| James Bates Thomson - 1847 - 422 pages
...324 SIMPLE [SECT. XIV. fieiiviisfrat-tfin. — If four numbers are proportional, we Lave seen th:\t **the product of the means is equal to the product of the** i-xtrimcs ; (Art. 4!)S:) therefore the pr id let of tile acca ul and t.hv'd terms must be equal to... | |
| Joseph Ray - Algebra - 1848 - 240 pages
...Ans< Or thus: Let x= one part; then 55— x= the other. By the question, x : 55 — x : : 2 : 3. Then, **since, in every proportion, the product of the means is equal to the product of the extremes,** we have 3z=2(55 — z)=110 — 2x 5*=110 z=22, and 55— x=33, as before. Or thus : Let x= one part,... | |
| Joseph Ray - Algebra - 1848 - 240 pages
...Let x= one part; then 55— £= the other. By the question, x : 55 — x : : 2 : 3. Then, since, m **every proportion, the product of the means is equal to the product of the extremes,** we have 3x=2(55 — x)=110 — 2x 5x=110 x=22, and 55— x=33, as before. Or thus : Let x= one part,... | |
| Almon Ticknor - Arithmetic - 1848 - 96 pages
...means, and the first and fourth terms the extremes : 2 : (4 : : 8) : 16 _4X _2X 32 32 Here we see that **the product of the means is equal to the product of the extremes.** If 2 pounds of tea cost 4 dollars, •what will 8 pounds cost 1 6. Here the price of the tea is 2 dollars... | |
| 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... | |
| 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... | |
| Joseph Ray - Algebra - 1848 - 240 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 - 396 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, .-.... | |
| 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... | |
| 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... | |
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