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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 Theorhetic [sic] and Practical Arithmetic: Designed ... - Page 73
by Zadock Thompson - 1832 - 168 pages

## Decimal Arithmetic Made Perfect: Or, The Management of Infinite Decimals ...

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...

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

Daniel Fenning - Algebra - 1802 - 274 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...

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

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...

## The Youth's Assistant in Theoretic and Practical Arithmetic, : Designed for ...

Zadock Thompson - Arithmetic - 1828 - 238 pages
...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...

## The Youth's Assistant in Theoretic and Practical Arithmetic, : Designed for ...

Zadock Thompson - Arithmetic - 1828 - 230 pages
...equals the product of the second and third, or in other words, that Ihe product of the meansis equal lo the product of the extremes. 194. In the proportion, 4 : 6 : : 12 : 18, the order of the terms may he altered without destroying the proportion, provided they he so placed, that the product of the means...

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

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...

## The student's algebra

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...

## A Description of the Visible Numerator: With Instructions for Its Use ...

Oliver A. Shaw - Arithmetic - 1832 - 108 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,...