Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera

Danuta Ciesielska

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2013)

  • Volume: 5, page 39-50
  • ISSN: 2080-9751

Abstract

top
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.

How to cite

top

Danuta Ciesielska. "Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 5 (2013): 39-50. <http://eudml.org/doc/296265>.

@article{DanutaCiesielska2013,
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.},
author = {Danuta Ciesielska},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {history of theory of elimination in XVII and XVII centuries; system of algebraic equations},
language = {pol},
pages = {39-50},
title = {Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera},
url = {http://eudml.org/doc/296265},
volume = {5},
year = {2013},
}

TY - JOUR
AU - Danuta Ciesielska
TI - Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2013
VL - 5
SP - 39
EP - 50
AB - 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.
LA - pol
KW - history of theory of elimination in XVII and XVII centuries; system of algebraic equations
UR - http://eudml.org/doc/296265
ER -

References

top
  1. Bezout, E.: 1765, Reserchers sur le degré des équations résultantes..., Memorier de l’academie des sciences, Paris. 
  2. Dumnicki, M., Winiarski, T.: 2007, Bazy Gröbnera – efektywne metody w układach równań wielomianowych, Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków. 
  3. Euler, L.: 1748, Introductio in analysin infinitorum, E102, vol. 2, Lusanne. 
  4. 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. 
  5. Euler, L.: 1766, Nouvelle methode d’eliminer les quantites inconnues des equations, E310, Memorier de l’academie des sciences de Berlin 20, 91-104. 
  6. Euler, L.: 1990, Introduction to analysis of the infinite, Book II, tłum. J. D. Blanton, Springer Verlag, New York, Berlin, Heidelberg. 
  7. 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. 
  8. Euler, L.: 2005b, New method to eliminate the unknown quantities in equations, tłum. T. Doucet, The Euler Archive. 
  9. Kirwan, F.: 1992, Complex Algebraic Curves, Cambridge University Press, Cambridge. 
  10. Maclaurin, C.: 1720, Geometrica organica sive descriptio linearum curvarum universalis, G. & J. Innys, London. 
  11. Newton, I.: 1722, Arithmetica universalis: sive de compositione et resolutione arithmetica liber, Benjamin & Samuel Tooke, London. 
  12. Stillwell, J.: 2002, Mathematics and its history, second edition, Springer UTM, New York, Berlin, Heidelberg. 
  13. Wimmer, H. K.: 1990, On the history of the bezoutian and the resultant matrix, Linear Algebra and its Applications 128, 27-34. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.