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algebraic quantity arithmetical progression binomial binomial theorem cent coefficient common difference continued fraction cube root decimal denote Divide the number dividend divisible by a—b dollars Eeduce equa equal equation whose roots equivalent fractions EXAMPLES exponent figure Find the cube Find the fourth Find the greatest Find the least Find the number Find the square Find the sum find the values following RULE fourth power geometrical progression Given greater greatest common divisor Hence indicates infinite series last term least common denominator least common multiple less logarithm miles mixed quantity monomial Multiply negative nth root number of terms obtain polynomial positive preceding Prob problem quan quotient radical sign ratio real roots Reduce remainder represent result second degree second term Solve the equation square root Sturm's Theorem Substituting Suppose surd three numbers tion tity unity unknown quantity whence whole number zero
Σελίδα 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Σελίδα 181 - 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 39 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers 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 284 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Σελίδα 192 - 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 are worth 2 dollars and 16 cents.
Σελίδα 295 - To find any root of a given number, divide the logarithm of the number by the index of the root. The quotient is the logarithm of the root.
Σελίδα 220 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Σελίδα 227 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.