## A Treatise on Algebra |

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### Términos y frases comunes

according added affected algebraic already applicable arithmetical assume becomes binomial called cents changed coefficients combinations complete consider contain continued cube root denominator denotes derived difference distance Divide dividend divisible divisor dollars employed equal equation example exponent expression factors fifth figure find the values five four fraction geometrical Given gives greater greatest common divisor Hence increased inequality infinite series involving known least less letters logarithm manner means method miles multiplied negative obtain operation original perform polynomial positive preceding principle Prob problem progression proportional proposed quotient radical raise ratio Reduce remainder represent Required Resolve result RULE second term seen simple solved square root substitute subtract successive suppose surd taken term THEOREM third tion traveled units unity unknown quantity variation Whence whole zero

### Pasajes populares

Página 229 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.

Página 28 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.

Página 231 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. 5. Double the whole root already found for a new divisor, and continue the operation as before, until all the periods are brought down.

Página 76 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...

Página 141 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.

Página 308 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Página 13 - Add all the positive coefficients together, and oho all those that are negative ; subtract the least of these results from the greater ; to the difference annex the common letter or letters, and prefix the sign of the greater sum. Thus, instead of 7a— 4a, we may write 3a, since these two expressions obviously have the same value.

Página 196 - Multiply the last term by the ratio, from the product subtract the first term, and divide the remainder by the ratio, less 1 ; the quotient will be the sum of the series required.

Página 28 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.