Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera

Danuta Ciesielska

Abstract


In the paper an early history of the Bézout theorem on algebraiccurves and effective methods in elimination theory is presented. The hypothesis,stated in 1665 by Newton, on the ”intersection number” of algebraiccurves is given. Effective methods on eliminations of one variable in the systemof algebraic variables come from Euler’s papers: Demonstration sur lenombre des points, ou deux lignes des ordres quelconques peuvent se couper(Euler, 1750), Nouvelle methode d’eliminer les quantites inconnues des equations(Euler, 1766) and the chapter De intersectiones curvarum from monographyIntroductio in analysin infinitorum (Euler, 1748). Finally, Bézout’s result from the paper Reserchers sur le degré des équations résultantes...(Bezout, 1765) is given.

Keywords


history of theory of elimination in XVII and XVII centuries, system of algebraic equations

References


Bezout, E.: 1765, Reserchers sur le degré des équations résultantes..., Memorier de l’academie des sciences, Paris.

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Euler, L.: 1748, Introductio in analysin infinitorum, E102, vol. 2, Lusanne.

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