| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...the extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, **the product of the means is equal to the product of the extremes.** APPLICATION OF THE FORMULAS. 364. The two primitive equations, ,««. ,given, the other two may be... | |
| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...the. extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, **the product of the means is equal to the product of the extremes.** APPLICATION OF THE FOKMULAS. 364. The two primitive equations, contain the five quantities, a, r, l,... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...thus : Let a;= one part ; then, 55 — £= the other. By the question, x : 55 — x : : 2 : 3. Then, **since, in every proportion, the product of the means is equal to the product of the extremes,** we have 3a;=2(55 — 2)=110 — 2x. 5z=110 3=22, and 55— 3=33, as before. Or, thus : Let x= one part;... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...are the first and last terms of a proportion called ? The second and third? 244. Proposition I. — **In every proportion, the product of the means is equal to the product of the extremes.** Let a : b • : c : d. Then, since this is a true proportion, we must hnve bd Clearing of fractions,... | |
| 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... | |
| 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 - 1888 - 480 pages
...: : 6 : 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... | |
| John Fair Stoddard - Arithmetic - 1868 - 430 pages
...: 2 :: 6 : 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... | |
| 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... | |
| Joseph Ray - Arithmetic - 1857 - 360 pages
...Thus, in 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... | |
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