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### Contents

PREFACE | 1 |

GAUSS | 7 |

FRANCE AND THE ECOLE POLYTECHNIQUE IN THE FIRST DECADES | 59 |

Copyright | |

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abelian abelian functions algebraic functions already analytic arbitrary automorphic basic Berlin calculus called Cartan Cauchy characteristic Clebsch completely compute concept condition connection consider constant construction coordinates corresponding Crelle's Journal curve defined definite denote determinant differential equations differential form Dirichlet domain elliptic functions example fiber finite foliation formulas fundamental Galois Gauss given Goettingen Grassmann Hence homogeneous icosahedron ideas infinitely integral interest intuition invariant Jacobi Klein l9th century lattice lectures Lie algebra manifold Math mathematical physics mathematicians mechanics modular nature number theory one-forms orbit paper parameterization plane Pluecker problem projective geometry proof purely quadratic differential quotient relations remarkable representation Riemann surface Riemannian metric satisfied scientific solution sphere structure subgroup submanifold Suppose symmetric tangent bundle theorem tion transformation triangle values variables vector bundle vector field vector space Volume Weierstrass Werke