## Abel's theorem and the allied theory: including the theory of the theta function |

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Abel's theorem Abelian integral adjoint polynomial algebraic arbitrary constants arbitrary place argument arise associated branch places Chap chapter condition congruences considered coresidual corresponding Crelle denote determinant differential coefficients dimension double points elements equal essential singularities exist expression factor factorial function finite places follows formula function of order fundamental equation given half-integer characteristics half-period Hence hyperelliptic infer infinite infinitesimal infinity integral function integral polynomial intersections inversion problem linear transformation linearly independent Math matrix multiple neighbourhood notation obtain odd functions period loops plane curve poles polynomial of grade polynomial vanishing positive integer prove quantities quartic rational function regard result Riemann surface right hand root of unity rows and columns second kind second order shew shewn similarly suppose symmetrical matrix tangents theory theta functions third kind values vanish identically variable wherein