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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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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 248 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 - 410 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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Stoddard's Practical Arithmetic

John Fair Stoddard - Arithmetic - 1852 - 324 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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Key to Ray's Algebra: Parts First and Second : Containing Statements and ...

Joseph Ray - Algebra - 1852 - 360 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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Rational arithmetic

Sarah Porter - 1852 - 286 pages
...multiplied by the third term : ji 1 fi for as 7 : 8 : : 14 : 16, therefore - = — = 8x14=16x7, or the product of the means is equal to the product of the extremes. Hence if any three numbers be given, a fourth proportional to them may be found, such as, this 4th...
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...to the quotient obtained by dividing the product of the extremes by the other mean. (5.) Hence, in a proportion — The product of the means is equal to the product of the extremes. 161. Practical Problems. (a.) The forming of a proportion from the conditions of a problem is called...
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Common School Algebra

Thomas Sherwin - Algebra - 1855 - 264 pages
...6 d b and d, we have ad=bc. But a and d are the extremes, and 6 and c are the means. Hence, In any proportion, the product of the means is equal to the product of the extremes. (п). Suppose we have the equation ad=bc. If we divide both members by b and d, we have — = —,...
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...to the quotient obtained by dividing the product of the extremes by the other mean. (b.) Hence, in a proportion — The product of the means is equal to the product of the extremes. 161 • Practical Problems. (a.) The forming of a proportion from the conditions of a probiem is called...
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The American Philosophical Arithmetic: Designed for the Use of Advanced ...

John Fair Stoddard - Arithmetic - 1856 - 312 pages
...obtained, by dividing the fourth term by the third, 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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The North American Arithmetic: Part Third, for Advanced Scholars

Frederick Emerson - Arithmetic - 1834 - 346 pages
...product of the extremes in every proportion is equal to the product of the means, one product may he taken for the other: now if we divide the product of the extremes by one extreme, the quotient is the other extreme; therefore, if we divide the product of...
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