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Books Books 41 - 50 of 195 on In any proportion, the product of the means is equal to the product of the extremes..
" In any proportion, the product of the means is equal to the product of the extremes. "
Treatise on the elements of algebra - Page 256
by James Bryce - 1837
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Common School Algebra

Thomas Sherwin - 1855
...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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The American Philosophical Arithmetic: Designed for the Use of Advanced ...

John Fair Stoddard - Arithmetic - 1856 - 292 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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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - Arithmetic - 1856 - 366 pages
...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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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1857 - 396 pages
...second, which fulfills the first condition. Then, 3a:+9 : 5x+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(5a:+ff)=7(3z+9). 30a+54=21 x+63, 30a:—21a;=63—54, 9*=9, x=l,...
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The Massachusetts Teacher, Volume 16

Education - 1863
...solution of problems. Some might prefer to show how any missing term may be found, by first showing that the product of the means is equal to the product of the extremes. In that case, such a method as the following might be adopted.] T. Let us now compare the product of...
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The Common-school Arithmetic: a Practical Treatise on the Science of Numbers

Dana Pond Colburn - 1858 - 276 pages
...quotient obtained by dividing the product of the extremes by the other mean. (k.) Hence, in a proportion, the product of the means is equal to the product of the extremes. 105. Problems in Proportion. NOTE.— These problems may be solved by analysis instead of proportion,...
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First Lessons in Algebra: Being an Easy Introduction to that Science ...

Ebenezer Bailey - Algebra - 1859 - 254 pages
...But ad is the product of the extremes, and be the product of the means. Hence, 212. In any proportion the product of the means is equal to the product of the extremes. Thus, if 2 : 5 : : 8 : 20, then 2 X 20 = 5 X 8. Again, if ad = be, we may divide both members by bd....
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Practical Arithmetic: Uniting the Inductive with the Synthetic Mode of ...

James Bates Thomson - Arithmetic - 1860 - 384 pages
...reason that dividing the product of the second and third terms by the flrst,gives the answer, is because the product of the means is equal to the product of the extremes ; and if the product of two numbers is divided by one of the numbers, the quotient will be the uther number. (Arts. 291, 324.)...
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - 1860
...obtained by dividing the product of the extremes by the oiher mean. (6.) 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 school arithmetic

Robert Johnston (F.R.G.S.) - Arithmetic - 1860 - 169 pages
...means (t) and 10) ; the first and fourth, extremes (15 and 6). When four numbers form a proportion, The product of the means is equal to the product of the extremes. Thus, 6 : 3 : : 8 : 4 ; here, 6X4, the extremes, =8X3, the means, = 24. 156. If the product of any...
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