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added algebraic arithmetical arranged assume balls binomial called changed coefficient column common condition contains continued fraction convergent corresponding decimal definition denominator determinant difference digits divided division divisor dollars elements equal equivalent evidently example EXERCISES expansion exponent expressions factors feet figure Find Find the value finite following expressions four fourth fraction function gallons give given equation graph greater Hence holds illustrate increases integral less letter limit logarithms manner means method miles minutes Multiplying negative Observe obtained partial positive preceding principle problem quotient ratio receive Reduce relation remainder result roots satisfy second term Simplify solution Solve the equation square stand Substituting subtracted surd taken term third tion units unknown number variations whence Write yards
Σελίδα 74 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Σελίδα 349 - We will now derive a formula for the number of permutations of n things, taken all at a time, when some of them are alike.
Σελίδα 313 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Σελίδα 216 - ... term by the exponent of a in that term, and dividing the product by a number greater by 1 than the exponent of b in that term.
Σελίδα 221 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Σελίδα 216 - ... the terms of the binomial is negative. Observe, as a check : (vii.) The sum of the exponents of a and b in any term is equal to the binomial exponent.
Σελίδα 416 - We therefore have : (i.) The characteristic of the, logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part.
Σελίδα 352 - That is, the number of combinations of n dissimilar things r at a time is equal to the number of combinations of the n things n — r at a time.