| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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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