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" In any proportion, the product of the means is equal to the product of the extremes. "
The Youth's Assistant in Theoretic and Practical Arithmetic, : Designed for ... - Page 128
by Zadock Thompson - 1828 - 225 pages
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Decimal Arithmetic Made Perfect: Or, The Management of Infinite Decimals ...

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...
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The Young Algebraist's Companion ...: New Ed. To which is Added a Supplement ...

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...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

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...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 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...
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The student's algebra

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...
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The Youth's Assistant in Theorhetic [sic] and Practical Arithmetic: Designed ...

Zadock Thompson - Arithmetic - 1832 - 168 pages
...antecedent and second consequent, or of the two extreme terms. Hence we discover that if four numbers are proportional, the product of the first and fourth...proportion, 4 : 6 : : 12 : 18, the order of the terms may be altered without destroying the proportion, provided they be so placed, that the product of the means...
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A Description of the Visible Numerator: With Instructions for Its Use ...

Oliver A. Shaw - Arithmetic - 1832 - 95 pages
...10000. 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,...
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The Youth's Assistant in Theoretic[!] and Practical Arithmetic ...

Zadock Thompson - Arithmetic - 1832 - 168 pages
...price, and this must be obvious from what was said m article 191. 196. Since, in every proportion, the product of the means is equal to the product of the extremes, one of these products may be taken for the other. Now if we divide the product of the 'means by one...
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Exercises in Algebra: Being Systematically Arranged and Adapted to the ...

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...
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Treatise on Arithmetic, Practical and Theoretical

Dionysius Lardner - Arithmetic - 1834 - 353 pages
...found. (379-) Since four numbers, which are in proportion, will continue to be in proportion so long as the product of the means is equal to the product of the extremes, it follows that we may make any of the following changes in the order of the four terms, without destroying...
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