 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.  New University Algebra - Page 266by Horatio Nelson Robinson - 1875 - 412 pagesFull view - About this book
 | 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.... | |
 | 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.... | |
 | 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.... | |
 | 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... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...-=о be The first extreme, a = -=• bc The second extreme. d = — ' a Hence, 1st. Either mean ù equal to the product of the extremes divided by the...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. Let... | |
 | 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.... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...mean proportional of two quantities is the square root of their product. * 18. Proposition — When the product of two quantities is equal to the product of two others, either two may be the extremes and the other two the means of a proportion. Let aXd = bXc represent... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...given in Article 240. Thus, 3 : 8 : : 2 : 5 is a false proportion, since 3x5 is not equal to 8x2. 245. Proposition II. — Conversely, If the product of...quantities is equal to the product of two others, two of them may le made the means, and the other two the extremes of a proportion. Let be— ad. Dividing... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...to 7 is less or r-ieatt-r than the ratio of 3 to 10, we have the two fractions I, aud y, 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 bc=ad. Dividing... | |
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