 | Daniel Fenning - Algebra - 1802 - 274 pages
....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
...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
...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 he altered without destroying... | |
 | Timothy Walker - Geometry - 1829 - 156 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... | |
 | Zadock Thompson - Arithmetic - 1832 - 182 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 - 108 pages
...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,... | |
 | Francis Joseph Grund - Algebra - 1833 - 224 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... | |
 | Francis Lieber, Edward Wigglesworth - Encyclopedias and dictionaries - 1835 - 618 pages
...proportion, the sum of the extremes is equal to that of the means, and, in geometrical proportions, the product of the means is equal to the product of the extremes, either extreme (or mean) may be found in the former, by subtracting the given extreme (or mean) from... | |
 | Silas Totten - Algebra - 1836 - 320 pages
...numerator of the second is the product of the mean terms ; hence, in every geometrical proportion, the product of the means is equal to the product of the extremes. The proof is independent of the particular numbers which enter into the proportion, as maybe shown... | |
 | James Bryce - Algebra - 1837 - 322 pages
...whence we easily find 4. Given, — £— : — ^ — : : 7 : 4, to find ». Since, in a proportion, the product of the means is equal to the product of the extremes (Eue. VI. 16), it follows that 126—7х 10х+8= - 4 - O2 By multiplication, 40 x +32 =126— 7x. whence,... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
