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" In any proportion, the product of the means is equal to the product of the extremes. "
Elements of Geometry - Σελίδα 202
των George Albert Wentworth - 1881 - 250 σελίδες
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Key to Ray's New Algebras, Elementary and Higher: Containing Statements and ...

Joseph Ray - 1867 - 240 σελίδες
...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,...

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

William Frothingham Bradbury - 1868 - 264 σελίδες
...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...

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

John Fair Stoddard - 1868 - 428 σελίδες
...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 - 1888 - 480 σελίδες
...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...

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

James Smith - 1869 - 459 σελίδες
...: 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...

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

James Smith - 1869 - 490 σελίδες
...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...

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

Henry Bartlett Maglathlin - 1869 - 332 σελίδες
...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 σελίδες
...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...

The Art of Teaching School: A Manual of Suggestions for the Use of Teachers ...

Josiah Rhinehart Sypher - 1872 - 340 σελίδες
...and second terms of a proportion must be the same as the relation between the third and fourth terms. The product of the means is equal to the product of the extremes. A missing extreme may be found by dividing the product of the means by the given extreme. A mean may...

The Quadrature and Geometry of the Circle Demonstrated

James Smith - 1872 - 330 σελίδες
...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....




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