| Robert Robinson (inspector of national sch, Ireland.) - 1867 - 388 pages
...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... | |
| William Frothingham Bradbury - Algebra - 1868 - 270 pages
...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... | |
| John Fair Stoddard - Arithmetic - 1868 - 430 pages
...: 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... | |
| John Fair Stoddard - Arithmetic - 1888 - 480 pages
...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... | |
| Joseph Ray - Arithmetic - 1857 - 360 pages
...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... | |
| Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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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