 | Elias Loomis - Algebra - 1856 - 280 pages
...the equation of fractions, we have ad— bc. Thus, if 3:4:: 9:12, then 3x12=4x9. (184.) Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes, and the other two the means of a proportion.... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...by the proposition, A xC=B xB, which is equal to B'. PROPOSITION ii. THEOEEM (Converse of Prop. /.). If the product of two quantities is equal to the product of twc other quantities, the first two may be made the extremes, and the other two the means of a proportion.... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...by the proposition, AXC = BXB, which is equal to B1. PROPOSITION n. THEOREM (Converse of Prop. /.). If the product of two quantities is equal to the product of twc other quantities, the first two may be made the extremes, and the other two the means of a proportion.... | |
 | Charles Davies - Algebra - 1859 - 324 pages
...to each 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...extremes, and the other two the means of a proportion. 195. If four quantities are proportional, what is the product of the two means equal to ? Thus, if... | |
 | 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 - 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... | |
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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. 
