 | Jeremiah Day - Algebra - 1814 - 304 pages
...quantities are proportional. We have only to multiply the means together, and also the extremes. If the two products are equal, the quantities are proportional....products, will not destroy the proportion. Thus, if a : b : : c:d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,... | |
 | Jeremiah Day - Algebra - 1831 - 358 pages
...c : d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence, 379. In mathematical investigations, when the relations...of the means equal to the product of the extremes. 380. If four quantities are proportional, THE ORDER op THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS... | |
 | Jeremiah Day - Algebra - 1832 - 360 pages
...products are equal, the quantities are proportional. If the products are not equal, the quantities arc not proportional. 379. In mathematical investigations,...quantities may be varied, in any way which will leave ad— be. Hence, 380. If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES,... | |
 | Silas Totten - Algebra - 1836 - 332 pages
...fractions being equal, and the denominators the same, the numerators must also be equal ; and hence, the product of the means equal to the product of the extremes. (66.) The property of geometrical proportions which has just been proved, is the fundamental principle... | |
 | George Willson - Arithmetic - 1838 - 194 pages
...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? ' What rule is founded on this equality ? Explain the common method of stating in the Single Rule... | |
 | Jeremiah Day - Algebra - 1841 - 362 pages
...demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leasre the product of the means equal to the product of the...products, will not destroy the proportion. Thus, if a : 6 : : c : d, the order of these four quantities may be varied, in any way which will leave ad=bc.... | |
 | Jeremiah Day - Algebra - 1842 - 356 pages
...proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of ihe ratios; or which will leave the product of the means...products, will not destroy the proportion. Thus, if o: 6:: c: d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,... | |
 | James Bates Thomson - Algebra - 1844 - 272 pages
...proportional. 343. It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the ratios ; or which will leave the...of the means equal to the product of the extremes. These changes are numerous, but they may be reduced to a few general principles. CASE I. Changes in... | |
 | Horatio Nelson Robinson - Arithmetic - 1845 - 310 pages
...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? What rule is founded on this equality ? Explain the common method of stating in the Single Rule of... | |
 | Admiralty - 1845 - 152 pages
...equation, Divide by 13 .-. ж=12 61. An equation may be formed from 4 proportional quantities, by making the product of the means equal to the product of the extremes. Let the proportional quantities be x, y, a, b ; or x : y : : a : b. Vy-J (Art. 15.) .-. bx=ay. (Art.... | |
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But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect... 
