 Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.  Manual of Algebra - Page 239by William Guy Peck - 1875 - 331 pagesFull view - About this book
 | James Thomson - 1847 - 196 pages
...the square of the mean, the radical will be imaginary, and the question absurd. It appears also, that the square of the mean is equal to the product of the extremes together with the square of the common difference. Exer. 35. Denoting the numbers by а — x, a, and... | |
 | Charles Davies - Algebra - 1848 - 300 pages
...Thus, if we have the proportion 3 : 6 : : 6 : 12, we shall also have 6x6=6a=3xl2=36. QUEST. — 155. If the product of two quantities is equal to the product of two other quantities, may the four be placed in a proportion ? How ? — 150. If three quartiues are proportional, what is... | |
 | Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...means in both cases is the same. So if na : b : : x : y, then a : b : : x : ny. 339. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion if they are so arranged, that those on one side... | |
 | Joseph Ray - Algebra - 1848 - 252 pages
...equul to 8X2, we infer that the proportion isfalie. .\,.t-'2l't. — PROPOSITION II. — Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...: B : : B : C ; then, by the proposition, I BOOK H. PROPOSITION ii. THEOREM (Converse of Prop. /.). If the product of two quantities is equal to the product...two other quantities, the first two may be made the extremes, and the other two the means of a proportion. Thus, suppose we have AXD=BXC; then will A :... | |
 | Uriah Parke - Arithmetic - 1849 - 414 pages
...extremes, and hence we find it by taking half the sum of the extremes; so in a geometrical series, the square of the mean is equal to the product of the extremes; and hence to find it we multiply the extremes together and take the square root of the product. Rules... | |
 | Uriah Parke - Arithmetic - 1850 - 402 pages
...extremes, and hence we find it by taking half the sum of the extremes; so in a geometrical series, the square of the mean is equal to the product of the extremes; and hence to find it we multiply the extremes together and take the square root of the product. Rules... | |
 | Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...first term. This is a part of the well known rule of three, in Arithmetic. PROPOSITION II. Conversely. If the product of two quantities is equal to the product of two others, then two of them may be taken for the means, and the other two for the extremes of a proportion.... | |
 | William Smyth - Algebra - 1851 - 272 pages
...From the continued proportion a : b : : b : d, we obtain b1 = ad. Whence, in a continued proportion, the square of the mean is equal to the product of the extremeS. To find, therefore, a mean proportional between two quantities, we take the square root of the product... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...to 2X8, we infer that 2, 3, 5, and 8, are not in proportion. ART. 268. PROPOSITION II. Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let be—... | |
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