## The Mathematical Papers of Sir William Rowan Hamilton: Volume 4, Geometry, Analysis, Astronomy, Probability and Finite Differences, MiscellaneousThis fourth and final volume of The Collected Papers of Sir William Rowan Hamilton (1805 1865) contains three previously unpublished and important manuscripts, namely Systems of Rays and two lengthy letters to de Morgan (on definite integrals) and Hart (on anharmonic coordinates). In addition the volume contains reprinted papers on geometry, analysis, astronomy, probability and finite differences, as well as a collection of papers on various topics. A cumulative index for all three volumes is provided, as well as a CD containing all four volumes of the Collected Papers. |

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### Contents

Two Letters to Augustus de Morgan 1858 | 34 |

Letter to Hart on Anharmonic Coordinates 1860 | 179 |

On Symbolical Geometry 184649 | 431 |

On Polygons inscribed on a Surface of the Second Order 1850 | 502 |

On Geometrical Nets in Space 1861 | 516 |

Elementary Proof that Eight Perimeters of the Regular inscribed Poly | 562 |

communication | 564 |

On a New System of Two General Equations of Curvature 1865 | 574 |

The Comet 1832 | 673 |

On the Day of the Vernal Equinox at the time of the Council of Nice | 681 |

On Differences and Differentials of Functions of Zero 1831 | 701 |

On the double refraction of light according to the principles of Fresnel | 711 |

Address as Secretary of the Dublin Meeting of the British Association | 716 |

also On a new theory of varying orbits | 728 |

Address as President of the Royal Irish Academy on Professor Mac | 739 |

Notice of a singular appearance of the clouds observed on the 16th | 745 |

On the Error of a received principle of Analysis respecting Functions | 581 |

Supplementary Remarks on Fluctuating Functions 1842 | 631 |

On a mode of expressing Fluctuating or Arbitrary Functions by mathe | 640 |

On the Integrations of certain Equations 1854 | 647 |

On the Calculation of Numerical Values of a certain class of Multiple | 653 |

Introductory Lecture on Astronomy 1832 | 663 |

on the History and Antiquities of Tara Hill 1839 | 752 |

Sir W Rowan Hamilton on the Elementary Conceptions of Mathematics | 762 |

Address to Academy of Sir W R Hamilton on Retiring from | 773 |

795 | |

801 | |

### Common terms and phrases

Algebra Almagest angle anharmonic coordinates arbitrary arcs axes axis biquadratic equation bisecting calculation centre chord circle coefficients collinear Comet common cone of revolution conic conjugate connected considered constant construction continued fraction converging corresponding cubic cubic equation curve cyclic cone cyclic plane deduced definite integral denote determined diverging series Dublin ellipsoid equal expression exscribed finite formula function geometrical fractions give given point given triangle harmonic harmonic conjugates harmonic equations Hipparchus homology imaginary infinite inscribed integral intersection involution Letter limits method namely notation pass pencil perpendicular points of inflexion points P2 positive present principles Quaternions quinary quotient rays real root refraction relation remarks respecting right line Royal Irish Academy satisfy scalar sides spherical supposed surface symbols tangent theorem theory triangle ABC unit-line unit-point variable vector whence whereof William Rowan Hamilton write