = the other. By the question, x : 55 — x : : 2 : 3. Then, since, in every proportion, the product of the means is equal to the product of the extremes, we have 3a;=2(55 — 2)=110 — 2x. 5z=110 3=22, and 55— 3=33, as before. Or, thus : Let x= one part;...
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Ray's Algebra, First Book: Primary Elements of Algebra, for Common Schools ...

Joseph Ray - Algebra - 1866 - 252 pages
...are the first and last terms of a proportion called ? The second and third? 244. Proposition I. — In every proportion, the product of the means is equal to the product of the extremes. Let a : b • : c : d. Then, since this is a true proportion, we must hnve bd Clearing of fractions,...
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Teacher's manual [&c.].

Robert Robinson (inspector of national sch, Ireland.) - 1867 - 388 pages
...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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Key to Ray's New Algebras, Elementary and Higher: Containing Statements and ...

Joseph Ray - Algebra - 1867 - 240 pages
...100—3z= B's gain, and 40z — 200= A's stock. Therefore, 4te— 200 : 20a; : : 3x : 100—3z. Since the product of the means is equal to the product of the extremes, 60z2=(40z— 200)(100— 3). Reducing, z2— J{x=— io. Whence, z=20; hence, &c=60= A's gain,...
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Stoddard's Complete Arithmetic: Being the New Practical Arithmetic of the ...

John Fair Stoddard - Arithmetic - 1888 - 480 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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Practical Arithmetic, Embracing the Science of Numbers and the Art of ...

John Fair Stoddard - Arithmetic - 1868 - 430 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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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 270 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 - 360 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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