 | Benjamin Greenleaf - 1857 - 452 σελίδες
...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... | |
 | Benjamin Greenleaf - 1858 - 458 σελίδες
...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... | |
 | 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,... | |
 | John Fair Stoddard, William Downs Henkle - 1859 - 538 σελίδες
...PROPOSITION (369.) 3. In a geometrical progression consisting of any number of terms the product of the extremes is equal to the product of any two terms equally distant from them. EXAMPLES. 1. Find the llth term of -."-3 : 8 : 12 : &c. Ans. 3072. 2. Find the sum of 9 terms... | |
 | 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 :... | |
 | Benjamin Greenleaf - 1860 - 456 σελίδες
...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 Jg4 = f g. Now, if we reduce... | |
 | Charles Davies - 1861 - 322 σελίδες
...»nd 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 between the numbers 2 : 10 : :... | |
 | Elias Loomis - 1862 - 312 σελίδες
...2:4::4:8, where 4 is a mean proportional between 2 and 8. (183.) If four quantities are proportional, the product 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, a_c... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...D:C, or A — B:B::C — D:D. PROPOSITION I. — THEOREM. 135. If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. Let A : B : : C : D ; then will AXD = BX C. For, since the magnitudes are in proportion,... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...C, or A — B:B::C — D:D. PROPOSITION I. — THEOREM. 135. If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. Let A : B : : C : D ; then will AXD = BX C. For, since the magnitudes are in proportion,... | |
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In any continued geometrical progression, the product of the two extremes is equal to the product of any two means... 
