| 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 - 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 by W we have... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...they form a continued 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 denomination, their numerators must be equal.... | |
| John Darby (teacher of mathematics.) - 1829 - 214 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... | |
| Zadock Thompson - Arithmetic - 1832 - 188 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 extremes.** 194. In the proportion, 4 : 6 : : 12 : 18, the order of the terms may be altered without destroying... | |
| 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 - 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... | |
| Frederick Emerson - Arithmetic - 1832 - 344 pages
...Since the product of the extremes in every proportion is equal to the product of the means, one product **may be taken for the other. Now, if we divide the product of the** extremes by one extreme, the quotient is the other extreme ; therefore, if we divide the product of... | |
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