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When Nine Points Are Worth But Eight: Euler’s Resolution of Cramer’s Paradox - References

Author(s): 
Robert E. Bradley (Adelphi University) and Lee Stemkoski (Adelphi University)
  1. [Boyer 1956] Boyer, C. B., History of Analytic Geometry, New York: Scripta Mathematica, 1956. Reprinted New York: Dover, 2004.
  2. [Bradley 2006] Bradley, R. E., "The Curious Case of the Bird's Beak," International J. Math. Comp. Sci. 1 (2006), no. 2, pp. 243-268.
  3. [Braikenridge 1733] Braikenridge, W. Exercitato Geometrica de Descriptione Curvarum, London, 1733.
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  12. [Euler 1744a] Euler, L,. Methodus inveniendi lineas curvas maximi minimive..., Lausanne: Bousquet, 1744. Also in [Euler], ser. I, vol. 24.
  13. [Euler 1744b] Euler, L., 1744/10/20, letter to G. Cramer, in Leonhard Euler Papers (MSS 490A), Dibner Library of the History of Science and Technology, Smithsonian Institution Libraries.
  14. [Euler 1748] Euler, L., Introductio in Analysin Infinitorum, 2 vols., Lausanne: Bousquet, 1748. Also in [Euler], ser. I, vols. 8-9.
  15. [Euler 1750a] Euler, L., "Sur un contradiction apparente dans la doctrine des lignes courbes," Mém. Berlin, IV (1748), 1750, 219-233. Also in [Euler], ser. I, vol. 26, 33-45.
  16. [Euler 1750b] Euler, L., "Démonstration sur le nombre des points, ou deux lignes des ordres quelconques peuvent se couper," Mém. Berlin, IV (1748), 1750, 234-248. Also in [Euler], ser. I, vol. 26, 46-59.
  17. [Euler 1751] Euler, L., "Sur le point de rebroussement de la seconde espece de M. le Marquis de l'Hôpital," Mém. Berlin, V (1749), 1751, 203-221. Also in [Euler], ser. I, vol. 27, 236-252.
  18. [Euler 1975] Euler, L., Opera Omnia, Series IVA, volume 1 (index of Euler's correspondence), eds. A. P. Juškevič, V. I. Smirnov, W. Habicht, Basel: Birkhäuser, 1975.
  19. [Euler 2015] Euler, L., Opera Omnia, Series IVA, volume 7 (correspondence of Euler with G. Cramer and 8 others), eds. S. Bodenmann, A. Kleinert, Basel: Birkhäuser, to appear in 2015.
  20. [Gua de Malves 1740] Gua de Malves, J. P. de, Usages de l'analyse de Descartes pour découvrir, sans le secours du Calcul Differentiel, les Propriétés, ou affectations principales des lingnes géometriques de tous les ordres, Paris: Briasson, 1740.
  21. [L'Hôpital 1696] L'Hôpital, G., Analyse des infiniment petits, pour l'intelligence des lignes courbes, Paris: l'Imprimerie royale, 1696.
  22. [Katz 2008] Katz, Victor J., A History of Mathematics, 3rd ed., Boston: Addison-Wesley, 2008.
  23. [Maclaurin 1720] Maclaurin, C., Geometrica Organica; Sive Descriptio Linearum Curvarum Universalis, London, 1720.
  24. [Mills 1984] Mills, S. "Note on the Braikenridge-Maclaurin Theorem," Notes and Records of the Royal Society 38 (1984), 235-240.
  25. [Sandifer 2007] Sandifer, C. E., "Cramer's Paradox," in How Euler Did It, Washington: Mathematical Association of America, 2007, 37-42. Also available from MAA Euler Archive: How Euler Did It (August 2004).
  26. [Scott 1898] Scott, C. A., "On the Intersections of Plane Curves," Bull. Amer. Math. Soc. 4 (1898), 260-273.

Robert E. Bradley (Adelphi University) and Lee Stemkoski (Adelphi University), "When Nine Points Are Worth But Eight: Euler’s Resolution of Cramer’s Paradox - References," Loci (February 2014)

Dummy View - NOT TO BE DELETED

When Nine Points Are Worth But Eight: Euler's Resolution of Cramer's Paradox