 | 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 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... | |
 | Silas Totten - 1836 - 320 σελίδες
...progression 2, 5, 8, 11, &c. to 31 terms. Ans. 1457. GEOMETRICAL PROPORTIONS. (65.) In every geometrical proportion, the product of the means is equal to the product of the extremes. Take the proportion 12 : 4 = 18 : 6, or -T- = -»-. Now, if 12 18 we reduce the fractions -j- and -^... | |
 | Silas Totten - 1836 - 360 σελίδες
...— . Putting x in the place of the unknown term, the proportion becomes 12 : 4 = 18 : x ; and since the product of the means is equal to the product of the extremes (05), we have 12 xx = 18 x 4, or 12 x - 72 ; and as 1£ times x = 72, it ja 72 evident that x, the... | |
 | 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
...= —•; one value of V. Solution 2.—By the third expression, v \ V ; ; - ; —. * i And because the product of the means is equal to the product of the extremes, and dividing by -, V = (4) "OT ; second value of V, by the third expression (which is here used for... | |
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In any proportion, the product of the means is equal to the product of the extremes. 
