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" In any proportion, the product of the means is equal to the product of the extremes. "
Elements of Plane Geometry: For the Use of Schools - Page 53
by Nicholas Tillinghast - 1844 - 96 pages
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A new treatise on mechanics, by the author of A new introduction to the ...

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...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

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,...
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The practical arithmetic

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....
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Elements of Arithmetic: For Schools and Academies. In which Decimal and ...

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...
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The Elements of Arithmetic ... in which Decimal and Integral Arithmetic are ...

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...
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The Economy of the Animal Kingdom, Considered Anatomically ..., Volume 1

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...
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Smith and Duke's The American Statistical Arithmetic: Designed for Academies ...

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...
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The American Statistical Arithmetic: Designed for Academies and Schools

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...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

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...
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Higher Arithmetic: Or, The Science and Application of Numbers; Combining the ...

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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