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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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Higher Arithmetic: Or, The Science and Application of Numbers: Combining the ...

James Bates Thomson - 1847 - 422 pages
...324 SIMPLE [SECT. XIV. fieiiviisfrat-tfin. — If four numbers are proportional, we Lave seen th:\t the product of the means is equal to the product of the i-xtrimcs ; (Art. 4!)S:) therefore the pr id let of tile acca ul and t.hv'd terms must be equal to...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 240 pages
...Ans< Or thus: Let x= one part; then 55— x= 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 3z=2(55 — z)=110 — 2x 5*=110 z=22, and 55— x=33, as before. Or thus : Let x= one part,...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 240 pages
...Let x= one part; then 55— = the other. By the question, x : 55 — x : : 2 : 3. Then, since, m every proportion, the product of the means is equal to the product of the extremes, we have 3x=2(55 — x)=110 — 2x 5x=110 x=22, and 55— x=33, as before. Or thus : Let x= one part,...
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Youth's Columbian Calculator: Being an Introductory Course on Arithmetic for ...

Almon Ticknor - Arithmetic - 1848 - 96 pages
...means, and the first and fourth terms the extremes : 2 : (4 : : 8) : 16 _4X _2X 32 32 Here we see that the product of the means is equal to the product of the extremes. If 2 pounds of tea cost 4 dollars, •what will 8 pounds cost 1 6. Here the price of the tea is 2 dollars...
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The Elements of Arithmetic...: In which Decimal and Integral ..., Part 2

Pliny Earle Chase - Arithmetic - 1848 - 240 pages
...consequents may, therefore, change places in a variety of ways, the proportion always continuing so long as the product of the means is equal to the product of the extremes. Then, whenever one of the extremes and the two means are given, to find the other extreme, Divide the...
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Higher Arithmetic, Or, The Science and Application of Numbers: Combining the ...

James Bates Thomson - Arithmetic - 1848 - 422 pages
...is simple proportion proved ? Demonstration.—If four numbers are proportional, we have seen that the product of the means is equal to the product of the extremes; (Art. 498;) therefore the product of the second and third terms must be equal to that of the first...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 240 pages
...of the question, we have the following proportions : z+5 : y+5 : : 5 : 6 a:— 5 : y— 5 : : 3 : 4. Since, in every proportion, the product of the means is equal to the product of the extremes, we have the two equations 6(x+5)=5(y+5) 4(x-5)=3(y-5) From these equations, the values of z and y are...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 396 pages
...her, and 5x for the second, which fulfills the first condition. Then, Sx-\-Q : 5*+9 : : 6 : 7. But in every proportion, the product of the means is equal to the product of the extremes. (Arith. Part 3rd, Art. 209.) Hence, 6(5o:+9)=7(3;c+9). 30*4-54=2 la-l-63, 30*— 21*=63— 34, .-....
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Key to Ray's Algebra: Parts First and Second : Containing Statements and ...

Joseph Ray - Algebra - 1852 - 343 pages
...100 — 3x= B's gain, and 40x — 200= A's stock. .-. 40ж— 200 : 20ж : ; 3ж : 100— 3ж. Since the product of the means is equal to the product of the extremes, 60x2=(40x — 200)(100— 3x) ; reducing ж'— fi!3=— 'Лр- • Whence x=20, hence 3x=60= A's...
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Stoddard's Practical Arithmetic

John Fair Stoddard - Arithmetic - 1852 - 299 pages
...obtained by dividing the third term by the fourth, we can readily deduce the following PROPOSITIONS. , 1. The product of the means is equal to the product of the extremes. Therefore. 2. If the product of the means be divided by one extreme, the quotient will be the other...
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