A Treatise on Algebra: Containing the Latest Improvements. Adapted to the Use of Schools and Colleges |
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Common terms and phrases
algebraic arithmetical arithmetical progression arithmetical series becomes binomial binomial theorem coefficients column common divisor consequently contain continued fraction contrary signs cube denominator derived functions determine difference divide divisible elimination equa EXAMPLE exponent expression extract final equation formula give given equation given number greater greatest common divisor Hence imaginary roots indeterminate inequation last term least common multiple letters logarithm method modulus monomial multiplied negative roots nth root number of terms number of variations obtain odd number permutations polynomial positive roots prime number problem proposed equation quadratic equation quotient radical ratio real roots reduced remainder represent result second degree second term solution square number square root substituting subtract successive suppose symmetric functions theorem third tion transformed equation Transposing unity unknown quantity V₁ whence whole number
Popular passages
Page 95 - ... 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.
Page 169 - 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...
Page 127 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 170 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 74 - Multiply the divisor thus increased, by the second term of the root, and subtract the product from the remainder.
Page 21 - 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 238 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.
Page xii - ALPHA BETA GAMMA DELTA EPSILON ZETA ETA THETA IOTA KAPPA LAMBDA MU NU XI OMICRON PI RHO SIGMA TAU UPSILON PHI CHI PSI OMEGA...
Page 261 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 168 - His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together.