| Joseph Denison - Mechanics - 1841 - 210 pages
...by one of the inclined sides ; that is, P = — S TT By theorem 1, P ; R ; ; — ; S ; and because **the product of the means is equal to the product of the extremes,** PS=R|; and dividing each of these equals by S, K! From theorem 2 we derive the following rule for finding... | |
| Thomas Sherwin - Algebra - 1842 - 300 pages
...denominators 5 and d, we have ad = b c. But a and d are the extremes, and 6 and c the means. Hence, In any **proportion the product of the means is equal to the product of the extremes.** 2. Suppose we have ad = bc. Dividing both members by 6 and d, we have r = -, or a : b = c : d. Hence,... | |
| John Darby (teacher of mathematics.) - 1843 - 236 pages
...the second T8T, and they are equal ; that is 4 : 6 :zz 8 : 12, Therefore £ = TV Whence 4x12:=eX8. **In Proportion, the product of the means is equal to the product of the extremes;** therefore 4 : 6 :: 8 : 12. In this proportion the 4 and 12 are the extremes, and the 6 and 8 the means.... | |
| Pliny Earle Chase - Arithmetic - 1844 - 248 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... | |
| Pliny Earle Chase - 1844 - 258 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... | |
| Emanuel Swedenborg - Physiology - 1845 - 602 pages
...that the rectangle of the means is equal to the rectangle of the extremes ; or as in arithmetic, that **the product of the means is equal to the product of the extremes.** Hence, the action of the second and third being equal to the action of the first and fourth, we have... | |
| 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... | |
| Francis Henney Smith - Arithmetic - 1845 - 712 pages
...fourth by multiplying the second and third terms together, and dividing by the first. For, by Art. 178, **the product of the means is equal to the product of the** first term by Ihe fourth. The fourth term must therefore be equal to the product of the means divided... | |
| 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... | |
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