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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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Rational arithmetic

Sarah Porter - 1852
...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 - 366 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 - 238 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 - 366 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 - 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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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1857 - 396 pages
...numo ber, and 5x for the 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 Common-school Arithmetic: a Practical Treatise on the Science of Numbers

Dana Pond Colburn - 1858 - 276 pages
...to the 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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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 school arithmetic

Robert Johnston (F.R.G.S.) - 1860
...are called 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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University Algebra : Embracing a Logical Development of the Science with ...

Charles Davies - Algebra - 1860 - 320 pages
...- • . . (1.) ac Clearing of fractions, we have, bc = ad (2.) Hence, 1 . If four quantities are in proportion, the product of the means is equal to the product of the extremes. Conversely, if we divide both members of ( 2 ) by ca, we shall have, - — - ; or, a : b : : c : d....
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