| Daniel Fenning - Algebra - 1802 - 274 pages
...in .if., either continued or interrupted (provided the interruption be between the 2d and 3d term), the product of the means is equal to the product of the extremes. EXAMPLE. Let the 4 numbers be 5, 15, 26, and 78 interrupted; then 5 x 78 = 15 x 26= 390.... | |
| Isaac Dalby - Mathematics - 1806 - 526 pages
...ac Or thus, since - z= -. • ba and f = > therefore 1=7. hdbh 68. If 4 quantities are proportional, the product of the means is equal to the product of the extremes. Thus suppose a : b : : c : d Then ad = he. For ? = ^ (s+)i and multiplying both fractions... | |
| Zadock Thompson - Arithmetic - 1828 - 238 pages
...price, and this must he ohvious from what was said in article 191. 195. Since, in every proportion, the product of the means is equal to the product of the extremes, one of these products may he taken for the other. Now if we divide the product of the means... | |
| Timothy Walker - Geometry - 1829 - 156 pages
...proportion. Thus 6 : 9 : : 10 : 15 : : 8 : 12 , is a continued proportion. 63. In every proportion, the product of the means is equal to the product of the extremes. For if two equal fractions be reduced to a common denominator, their numerators must be equal.... | |
| 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... | |
| Zadock Thompson - Arithmetic - 1832 - 186 pages
...price, and this must be obvious from what was said m article 191. 196. Since, in every proportion, the product of the means is equal to the product of the extremes, one of these products may be taken for the other. Now if we divide the product of the 'means... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
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