| John Marsh (writing-master.) - Arithmetic - 1742 - 197 pages
...12, as 7 is to 28 ; or 3 is to 7, ať i2 is to 28. And when four Numbers.are thus Proportional, then **the Product of the Means is equal to the Product of the** Extreams. For 12x7=84 the Product of the Means. And 3x28=84 the Product of the Extreams. Wherefore... | |
| Daniel Fenning - Algebra - 1802 - 219 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. It will be... | |
| Isaac Dalby - Mathematics - 1806
...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 by W we have... | |
| Timothy Walker - Geometry - 1829 - 129 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. Thus... | |
| John Darby (teacher of mathematics.) - 1829
...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... | |
| Zadock Thompson - Arithmetic - 1832 - 168 pages
...antecedent and second consequent, or of the two extreme terms. Hence we discover that if four numbers **are proportional, the product of the first and fourth...proportion, 4 : 6 : : 12 : 18, the order of the terms may** be altered without destroying the proportion, provided they be so placed, that the product of the means... | |
| Oliver A. Shaw - Arithmetic - 1832 - 95 pages
...10000. 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 - 168 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 by one... | |
| Francis Joseph Grund - Algebra - 1833 - 197 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 - 353 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... | |
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