Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera

• Authors: Danuta Ciesielska

Title variants

EN

Bézout’s theorem in Euler’s papers

Abstracts

EN

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

EN

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

• Publisher: Uniwersytet Komisji Edukacji Narodowej w Krakowie
• Journal: Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
• Year: 2013
• Volume: 5
• Pages: 39-50

Dates

published

2013

Contributors

author

Danuta Ciesielska

• Instytut Matematyki, Uniwersytet Pedagogiczny w Krakowie

Identifiers

Biblioteka Nauki

1789396