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according to Art arithmetical progression binomial cent coefficients common logarithm Completing the square continued fraction contrary sign cube root cubic equation denotes Divide the number dividend divisible dollars equa equation containing equation whose roots exponent extracting the square factors figure Find the square find the values following RULE fourth power fourth root geometrical geometrical progression given equation greater greatest common divisor Hence inequality infinite series last term less letters taken method metic miles monomial multiplied negative nth root number of permutations number of terms obtain order of differences positive Prob problem quadratic equations quotient radical quantities ratio real roots Reduce remainder represent Required the cube Required the fourth Required the number Required the square Required the sum result second degree second term simple form solved square root subtract suppose surd THEOREM three numbers tion tities unity unknown quantity Whence whole number zero
Pàgina 227 - 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.
Pàgina 229 - 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.
Pàgina 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...
Pàgina 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.
Pàgina 306 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Pàgina 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.
Pàgina 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.
Pàgina 332 - The number of deaths in a besieged garrison amounted to 6 daily ; and allowing for this diminution, their stock of provisions was sufficient to last 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the...