| Frederick Emerson - Arithmetic - 1834 - 300 pages
...Since the product of the extremes in every proportion is equal to the product of the means, one product **may be taken for the other: now if we divide the product of the** extremes by one extreme, the quotient is the other extreme; therefore, if we divide the product of... | |
| Dionysius Lardner - Arithmetic - 1834 - 353 pages
...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 - Encyclopedias and dictionaries - 1835 - 618 pages
...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 - Algebra - 1836 - 320 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 - 362 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 - 322 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 - 194 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,... | |
| George Willson - Arithmetic - 1838 - 194 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... | |
| Frederick Emerson - Arithmetic - 1839 - 300 pages
...Since the product of the extremes in every proportion is equal to the product of the means, one product **may be taken for the other: now if we divide the product of the** extremes by one extreme, the quotient is the other extreme; therefore, if we divfde the product of... | |
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