| Francis Henney Smith - Arithmetic - 1845 - 300 pages
...fourth by multiplying the second and third terms together, and dividing by thefirst. For, by Art. 178, **the product of the means is equal to the product of the** first term by the fourth. The fourth term must therefore be equal to the product of the means divided... | |
| Frederick Emerson - Arithmetic - 1846 - 268 pages
...Since. the product of the extremes m every proportion is equal to the product of the means, one product **may be 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... | |
| Euclides - 1846 - 272 pages
...dividing the antecedent by the consequent is called the ratio. If four quantities are proportional, **the product of the means is equal to the product of the extremes;** in the proportion a : 6 ; ; c : d, a and d are the extremes, b and c the means. Wherefore, in order... | |
| James Bates Thomson - Arithmetic - 1847 - 434 pages
...the work is right. (Art. 500.) 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 prDcliict of the second and third terms must be equal to that of the first... | |
| James Bates Thomson - Arithmetic - 1847 - 424 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 - 252 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 - 250 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,... | |
| 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 - 432 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... | |
| Almon Ticknor - Arithmetic - 1848 - 122 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... | |
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