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. Elements of Algebra - Page 1851839 - 355 pagesFull view - About this book
| 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;... | |
| 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... | |
| Charles Davies - Algebra - 1860 - 330 pages
...proportion. 195. If four quantities are proportional, what is the product of the two means equal to ? 196. If the product of two quantities is equal to the product of two other quantities, may the four be placed in a proportion ? How ? Thus, if we have, • 2X8 = 4X4, we also have, 2 : 4... | |
| Charles Davies - Algebra - 1860 - 328 pages
...eatíh other, that AXD = BX (?, 7? /î we shall also have ~т — ~7Г' А С and hence, A : В : : С : D. That is : If the product of two quantities is equal to the prа duct of two other quantities, two of them may be made ike e& tremes, and the other two the means... | |
| 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... | |
| 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...two other quantities, two of them may be made the means, and the other two the extremes of a proportion. If we have, AD = J?(7, by changing the members... | |
| Benjamin Greenleaf - 1863 - 338 pages
...— • • THEOREM II. 316. If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion. Let ad = be. СЕ С Dividing by bd and reducing, ^ — -, or, a : b : : с : d. THEOREM III. 317i... | |
| 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.... | |
| Charles Davies - Algebra - 1864 - 316 pages
...each other, that AXD = В X <7, we shall also have, —¡ = -~ ; А. С and hence, A : В : : С : D. That is : If the product of two quantities is....to the product of two other quantities, two of them tnay be made the extremes, and the other two the means of a proportion. . 195. If four quantities are... | |
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