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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 73
by Zadock Thompson - 1832 - 168 pages
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New Practical Arithmetic in which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...repeated between the other 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 geometry of the circle and mathematics as applied to geometry by ...

James Smith - 1869 - 490 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 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...
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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...
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Elements of Algebra: For Colleges, Schools and Private Students

Joseph Ray - Algebra - 1866 - 420 pages
...other as 6 to 7? Let 3a:= the first, and 5x= the second number. Then, 3z-|-9 : 5.r+9 : : 6 : 7. But in every proportion, the product of the means is equal to the product of the extremes. (RAT'S ARTTH., 3d Book, Art. 200.) Hence, 6(5a;+9)=7(3a;+9). From which the answer is readily found....
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The Art of Teaching School: A Manual of Suggestions for the Use of Teachers ...

Josiah Rhinehart Sypher - Teaching - 1872 - 340 pages
...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...
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The Art of Teaching School.

Josiah Rhinehart Sypher - History - 1872 - 336 pages
...second terms of a proportion must be the same as the relation between the third a^id 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...
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The Quadrature and Geometry of the Circle Demonstrated

James Smith - Circle-squaring - 1872 - 330 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....
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 pages
...dividing the antecedent by the consequent is called the ratio. If four quantities are proportional, the product of the means is equal to the product of the extremes; in the proportion a : b : : c : d, a and d are the extremes, b and c the means. Wherefore, in order...
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New Practical Arithmetic: In which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1873 - 362 pages
...a term repeated between the other two. Thus, In 12 : 6 :: 6 : 3, 6 is a mean proportional. 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), we have f = -J- Now,...
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