 | John Marsh (writing-master.) - Arithmetic - 1742 - 238 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 - 270 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... | |
 | Zadock Thompson - Arithmetic - 1828 - 238 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 - 138 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 - 212 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... | |
 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 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 - 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 - 180 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 - 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... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
