Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera
Keywords:
history of theory of elimination in XVII and XVII centuries, system of algebraic equationsAbstract
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.Downloads
Metrics
References
Bezout, E.: 1765, Reserchers sur le degré des équations résultantes..., Memorier de l’academie des sciences, Paris.
Dumnicki, M., Winiarski, T.: 2007, Bazy Gröbnera – efektywne metody w układach równań wielomianowych, Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków.
Euler, L.: 1748, Introductio in analysin infinitorum, E102, vol. 2, Lusanne.
Euler, L.: 1750, Demonstration sur le nombre des points, ou deux lignes des ordres quelconques peuvent se couper, E148, Memorier de l’academie des sciences de Berlin 4, 234-248.
Euler, L.: 1766, Nouvelle methode d’eliminer les quantites inconnues des equations, E310, Memorier de l’academie des sciences de Berlin 20, 91-104.
Euler, L.: 1990, Introduction to analysis of the infinite, Book II, tłum. J. D. Blanton, Springer Verlag, New York, Berlin, Heidelberg.
Euler, L.: 2005a, A proof concerning the number on points in which two lines of arbitrary orders may intersect, tłum. W. Marshall, The Euler Archive.
Euler, L.: 2005b, New method to eliminate the unknown quantities in equations, tłum. T. Doucet, The Euler Archive.
Kirwan, F.: 1992, Complex Algebraic Curves, Cambridge University Press, Cambridge.
Maclaurin, C.: 1720, Geometrica organica sive descriptio linearum curvarum universalis, G. & J. Innys, London.
Newton, I.: 1722, Arithmetica universalis: sive de compositione et resolutione arithmetica liber, Benjamin & Samuel Tooke, London.
Stillwell, J.: 2002, Mathematics and its history, second edition, Springer UTM, New York, Berlin, Heidelberg.
Wimmer, H. K.: 1990, On the history of the bezoutian and the resultant matrix, Linear Algebra and its Applications 128, 27-34.
Downloads
Published
How to Cite
Issue
Section
License
Read the full statement of the license to publish PDF file.
(see English version) (see Polish version)
