If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. A Text-book of Geometry - Page 128by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
| 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 the equal products.... | |
| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...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... | |
| Joseph Ray - Algebra - 1852 - 422 pages
...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... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...2 : 5 is a false proportion, since 3X5 is not equal to 8x2. 245. 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 6c=ad. Dividing... | |
| Joseph Ray - Algebra - 1866 - 250 pages
...2 : 5 is a false proportion, since 3x5 is not equal to 8x2. 245. Proposition II. — Conversely, If **the product of two 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... | |
| Eli Todd Tappan - Geometry - 1868 - 444 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 the equal products.... | |
| William Frothingham Bradbury - Algebra - 1868 - 270 pages
...d ac ie r = 3 bd Clearing of fractions, ad = bc P RATIO AND PROPORTION. 209 THEOREM II. 203 • If **the product of two quantities is equal to the product of two others,** the factors of either product may be made the extremes, and the factors of the other the means of a... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...Then | = J, Art. 292. Multiplying each of these equals by bd, we have ad—be. 9 300.^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.... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers **is equal to the product of two others, either two may be made the extremes,** and the other two the means, of a proportion. For, if we have given ab' = a'b, then, dividing by bb',... | |
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