| Silas Totten - Algebra - 1836 - 304 pages
...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 - Algebra - 1836 - 304 pages
...— . 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 - Algebra - 1837 - 80 pages
...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,... | |
| George Willson - Arithmetic - 1838 - 192 pages
...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,... | |
| Arithmetic - 1838 - 204 pages
...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 - Arithmetic - 1838 - 192 pages
...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,... | |
| Thomas H. Palmer - Education - 1840 - 263 pages
...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 - Mechanics - 1841 - 184 pages
...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... | |
| Joseph Denison - Mechanics - 1841 - 184 pages
...= —•; 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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