## Principles of Geometry, Volumes 1-3Henry Frederick Baker (1866-1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the second volume, describes the principal configurations of space of two dimensions. |

### Contents

INTRODUCTORY ACCOUNT | 1 |

Greatest possible number of double points of a plane curve 1011 | 10 |

Examples of elliptic curves Coresiduation Salmons | 18 |

THE ELIMINATION OF THE MULTIPLE | 24 |

Examples of transformation of curves 3134 | 31 |

The parametric expression of a branch of a curve 3943 | 39 |

General theorem for infinities of a rational function 4649 | 46 |

Examples of Abels theorem 5557 | 55 |

Riemann surfaces | 121 |

INTEGRALS RELATIONS AMONG PERIODS | 136 |

Modular expression of a rational function | 147 |

A significant matrix identity | 157 |

The structure of a certain fundamental rational function | 169 |

Some particular applications Return to theory of special | 176 |

Examples Composite curve intersection of two surfaces | 178 |

General formulae connecting characteristics of a curve | 182 |

MENTALS OF THE THEORY OF LINEAR SERIES | 59 |

Equivalent or coresidual sets of points on the curve | 65 |

Applications of the RiemannRoch formula | 78 |

The existence of a rational function with assigned poles | 86 |

Examples of existing special series | 99 |

Related theorem as to intersections of plane curves | 107 |

The method of loops in a plane | 113 |

Curves which are the complete intersection of two surfaces | 201 |

Curves which are the partial intersection of two surfaces | 208 |

Linear series upon a curve in space | 215 |

Another proof of the determination of the canonical series | 226 |

Examples for cases of composite intersections | 234 |

243 | |

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### Common terms and phrases

a₁ adjoint curves aggregate algebraic arbitrary arise assume branch branch place C₁ C₂ called coefficients coincident columns common complete complete intersection conic consider constant contain coordinates corresponding cubic curve curve of order cusp defined definite denote determinant dimensions double points drawn equal equation exists expression fact follows formula freedom fundamental further genus give given hence homogeneous independent infinite infinity integral intersections linear series linearly lying matrix meets multiple points namely neighbourhood obtained ordinary original osculating plane parameter particular pass places plane curve poles polynomial positive possible primals prime projection proof proved quadric surface quintic curve rational function regard remaining remarked represented respectively result rows satisfying shewn simple single space suppose surfaces of order taken tangent line theorem theory values vanishes variable zero