| 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... | |
| 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, .-.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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