 | Francis Joseph Grund - 1833 - 224 σελίδες
...; (because 450 — г is A's gain, and 450 — (500 — x) = — 50 -f- x is B's gain,) and because the product of the means is equal to the product of the extremes, 450,000 — 900 x — 1,000 x -j- 2 x2 = 5 z2 — 250 *. This equation, when reduced, may be written... | |
 | Dionysius Lardner - 1834 - 378 σελίδες
...found. (379-) Since four numbers, which are in proportion, will continue to be in proportion so long as the product of the means is equal to the product of the extremes, it follows that we may make any of the following changes in the order of the four terms, without destroying... | |
 | Francis Joseph Grund - 1834 - 212 σελίδες
...in a geometrical proportion (Theory of Prop., Prin. 3d) ; that is, we have AD : HD = DG: BD; and as, in every geometrical proportion, the product of the means is equal to that of the extremes (Theory of Prop., Principle 10th), we have HD multiplied by DG, equal to AD multiplied... | |
 | Francis Lieber, Edward Wigglesworth - 1835 - 618 σελίδες
...proportion, the sum of the extremes is equal to that of the means, and, in geometrical proportions, the product of the means is equal to the product of the extremes, either extreme (or mean) may be found in the former, by subtracting the given extreme (or mean) from... | |
 | James Bryce - 1837 - 322 σελίδες
...72— 4я+8; whence we easily find 4. Given, — £— : — ^ — : : 7 : 4, to find ». Since, in a proportion, the product of the means is equal to the product of the extremes (Eue. VI. 16), it follows that 126—7х 10х+8= - 4 - O2 By multiplication, 40 x +32 =126— 7x. whence,... | |
 | 1838 - 218 σελίδες
...rule of three is derived.. In the following proportions the pupil will perceive that in every case the product of the means is equal to the product of the extremes. As 2 : 4 :: 6 : 12 2 : 8 :: 5 : 20 3 : 5 :: 6 : 10 7 : 11 :: 14 : 22 , Now suppose that we had the... | |
 | George Willson - 1838 - 194 σελίδες
...geometrical proportion consisting of four terms, have been explained on page 92, and the reason assigned why the product of the means is equal to the product of the extremes. This equality between their products suggests an obvious method of rinding any term of a proportion,... | |
 | George Willson - 1838 - 194 σελίδες
...geometrical proportion consisting of four terms, have been explained on page 92, and the reason assigned why the product of the means is equal to the product of the extremes. This equality between their products suggests an obvious method of finding any term of a proportion,... | |
 | Thomas H. Palmer - 1840 - 328 σελίδες
...whatever. Now, as these equal products are those of the extremes and means, we thus have the rule of proportion : The product of the means is equal to the product of the extremes. [Let this be demonstrated, a few times, on the blackboard, till it has become familiar. It will be... | |
 | Joseph Denison - 1841 - 210 σελίδες
...by one of the inclined sides ; that is, P = — S TT By theorem 1, P ; R ; ; — ; S ; and because the product of the means is equal to the product of the extremes, PS=R|; and dividing each of these equals by S, K! From theorem 2 we derive the following rule for finding... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
