## Backgrounds of Arithmetic and Geometry: An IntroductionThe book is an introduction to the foundations of Mathematics. The use of the constructive method in Arithmetic and the axiomatic method in Geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

PREFACE | 1 |

ARITHMETIC | 18 |

AXIOMATIC THEORIES | 48 |

ALGEBRAIC BASES OF GEOMETRY | 63 |

THE BASES OF EUCLIDEAN GEOMETRY | 87 |

BIRKHOFFS AXIOMATIC SYSTEM | 122 |

GEOMETRICAL TRANSFORMATIONS | 139 |

THE ERLANGEN PROGRAM | 167 |

BACHMANNS AXIOMATIC SYSTEM Francise Radó | 236 |

HINTS | 253 |

261 | |

### Other editions - View all

### Common terms and phrases

absolute Geometry according to Theorem affine Geometry affine space analogously angle arbitrary axiomatic system axiomatic theory belongs bijection binary relation called cardinal numbers Cauchy sequence centre Chapter circle co-linear points coincide congruent construction Corollary deduce defined Definition denote distinct points element enunciation equality equivalence Euclidean Geometry Euclidean space exists follows formula function f given h-ray h-straight h-transformation Hilbert's axiomatic system holds homothety hyperbolic Geometry hypothesis independent integer inversion Inviſ isometry isomorphism Klein space Let us consider Let us suppose linear space Mathematics natural number non-contradictory non-null notation notions and relations obtain obviously oriented parallel Pasch's axiom perpendicular primary notions projective Geometry Proof Proposition prove rational numbers real numbers reductio ad absurdum satisfied segment sequence straight line subset super-parallel symmetry related system of axioms Theorem Theorem 5.1 totally ordered triangle ABC unique vector zºv zºv