| John Marsh (writing-master.) - 1742 - 238 σελίδες
...12, as 7 is to 28 ; or 3 is to 7, a» 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 - 1802 - 274 σελίδες
...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 - 1806 - 526 σελίδες
...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 - 1829 - 138 σελίδες
...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 - 212 σελίδες
...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 - 1832 - 182 σελίδες
...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 - 1832 - 112 σελίδες
...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 - 1832 - 186 σελίδες
...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 - 1833 - 224 σελίδες
...; (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 - 1832 - 344 σελίδες
...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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