 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
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...4 > Are ax, abx, bx in proportion ? 5, Are ax, xVab, bx in proportion ? PROPOSITION (38 4i) 3. When the product of two quantities is equal to the product of two other quantities, the four quantities may be expressed in the form of three different, proportions. DEMONSTRATION. Let od=6c.... | |
 | Charles Davies - Algebra - 1859 - 324 pages
...other, that A x D = В x (7, we shall also have, -j = -~ ; А ъ and hence, A : В : : С : D. That is : If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion. 195. If four quantities... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...square root of their product. Thus from the equation ax=b2, we find b = (ax)*. THEOREM IV. (153.) When the 'product of two quantities is equal to the product of two other quantities, either pair of factors may be made the extremes, and the other the means, of a Proportion. Let ab=xy;... | |
 | Chambers W. and R., ltd - 1859 - 344 pages
...is a mean proportional between the 4 and 9. Since —^- = 9, .'.6X6 = 9X4; that is, 62 = 9 X 4 ; or the square of the mean is equal to the product of the extremes. Hence — , To FIND THE MEAN PROFORTIONAL BETWEEN TWO GIVEN NUMBERS. Multiply the one number by the... | |
 | Thomas Sherwin - Algebra - 1841 - 318 pages
...transposition we obtain a — b = c — d. Therefore, if the sum of two quantities is equal to the sum of twn other quantities, the first two may be made the means, and the last two the extremes, or the reverse, of an equidifference. When three quantities, a, b, c, either... | |
 | Charles Davies - Algebra - 1861 - 322 pages
...Thus, if we have the proportion 3 : 6 : r 6 : la, we shall also have 6 X 6 = 62 = 3 X 12 = 30. 155. If the product of two quantities is equal to the product of 170 other quantities, may the four be placed in a proportion ? He wt 157. If we have 7? 7) A : B :... | |
 | Thomas Sherwin - 1862 - 252 pages
...equation ad—be. If we divide both members by 6 and d, we have — = —, or a : b = c : d. Therefore, bd If the product of two quantities is equal to the product of two other quantities, the two factors of one product may be made the means, and the two factors of the other product, the extremes... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...this case, the square of the mean is equal to the product of the extremes. PROPOSITION II. THEOREM. jy the product of two quantities is equal to the product of two other quantities, two of them may be made the means, and the other two the extremes of a proportion. If we have, AD =... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...to the product of the means divided by the other extreme. (2) 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 tico for the extremes of a proportion.... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...to tJte product of the means divided by the other extreme. (2) 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.... | |
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