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" In any proportion, the product of the means is equal to the product of the extremes. "
A New Introduction to the Science of Algebra ... - Σελίδα 78
των Silas Totten - 1836 - 304 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Teacher's manual [&c.].

Robert Robinson (inspector of national sch, Ireland.) - 1867 - 388 σελίδες
...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...

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 - 270 σελίδες
...fourth 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 ie a : b = c : d Clearing of fractions, ad = be A proportion is an equation ; and making the product...

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

John Fair Stoddard - 1888 - 480 σελίδες
...3 4 6 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...

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

John Fair Stoddard - 1868 - 428 σελίδες
...: 3 4 6 becomes s=o> multiplying each member by 2 and 3, we 2i o 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...

Practical Arithmetic, by Induction and Analysis

Joseph Ray - 1857 - 358 σελίδες
...the proportion 2 : 3 : : 4 : 6, 2 and 6 are the extremes, and 3 and 4 the means. ART. 200. In every proportion, the product of the means is equal to the product of tJie extremes. ILLUSTRATIONS. — If we have 3 : 4 : : 6 : 8, the ratios of each couplet being equal...

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

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

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...

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...




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