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accurate algebraical prime factor angle approximation complete quotient congruence convergent coordinates corresponding cos'a cosh cosV cot'a cotr ft criterion cubic cycles deduced denote determinant discriminant displacements elliptic elliptic functions elliptic integral equal equianharmonic exact differential expression follows formula fractions functions geodesic given gives group of degree Hence Hessian hypersphere inclusive invariant of degree irreducible invariant Jacobi latitude linear modulus negative non-residue number of interchanges numerical multiple obtained octavic character pairs paper plane primitive root proved quadratic form quadratic function quadratic residue quadric quantities quartic quintic reciprocal factor reduced reduced latitude respectively result rows and columns satisfied sectorial point sextic sin'a sin'y sina0 sinh sinV sphere spheroid square subgroup of order substitution suppose synodic periods tangents terms free theorem transform tres ft triangle values vanish variables write zero
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