 | John Darby (teacher of mathematics.) - 1829 - 212 pages
...are read, a is to b as c to d; therefore -r- = —r 2. When four quantities are proportionals, tha product of the means is equal to the product of the extremes ; that is, if a ; b ; ' c ; d, then will ad = be. Also, if a ; 6 ; rb ; c, then will ac = 62. Whence... | |
 | Oliver A. Shaw - Arithmetic - 1832 - 112 pages
...The other principles of the doctrine of proportion may also be demonstrated; as the proposition that the product of the means is equal to the product of the extremes, proportion by alternation, or that if the first term be to the second as the third is to the fourth,... | |
 | Zadock Thompson - Arithmetic - 1832 - 186 pages
...product of the first and fourth equals the product of the second and third, or, in other words, that the product of the means is equal to the product of the may stand, 4 : 12 : : 6 : 18, or 18 : 12 : : 6 : 4, or 18 : 6 :": 12 • 4 or 6 : 4 : : 18 : 12, or... | |
 | Francis Joseph Grund - Algebra - 1833 - 224 pages
...; (because 450 — г is A's gain, and 450 — (500 — x) = — 50 -f- x is B's gain,) and because the product of the means is equal to the product of the extremes, 450,000 — 900 x — 1,000 x -j- 2 x2 = 5 z2 — 250 *. This equation, when reduced, may be written... | |
 | Dionysius Lardner - Arithmetic - 1834 - 378 pages
...found. (379-) Since four numbers, which are in proportion, will continue to be in proportion so long as the product of the means is equal to the product of the extremes, it follows that we may make any of the following changes in the order of the four terms, without destroying... | |
 | Francis Lieber, Edward Wigglesworth - Encyclopedias and dictionaries - 1835 - 618 pages
...proportion, the sum of the extremes is equal to that of the means, and, in geometrical proportions, the product of the means is equal to the product of the extremes, either extreme (or mean) may be found in the former, by subtracting the given extreme (or mean) from... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...4.), the product of the extremes will be equal to the square of the mean. PROPOSITION II. THEOREM. If the product of two quantities be equal to the product of two other quantities, two of them will be the extremes and the other two the means of a proportion. Let... | |
 | Silas Totten - Algebra - 1836 - 360 pages
...— . Putting x in the place of the unknown term, the proportion becomes 12 : 4 = 18 : x ; and since the product of the means is equal to the product of the extremes (05), we have 12 xx = 18 x 4, or 12 x - 72 ; and as 1£ times x = 72, it ja 72 evident that x, the... | |
 | William Whewell - 1837 - 226 pages
...product of the extremes is equal to the square of the mean. For (Art. 39) if a : x :: x : 6, ab = a?. 41. If the product of two quantities be equal to the product of two others, the four are proportionals, making the terms of one product the means, and the terms of the other the extremes.... | |
 | Arithmetic - 1838 - 218 pages
...rule of three is derived.. In the following proportions the pupil will perceive that in every case the product of the means is equal to the product of the extremes. As 2 : 4 :: 6 : 12 2 : 8 :: 5 : 20 3 : 5 :: 6 : 10 7 : 11 :: 14 : 22 , Now suppose that we had the... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
