 | 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... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...related to each other, that the product of two of them is equal to the product of the other two ; then two of them may be made the means, and the other two the estremes of a proportion. Let A, B, C, and D, have such values that BxC=AxD Divide both sides of the... | |
 | 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 extremes of a proportion. Let . .......... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...this case, the square of the mean w equal to the product of the extremes. PROPOSITION II. THEOREM. If the product of two quantities is equal to the product of two other quantit1es, two nf them may be made the means, and the other two the extremes of a proportion. If we... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...equal to the product of the means is merely clearing the equation of fractions. THEOREM II. 141 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... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...equal to the product of the means is merely clearing the equation of fractions. THEOREM II. 14, If the product of two quantities is equal to the product of two others, the factors of eiIher product may be made the extremes, and the factors of the other the means... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...: d. Then | = |,Art.292. Multiplying each of these equals by bd, we have ad=bc. 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. Let ad— be.... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...this case, the square of the mean is equal to the product of the extremes. PROPOSITION n. THEOREM. If the product of two quantities is equal to the product...other two the extremes of a proportion. If we have, AD = BC, by changing the members of the equation, we have, BQ = AD; dividing both members by AC, we have,... | |
 | Charles Davies - Algebra - 1875 - 318 pages
...have, -j = -^ ; and hence, u4 : -Z? : : C : D. That is: If the product of two quantities is eqital 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 are proportional, what... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
...Conversely, if we divide both members of (2) by ca, we have, - = -; or, a : b :: c : d; hence, ac If the product of two quantities is equal to the product of two other quantities, the first two may be made the means, and the second two the extremes, of a proportion. It follows,... | |
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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. 
