Skip to main content
SpringerLink
Log in

Incommensurability, the Heptagon of Ignacio Muñoz (1684), and Kepler’s Heresy

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8
Figure 9.
Figure 10.
Figure 11.
Figure 12:

References

  1. J. Aiton, A. M. Duncan, and J. V. Field. The Harmony of the World by Johannes Kepler. The American Philosophical Society, 1997.

  2. G. Cardano. De subtilitate libri XXI. Nuremberg: Ioh. Petreium, 1550.

  3. G. Cardano. Subtilitate Libri XXI. Lyon: Gulielmum Rouillium, 1559.

  4. C. A. Cardona Suárez et al. La geometría de Alberto Durero: estudio y modelación de sus construcciones. Fundación Universidad de Bogotá Jorge Tadeo Lozano, 2006.

  5. M. Caspar, editor. Johannes Kepler Gesammelte Werke. Vol. 1. Mysterium cosmographicum: de stella nova. C. H. Beck’sche Verlagsbuchhandlung, 1938.

  6. M. Caspar, editor. Johannes Kepler Gesammelte Werke. Vol. 6. Harmonices Mundi. C.H. Beck’sche Verlagsbuchhandlung, 1940.

  7. M. Caspar, editor. Johannes Kepler Gesammelte Werke. Vol. 15. Briefe 1604–1607. C. H. Beck’sche Verlagsbuchhandlung, 1951.

  8. C. Clavius. Euclidis Elementorum libri XV: accessit XVI de solidorum regularium comparatione. Rome: Vincentium Accoltum, 1574.

  9. C. Clavius. Elementorum libri XV; accessit XVI de solidorû regularium cuiuslibet intra quodlibet comparatione: omnes perspicuis demonstrationibus, accuratisque scholijs illustrate. Rome: Bartholomaeum Grassium, Sanctium, & Soc, 1589.

  10. C. Clavius. Geometria practica. Rome: Aloisij Zannetti, 1604.

  11. C. Clavius. Geometria practica. Mainz: Typographeo Ioannis Albini, 1606.

  12. M. Curtze. Jordani Nemorarii Geometria vel de triangulis libri IV. Mitteilungen des Coppernicus-Vereins, 6, iv, n2, 1887.

  13. A. Deville. Les fortifications du chevalier Antoine de Ville, contenans la manière de fortifier toute sorte de places. Lyon: Philippe Borde, 1640.

  14. M. Dögen. Dramburgensis marchici Architectura militaris moderna: varijs historijs, tam veteribu Matthiae … Amsterdam: Apud Ludovicum Elzevir, 1647.

  15. A. Dürer. Underweysung der Messung, mit dem Zirckel und Richtscheyt: in Linien Ebnen vo gantzen Corporen. Nüremberg: Hieronymus Andreae, 1525.

  16. G. Friedlein. De institutione arithmetica libri duo. De institutione Musica libri quinque. In Accedit geometria quae fertur Boetii. Leipzig: Teubner, 1867.

  17. C. Gauss. Disquisitiones Arithmeticae. Leipzig: Gerhard Fleischer, 1801.

    Book  MATH  Google Scholar 

  18. J. P. Hogendijk. Greek and Arabic constructions of the regular heptagon. Archive for History of Exact Sciences 30 (1984), 197–330.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Kepler. Prodromus dissertationum cosmographicarum, continens mysterium cosmographicum, de admirabili proporione orbium coelestium, deque causis coelorum numeri, magnitudinis, motuumque periodicorum genuinis & propriis, demostratum, per quinque regularia corpora geométrica. Tübingen: Georgius Gruppenbachius, 1596.

  20. J. Kepler. Ioannis Keppleri Harmonices mundi libri V.: quorum primus Geometricus, de figurarum regularium, quae proportiones harmonicas constituunt, ortu & demonstrationibus. Linz: Godofredi Tampachii, 1619.

  21. W. R. Knorr. On Archimedes’ construction of the regular heptagon. Centaurus 32 (1998), 257–271.

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Lluis i Ginovart et al. Gothic construction and the traça of a heptagonal apse: the problem of the heptagon. Nexus Network Journal 15 (2013), 325–348.

  23. J. Lluis i Ginovart. Mathematics and the art and science of building medieval cathedrals. In Handbook of the Mathematics of the Arts and Sciences, edited by B. Sriraman. Springer, 2019.

  24. I. Muñoz. Observationes diversarum artium. Manuscript 7111. Madrid: Biblioteca Nacional España, 1669.

  25. I. Muñoz. Manifiesto geometrico, plus ultra de la geometria practica: addicion al IV libro de los Elementos de Euclides: construccion y demostracion geometrica del triangulo isosceles propio del heptagono regular y descripcion de la misma figura. Brussels: Francisco Foppens, 1684.

  26. R. Rashed. Ibn al-Haytham’s construction of the regular heptagon. Journal Historical Arabic Science 3 (1976), 387–409.

    MathSciNet  Google Scholar 

  27. D. Raynaud. Abū al-Wafā’ Latinus?: a study of method. Historia Mathematica 39 (2012), 34–83.

    Article  MathSciNet  MATH  Google Scholar 

  28. M. Roriczer. Das Büchlein von der Fialen Gerechtigheit (fak. Regensburg 1486) und Die Geometria Deutsch (facsimile ed. ms. Regensburg un 1487/88). Regensburg: Hürtgenwald Guido Pressler, 1999.

  29. D. E. Rowe, A. Heeffer, and T. Rothman. On remembering Cardano anew. Mathematical Intelligencer 36 (2014), 53–66,

    Article  MathSciNet  MATH  Google Scholar 

  30. H. Schoene. Heronis Alexandrini opera quae supersunt omnia. Vol III: Rationes dimetiendi et commentatio dioptrica. Leipzig: Teubner, 1903.

  31. S. Stevin. Tomus Secundus Mathematicarum hypomnematun de Geometriae Praxi. Lyon: Ioannis Patii, Academiae Typographi, 1605.

  32. G. Valla. De expetendis et fugiendis rebus. Venice: Aldo Manuce, 1501.

  33. F. Viète. Opera Mathematica. In unum Volumen congesta ac recognita. Lyon: Bonaventurae & Abrahami Elzeviriorum, 1696.

  34. M. F. Woepcke. Recherches sur l’historie des sciences mathématiques chez les orientaux, d’ápres des traités inedits Arabes et Persans. Deuxième siecle. Analyse et extrait d’un recueil de constructions géométriques par Abûl Wafa. Journal asiatique 5 (1855}, 218–256 and 309–359.

  35. J. Zaragoza. Geometria practica Euclidis: problemata continens. Madrid: Bernardum à Villa-Diego, 1672.

Download references

Acknowledgments

We thank Arch. Valentina Risemberg for proofreading our text.

Author information

Authors and Affiliations

  1. Universitat Internacional de Catalunya, Barcelona, Spain

    Josep Lluis i Ginovart & Cinta Lluis-Teruel

Authors
  1. Josep Lluis i Ginovart
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cinta Lluis-Teruel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cinta Lluis-Teruel.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lluis i Ginovart, J., Lluis-Teruel, C. Incommensurability, the Heptagon of Ignacio Muñoz (1684), and Kepler’s Heresy. Math Intelligencer 45, 108–117 (2023). https://doi.org/10.1007/s00283-022-10247-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-022-10247-1

Search

Navigation