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Books Books 61 - 70 of 188 on In any proportion, the product of the means is equal to the product of the extremes..
" In any proportion, the product of the means is equal to the product of the extremes. "
Treatise on the elements of algebra - Page 256
by James Bryce - 1837
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Teacher's manual [&c.].

Robert Robinson (inspector of national sch, Ireland.) - 1867
...leads to the least misconception of what is really stated, and forms the best test of its accuracy. The product of the means is equal to the product of the extremes. Those who know that the expressions 3 : 4 : : 6 : 8 and are equivalent, and who understand some little...
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Key to Ray's New Algebras, Elementary and Higher: Containing Statements and ...

Joseph Ray - Algebra - 1867 - 224 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=— io. Whence, z=20; hence, &c=60= A's gain,...
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Stoddard's Complete Arithmetic: Being the New Practical Arithmetic of the ...

John Fair Stoddard - Arithmetic - 1888 - 456 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...
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 252 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...
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Practical Arithmetic, Embracing the Science of Numbers and the Art of ...

John Fair Stoddard - Arithmetic - 1868 - 380 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...
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The Geometry of the Circle and Mathematics as Applied to Geometry by ...

James Smith - Circle-squaring - 1869 - 405 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...
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THE GEOMETRY OF THE CIRCLE AND MATHEMATICS

JAMES SMITH - 1869
...: 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...
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New Practical Arithmetic in which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1869 - 324 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,...
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The Ratio Between Diameter and Circumference in a Circle Demonstrated by ...

Circle-squaring - 1870 - 290 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...
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The Quadrature and Geometry of the Circle Demonstrated

James Smith - Circle-squaring - 1872 - 269 pages
...the area of a circumscribing square to the latter = 16. Hence: r28 : 1-6384 :: 12-5 : 16 ; therefore, the product of the means is equal to the product of the extremes, and proves that the areas of circles are to each other as the areas of their circumscribing squares. I...
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