| 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'— ïfi!3=— 'Лр- • Whence x=20, hence 3x=60= A's... | |
| 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... | |
| 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 — = —,... | |
| 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... | |
| 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... | |
| Joseph Ray - Algebra - 1857 - 408 pages
...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,... | |
| Dana Pond Colburn - 1858 - 290 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,... | |
| Education - 1863 - 744 pages
...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... | |
| Charles Davies - Algebra - 1860 - 332 pages
...or, - = - • . . (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.... | |
| Robert Johnston (F.R.G.S.) - 1860 - 188 pages
...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... | |
| |