| 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.... | |
| 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.... | |
| 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.... | |
| 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
...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.... | |
| 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.... | |
| 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. Let... | |
| 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 - 420 pages
...: 8, is not a true proportion, since 3X5 is not equal to 2x8. 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 extreme* of a proportion. Let ........ bc... | |
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