## Analytical and Arithmetical Essays |

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absolute number affirmative roots annexed arithmetical ascer binomial factorials coefficients column common difference contains continued fraction converging fractions Corollary 2.—Hence Corollary.—Hence corresponding cosine 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 greater hypothenuse indeterminate equation infinite series involution l)th term last term less letter m+l)th term mth term Multiply negative Newton's method nth order number of figures obtain order of elections order of figurate original equation preceding Problem Prop proposed equation PROPOSITION quadratic equation quotient radius Raphson's method remainder respectively result right angled right-hand roots of equations rule Scholium series of converging side substituted subtract succeeding supposed tangent Theorem third tion transform the equation transformed equation transformed series trehedral triangle unity unknown quantity whole number write