## Collected Mathematical Papers, Volume 1This publication includes all the mathematical papers of H.J.S. Smith in chronological order, enabling readers to trace the course of his mathematical studies and tastes. Most of the papers are in English, some of the papers or notes are in French. His work falls into three distinct groups: Geometry, Theory of Numbers, and Elliptic Functions. The first paper in Volume II (""Memoire sur quelques problems cubiques et biquadratiques"") was a prize memoir for which, cojointly with another memoir, the Steinder Prize of the Berlin Academy was awarded. This publication also includes a ""Biographical Sketch"" by Charles H. Pearson; ""Recollections of Henry J.S. Smith"" by Jowett, Lord Bowen, J.L. Strachan-Davidson and Alfred Robinson; ""Introduction to the Mathematical Papers"" by the Editor, J.W.L. Glaisher. |

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### Contents

I | ix |

II | xxxvii |

III | lxi |

IV | 1 |

V | 25 |

VI | 33 |

VII | 35 |

VIII | 38 |

XIV | 365 |

XV | 367 |

XVI | 410 |

XVII | 412 |

XVIII | 418 |

XIX | 443 |

XX | 455 |

XXI | 510 |

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ambiguous classes angles appertaining Arith arithmetical automorphics axes character circle coefficients complex numbers confocal congruence congruous conic conies conjugate consider contained Crelle Crelle's Journal curvature curve deduced demonstration denote Dirichlet Disq divisible Eisenstein elliptic functions equal equi-segmental equivalent evanescent exponent expression factors focal foci form of determinant forms f formula Gauss Geometry greatest common divisor harmonically Henry Smith homographic imaginary improperly indeterminates integral numbers intersection invariants involution Jacobi law of reciprocity linear Liouville mathematical matrix memoir method modular equation modulus multiplication number of classes number prime observed obtain plane polar positive prime dividing prime number primitive representation primitive root problem properly primitive classes properly primitive forms quadratic forms quadratic residue quotient relatively prime represent resoluble respectively roots of unity satisfy the congruence satisfy the equation square symbol tangent ternary form theorem Theta functions transformation triangle uneven number uneven prime values zero