| 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 — = —,... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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.... | |
| 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.)... | |
| 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... | |
| 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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