 | Francis Henney Smith - 1845 - 300 σελίδες
...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 - 1846 - 266 σελίδες
...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 σελίδες
...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 - 1847 - 434 σελίδες
...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 - 1847 - 426 σελίδες
...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 - 1848 - 252 σελίδες
...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 - 1848 - 250 σελίδες
...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 - 1848 - 244 σελίδες
...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 - 1848 - 432 σελίδες
...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 - 1848 - 124 σελίδες
...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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In any proportion, the product of the means is equal to the product of the extremes. 
