 | Ezra S. Winslow - 1853 - 264 σελίδες
...and in the last, or in the progression 2, 10, 50, 250, 5 is the ratio. In a geometrical progression, the product of the two extremes is equal to the product of any two means that are equally distant from the extremes, and, also, equal to the square of the middle... | |
 | Charles Davies - 1854 - 436 σελίδες
...their product is constant. BOOK II. 61 PROPOSITION I. THEOREM. When four magnitudes are in proport'on, the product of the two extremes is equal to the product of the two means. Let A, If, C, D, be any four magnitudes, and M} N, P, Q, their numerical representatives ; then, if... | |
 | C W. Thornhill - 1854 - 228 σελίδες
...Proportion contains the following theorems. THEOREM 1. — In any continued Geometrical Progression, the product of the two extremes is equal to the product of any two means that are equally distant from them. When the number of terms are odd it is equal to the... | |
 | Charles Davies, William Guy Peck - 1855 - 628 σελίδες
...equal to the half sum of the extremes multiplied by the number of terms. In a geometrical progression, the product of the two extremes is equal to the product of any two means equally distant from the extremes. In a geometrical progression, any term is a mean proportional... | |
 | Elias Loomis - 1856 - 280 σελίδες
...three quantities said to be proportional ? (183.) If four quantities are proportional, the prod' uct of the two extremes is equal to the product of the two means. Let a:b::c:d; then will . ad=bc. For, since the four quantities are proportional, ac b=d' and, by clearing... | |
 | Benjamin Greenleaf - 1857 - 452 σελίδες
...will be equal. The effect is the same when the terms are multiplied by the same number. 336i In every proportion the product of the two extremes is equal to the product of the two means. Thus, the proportion 16 : 8 : : 20 : 10 may be expressed *$- = \ %. Now, if we reduce these fractions... | |
 | Benjamin Greenleaf - 1858 - 458 σελίδες
...will be equal. The effect is the same when the terms are multiplied by the same number. 336. In every proportion the product of the two extremes is equal to the -product of the two means. Thus, the proportion 16 : 8 : : 20 : 10 may be expressed J^- = f§. Now, if we reduce these fractions... | |
 | Elias Loomis - 1858 - 256 σελίδες
...equimultiples, are equal to each other. PROPOSITION I. THEOREM. If four quantities are proportional, the product of the two extremes is equal to the product of the two means. It has been shown that the ratio of two magnitudes, whether they are lines, surfaces, or solids, is... | |
 | Jeremiah Day - 1859 - 422 σελίδες
...the subject of a future section, so far as to admit the principle that " when four quantities are in proportion, the product of the two extremes is equal...Arithmetic. Thus, if a '. b ' '. c '. d, then ad=bc. And if 3:4" 6: 8, then 3X8— 4X6. Hence, Ex. 1. Reduce to an equation ax'.b'.'.ch'.d. The product of the... | |
 | Charles Davies - 1859 - 324 σελίδες
...by clearing the equation of fractions, we have, BO = AD. That is : Of four proportional quantities, the product of the two extremes is equal to the product of the two means. This general principle is apparent in the proportion b*v tween the numbers, 2 : 10 : : 12 : 60, which... | |
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If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. 
