A Treatise on Algebra |
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Common terms and phrases
a+b+c a₁ algebraical expression arithmetic mean arithmetical progression ascending powers ax² b₁ binomial series Binomial Theorem C₁ common factor contain continued fraction continued product cube root degree denominator digits divergent divide divisible divisor equal equation ax example expansion Find the coefficient find the factors Find the number Find the sum finite follows given expression greater Hence the required infinity less than unity letters logarithm monomial Multiply negative nth root nth term number of terms obtained partial fractions positive integer prime number Prove quadratic equation quadratic surd quotient ratio remainder Shew Solve the equation square root subtract suppose surds u₁ U₂ unknown quantities vanish whole number zero
Popular passages
Page 158 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Page 280 - To find the number of permutations of n different things taken r at a time.
Page 236 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.
Page 47 - 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 244 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 250 - Given that the area of a circle varies as the square of its radius...
Page 513 - Laplace's own words, which join the condition of equal likelihood to the fractional relationship, "the probability of an event is the ratio of the number of cases which favor it to the number of all possible cases...
Page 14 - To multiply one number by a second is to do to the first what is done to unity to obtain the second.
Page 512 - DEFINITION. If an event can happen in a ways and fail in b ways, and. each of these ways is equally likely, the probability, or the chance, of its happening is , and...
Page 244 - This is sometimes expressed by the notation a : b :: с : d, which is read