| Joseph Ray - Algebra - 1848 - 240 pages
...c is called a third proportional to a and b. ART. 244. — PROPOSITION I. — In every proportion, **the product of the means is equal to the product of the extremes.** Let a : b : : c : d. Then, since this is a true proportion, the quotient of the second divided by the... | |
| James Bates Thomson - Arithmetic - 1848 - 422 pages
...is simple proportion proved ? Demonstration.—If four numbers are proportional, we have seen that **the product of the means is equal to the product of the extremes;** (Art. 498;) therefore the product of the second and third terms must be equal to that of the first... | |
| Pliny Earle Chase - Arithmetic - 1848 - 240 pages
...consequents may, therefore, change places in a variety of ways, the proportion always continuing so long as **the product of the means is equal to the product of the extremes.** Then, whenever one of the extremes and the two means are given, to find the other extreme, Divide the... | |
| Zadock Thompson - Arithmetic - 1848 - 168 pages
...product rr the first and fourth equals the product of the second and third, or, m other words, that tlie **product of the means is equal to the product of the extremes.** 194. In the proportion, 4 : 6 : : 12 : 18, the order of the terms may be altered without destroying... | |
| Joseph Ray - Algebra - 1852 - 396 pages
...consecutive, they are said to form a continued proportion. ART. 267. PROPOSITION I. — In every proportion, **the product of the means is equal to the product of the extremes.** Let a : 6 : : c : d. Since this is a true proportion, the ratio of the first term to the second, is... | |
| Joseph Ray - Algebra - 1852 - 343 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 - Arithmetic - 1852 - 263 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... | |
| John Fair Stoddard - Arithmetic - 1852 - 299 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 - 1848 - 240 pages
...c is called a third proportional to a and &. ART. 244. — PROPOSITION I. — In every proportion, **the product of the means is equal to the product of the extremes.** Let a : b : : c : d. Then, since this is a true proportion, the quotient of the second divided by the... | |
| Dana Pond Colburn - Arithmetic - 1855 - 366 pages
...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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