A Treatise on Algebra |
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Common terms and phrases
according to Art algebraic arithmetical progression binomial cent coefficients common denominator Completing the square continued fraction contrary sign cube root denotes Divide the number dividend divisible dollars equa equation whose roots exponent expression extracting the square factors figure Find the square find the values following RULE fourth power fourth root geometrical progression given equation greatest common divisor Hence inequality infinite series last term least common least common multiple less letters taken method monomial multiplied negative nth root number of terms obtain original equation polynomial Prob problem proportional quadratic equations quotient radical quantities ratio real roots Reduce remainder Required the cube Required the number Required the square Required the sum result second degree second term solved square root substitute subtract surd THEOREM third three numbers tion tity unity unknown quantity values of x Whence whole number zero
Popular passages
Page 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.
Page 48 - To reduce fractions to a common denominator. RULE. Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 47 - To reduce a mixed number to an improper fraction, — RULE : Multiply the whole number by the denominator of the fraction, to the product add the numerator, and write the result over the denominator.
Page 25 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page 142 - 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.
Page 38 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 355 - 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...
Page 235 - Whence it follows, that the cube of a number composed of tens and units, is equal to the cube of the tens, plus three times the product of the square of the tens by the units, plus three times the product of the tens by the square of the units, plus the cube of the units. This being the case, the cube of the tens...
Page 172 - The first term, a, is called the antecedent of b the ratio ; the last term, b, is called the consequent of the ratio. Hence it appears that the theory of ratios is included in the theory of fractions ; and a ratio may be considered as a fraction whose numerator is the antecedent, and whose denominator is the consequent.
Page 152 - In a parcel which contains 24 coins of silver and copper, each silver coin is worth as many cents as there are copper coins, and each copper coin is worth as many cents as there are silver coins ; and the whole is worth 2 dollars and 16 cents.