A Treatise on AlgebraHarper & brothers, 1855 - 316 σελίδες |
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Σελίδα v
... Coefficient . - Exponent . - Power . - Root Algebraic Quantity . - Monomial . - Polynomial . Degree of a Term ... Coefficients . SECTION VI . FRACTIONS . Fundamental Principles . - Signs of the Terms To reduce a Fraction to lower ...
... Coefficient . - Exponent . - Power . - Root Algebraic Quantity . - Monomial . - Polynomial . Degree of a Term ... Coefficients . SECTION VI . FRACTIONS . Fundamental Principles . - Signs of the Terms To reduce a Fraction to lower ...
Σελίδα vii
... Coefficients Binomial Theorem Theorem applied to any Polynomial When the Exponent is Negative When the Exponent is a Fraction . When the Exponent is a Negative Fraction Theorem applied to find the Roots of Numbers 215 216 219 221 222 ...
... Coefficients Binomial Theorem Theorem applied to any Polynomial When the Exponent is Negative When the Exponent is a Fraction . When the Exponent is a Negative Fraction Theorem applied to find the Roots of Numbers 215 216 219 221 222 ...
Σελίδα viii
... Coefficients . - Rule ... SECTION XIX . GENERAL THEORY OF EQUATIONS . Definitions . - General Form of Equations An Equation whose Root is a is divisible by x - a An Equation of the mth Degree has m Roots .. Law of the Coefficients of ...
... Coefficients . - Rule ... SECTION XIX . GENERAL THEORY OF EQUATIONS . Definitions . - General Form of Equations An Equation whose Root is a is divisible by x - a An Equation of the mth Degree has m Roots .. Law of the Coefficients of ...
Σελίδα 6
... coefficient of a . In like manner , 10ab signifies ten times the product of a and b . The coefficient may be either a whole number or a fraction . Thus , a signifies three fourths of a . When no co- efficient is expressed , 1 is always ...
... coefficient of a . In like manner , 10ab signifies ten times the product of a and b . The coefficient may be either a whole number or a fraction . Thus , a signifies three fourths of a . When no co- efficient is expressed , 1 is always ...
Σελίδα 12
... coefficients of the several quantities together , and to their sum annex the common letter or letters , prefixing the com- mon sign . Thus , the sum of 3a and 5a is obviously 8a . So , also , -3a and -5a make -8a ; for the minus sign ...
... coefficients of the several quantities together , and to their sum annex the common letter or letters , prefixing the com- mon sign . Thus , the sum of 3a and 5a is obviously 8a . So , also , -3a and -5a make -8a ; for the minus sign ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
according to Art algebraic arithmetical progression binomial Binomial Theorem coefficients Completing the square continued fraction contrary sign cube root Divide the number dividend divisible equa equation whose roots example exponent expression extracting the square factors figure Find the square find the values following RULE four quantities fourth power fourth root geometrical progression given equation greater greatest common divisor Hence inequality infinite series last term less letters taken method miles monomial multiplied negative nth root number of combinations number of permutations number of terms obtain original equation polynomial preceding Prob problem QUADRATIC EQUATIONS quotient radical quantities ratio real roots Reduce remainder represent Required the cube Required the number Required the square Required the sum result second degree second term square root subtract surd Theorem three numbers tion tities unity unknown quantity values of x Whence whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 308 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Σελίδα 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.
Σελίδα 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.
Σελίδα 334 - 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...
Σελίδα 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.