## Analytical and Arithmetical Essays |

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absolute number affirmative roots annexed arithmetical binomial factorials coefficients column common difference contains continued fraction converging fractions Corollary Corollary.—Hence corresponding cube cubic equation decompose denominator diagonal series digit diminishing the root divisor equa equal to zero evident ExAMPLE exhibited expansion exponent extracting the root figurate numbers ginal given equation gives greater hypothenuse indeterminate equation infinite series last term less letter m+1)th term method mth term Multiply negative Newton's method nth order number of figures obtain order of elections order of figurate original equation parcel plane ABCD preceding PROBLEM Prop proposed equation quadratic equation quotient Raphson's remainder respectively result right angled right-hand roots of equations rule ScholIUM series of converging side sine substituted subtract supposed tangent THEOREM third tion transformed equation transformed series trehedral triangle unity unknown quantity whole number write