 | Horatio Nelson Robinson - 1863 - 432 σελίδες
...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 - 1864 - 444 σελίδες
...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 - 1866 - 250 σελίδες
...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 - 1866 - 252 σελίδες
...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 - 384 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... | |
 | 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,... | |
 | John Fair Stoddard - 1888 - 480 σελίδες
...: : 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 - 1868 - 428 σελίδες
...: 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 - 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... | |
 | Joseph Ray - 1857 - 358 σελίδες
...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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In any proportion, the product of the means is equal to the product of the extremes. 
