Über die Anwendung der elliptischen Funktionen auf Probleme der Geometrie

Adolf Hurwitz

Chapter XCII in Mathematische Werke, 1963, pp 687-698 from Springer

Abstract: Zusammenfassung Bekanntlich ist die Gleichung (1) f ( λ 1 , λ 2 ) = A 2 λ 1 2 + 2 B 2 λ 1 + C 2 = A 1 λ 2 2 + 2 B 1 λ 2 + C 1 = 0 $$f\left( {{\lambda _1},{\lambda _2}} \right) = {A_2}\lambda _1^2 + 2{B_2}{\lambda _1} + {C_2} = {A_1}\lambda _2^2 + 2{B_1}{\lambda _2} + {C_1} = 0$$ wo A i , B i , C i ganze rationale Funktionen zweiten Grades von λ i bedeuten, das allgemeine Integral der elliptischen Differentialgleichung: (2) d λ 1 B 1 2 − A 1 C 1 = d λ 2 B 2 2 − A 2 C 2 $$\frac{{d{\lambda _1}}}{{\sqrt {B_1^2 - {A_1}{C_1}} }} = \frac{{d{\lambda _2}}}{{\sqrt {B_{^2}^2 - {A_{^2}}{C_2}} }}$$

Date: 1963
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DOI: 10.1007/978-3-0348-4160-3_49

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