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45 cents 90 cents algebraic arithmetical arithmetical progression arithmetical series becomes binomial binomial theorem coefficients column common divisor consequently contain continued fraction cube root determine difference divide dividend divisible elimination equa example exponent expression final equation formula give given equation given number greater greatest common divisor greatest common measure Hence imaginary roots indeterminate last term least common multiple letters logarithm manner method modulus monomial multiplied negative roots number of terms number of variations obtain odd number permutations polynomial positive roots prime number problem proposed equation quadratic quadratic equation quotient r-Ha radical ratio real roots reduced remainder represent result rule second term solution square number square root substituting subtract successive suppose symmetric functions theorem third tion transformed equation Transposing unity unknown quantity whence whole number
Page 129 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 107 - There will be as many figures in the root as there are periods in the given number.
Page 237 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.
Page 23 - 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 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 184 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.
Page 128 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c.
Page 48 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.