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In any proportion, the product of the means is equal to the product of the extremes.
Elements of Plane and Solid Geometry - Page 202
by George Albert Wentworth - 1877 - 398 pages

## Key to Ray's New Algebras, Elementary and Higher: Containing Statements and ...

Joseph Ray - Algebra - 1867 - 240 pages
...100—3z= B's gain, and 40z — 200= A's stock. Therefore, 4te— 200 : 20a; : : 3x : 100—3z. Since the product of the means is equal to the product of the extremes, 60z2=(40z— 200)(100— 3«). Reducing, z2— J{°x=— i°o°. Whence, z=20; hence, &c=60= A's gain,...

## Practical Arithmetic, Embracing the Science of Numbers and the Art of ...

John Fair Stoddard - Arithmetic - 1868 - 428 pages
...denoting the equality of two ratios, either, or both, being compound. As in Simple Proportion, 386, The product of the means is equal to the product of the extremes. Hence, 1. A factor in either extreme equals the product of the means divided by the product of the...

## Stoddard's Complete Arithmetic: Being the New Practical Arithmetic of the ...

John Fair Stoddard - Arithmetic - 1888 - 480 pages
...becomes 5=5. multiplying each member by 2 and 3, we jy *_) have 4x3=6x2. Hence, 382. In every proportion, the product of the means is equal to the product of the extremes. 1. Either extreme is equal to the product of the means divided by the other extreme. 2. Either mean...

## Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 264 pages
...terms of a proportion are called the extremes, and the second and third the means. 106. In a proportion the product of the means is equal to the product of the extremes. Let a : b = c : d ac l = d Clearing of fractions, ad = be A proportion is an equation ; and making...

## The geometry of the circle and mathematics as applied to geometry by ...

James Smith - Mathematics - 1869 - 492 pages
...or proportion, A : B : : B : C, when A denotes * ^* and B denotes I ; then, -8 : I : : I : -125, and the product of the means is equal to the product of the extremes. Now, if the radius of a circle = -125, then, (6 x -125) = 75 = the perimeter of a regular inscribed...

## The Geometry of the Circle and Mathematics as Applied to Geometry by ...

James Smith - Circle-squaring - 1869 - 459 pages
...: B : C. When A denotes ^-^ and B denotes i, then, C = 1-28 : that is, 78125 : i : : I : 1-28, and the product of the means is equal to the product of the extremes. Hence : -~I*±*A and —-^ are equivalent ratios, and it follows, that the product of any number multiplied...

## New Practical Arithmetic in which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...two. Thus, In 12 : 6 :: 6 : 3, 6 is a mean proportional. TOIIVCIIVLES. 328. 1. In every proportion the product of the means is equal to the product of the extremes. For, in the proportion 6 : 3 : : 4 : 2, since the ratios are equal (Art. 326), WB have \$ = £. Now,...

## The ratio between diameter and circumference in a circle demonstrated by ...

James Smith - 1870 - 634 pages
...63 agreed. If I : 2 : : 2 : 4, the converse of this proportional holds good ; 4 : 2 : : 2 : I, and the product of the means is equal to the product of the extremes : mxn = « xm, whatever values we may put upon m and «, and in either way, works out to the same result...