 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...definition, that the product of the extremes is equal to the product of the menus ; and conversely, if the product of two quantities is equal to the product of two others, the first two may be taken as the structed with a groove in each leg, so that extremes, and... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...expression becomes abd bcd ~b~=~d' or ad=bc. Thus, if 3 : 4 : : 9 : 12, .hen 3X12=4X9. (213.) 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.... | |
 | Thomas Sherwin - Algebra - 1855 - 318 pages
...product of the extremes. 2. Suppose we have ad=bc. Dividing both members by b XLIX. PROPORTIONS. 221 If the product of two quantities is equal to the product of two otner quantities, the two factors of either product may be made the means, and the two factors of the... | |
 | Elias Loomis - Algebra - 1856 - 280 pages
...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.... | |
 | Charles Davies - Algebra - 1859 - 324 pages
...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...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... | |
 | 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... | |
 | Thomas Sherwin - 1862 - 252 pages
...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... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...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.... | |
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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. 
