| John Marsh (writing-master.) - Decimal fractions - 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... | |
| Zadock Thompson - Arithmetic - 1828 - 225 pages
...nomher to their 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 hy one... | |
| Timothy Walker - Geometry - 1829 - 104 pages
...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
...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... | |
| Francis Joseph Grund - Geometry, Plane - 1830 - 255 pages
...in a geometrical proportion (Theory of prop. prin. 3d); that is, we have AD : HD = DG : BD ; and as **in every geometrical proportion the product of the means is equal to** that of the extremes (Theory of prop, princ. 8th), we have HD multiplied by DG equal to AD multiplied... | |
| Oliver A. Shaw - Arithmetic - 1832 - 95 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 - 168 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... | |
| Zadock Thompson - Arithmetic - 1832 - 168 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... | |
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