Bibliography & Primary Editions¶
Primary Public-Domain Editions of Johannes Kepler¶
Kepler (1596) — Johannes Kepler, Prodromus Dissertationum Cosmographicarum, continens Mysterium Cosmographicum, de admirabili proportione orbium coelestium, Tübingen: Georgius Gruppenbachius, 1596 (ETH-Bibliothek Zürich Rar 1371 / e-rara-445). (Editio princeps, with appendix and orbital calculations by Michael Mästlin; Public Domain.)
Kepler (1621) — Johannes Kepler, Prodromus Dissertationum Cosmographicarum, continens Mysterium Cosmographicum (Editio altera cum notis authoris), Frankfurt am Main: Erasmus Kempfer / Godefridus Tampachius, 1621. (Author’s annotated second edition linking the 1596 treatise to Astronomia Nova and Harmonices Mundi; Public Domain.)
Kepler (1597) — Johannes Kepler, Epistola ad Michaelem Mästlinum (Graz, October 1597), in Joannis Kepleri Astronomi Opera Omnia, ed. Ch. Frisch, Vol. I (1858), p. 377. (Formulates the Kepler Right Triangle $1 : \sqrt{\phi} : \phi$; Public Domain.)
Kepler (1609) — Johannes Kepler, Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ, seu Physica Coelestis, tradita commentariis de Motibus Stellae Martis, Heidelberg: Gotthard Vögelin, 1609. (Establishes Kepler’s First and Second Laws of focal elliptical planetary motion; Public Domain.)
Kepler (1611) — Johannes Kepler, Ioannis Kepleri S. Cæs. Maiest. Mathematici Strena seu de Nive Sexangula, Frankfurt am Main: Godefridus Tampachius, 1611 (24 pp.). (Editio princeps of On the Six-Cornered Snowflake; Public Domain.)
Kepler (1619) — Johannes Kepler, Ioannis Keppleri Harmonices Mundi Libri V, Linz: Godofredus Tampachius / excudebat Ioannes Plancus, 1619 ([8], 66, 255 pp., 5 engraved plates). (Editio princeps of The Harmony of the World; Public Domain.)
Frisch (1858, Vol. I) — Christian Frisch (ed.), Joannis Kepleri Astronomi Opera Omnia, Volumen I, Frankfurt a. M. & Erlangen: Heyder & Zimmer, 1858, pp. 95–214, 377. (Critical Latin edition of Mysterium Cosmographicum 1596/1621 and the Mästlin correspondence; Public Domain.)
Frisch (1864, Vol. V) — Christian Frisch (ed.), Joannis Kepleri Astronomi Opera Omnia, Volumen V, Frankfurt a. M. & Erlangen: Heyder & Zimmer, 1864, pp. 75–334. (Critical Latin edition of Harmonices Mundi Libri V; Public Domain.)
Frisch (1868, Vol. VII) — Christian Frisch (ed.), Joannis Kepleri Astronomi Opera Omnia, Volumen VII, Frankfurt a. M. & Erlangen: Heyder & Zimmer, 1868, pp. 715–730. (Critical Latin edition of Strena seu de Nive Sexangula; Public Domain.)
Classical, Medieval & Renaissance Authorities¶
Euclid — Stoicheia (Elements, ed. J. L. Heiberg / trans. T. L. Heath), Books I, II, IV, VI, X, XIII; Digital Scriptorium
geometor/euclid&geometor/elements.
Proclus Diadochus — In Primum Euclidis Elementorum Librum Commentarii (ed. G. Friedlein, Leipzig: Teubner, 1873); Digital Scriptorium
geometor/proclus.
Pappus of Alexandria — Synagoge (Mathematical Collection), Book V, Props. 1–19 (Honeycomb planimetry & the 13 Archimedean semi-regular solids);
geometor/pappus.
Nicolaus Cusanus — De Docta Ignorantia Libri Tres (1440), Book I, Chs. 11–21 (Curved and Straight as theological-mathematical exemplars).
Luca Pacioli — De Divina Proportione, Venice: Paganino Paganini, 1509; Digital Scriptorium
geometor/pacioli.
Albrecht Dürer — Underweysung der Messung, mit dem Zirckel und Richtscheyt, Nuremberg, 1525.
Georg Joachim Rheticus — Narratio Prima (Danzig, 1540; reprinted by Michael Mästlin in Kepler’s 1596 Mysterium Cosmographicum).
Nicolaus Copernicus — De revolutionibus orbium coelestium Libri VI, Nuremberg: Johannes Petreius, 1543.
Modern Mathematical Developments¶
Gauss (1801) — Carl Friedrich Gauss, Disquisitiones Arithmeticae, Leipzig: Gerhard Fleischer, 1801, Sectio VII, §§335–366.
Poinsot (1810) — Louis Poinsot, Mémoire sur les polygones et les polyèdres, Journal de l’École Polytechnique 10 (1810), pp. 16–48.
Wantzel (1837) — Pierre Laurent Wantzel, Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas, Journal de Mathématiques Pures et Appliquées 2 (1837), pp. 366–372.
Thompson (1942) — D’Arcy Wentworth Thompson, On Growth and Form (2nd ed.), Cambridge University Press, 1942.
Coxeter (1973) — H. S. M. Coxeter, Regular Polytopes (3rd ed.), New York: Dover Publications, 1973.
Penrose (1974) — Roger Penrose, The Role of Aesthetics in Pure and Applied Mathematical Research, Bulletin of the Institute of Mathematics and its Applications 10 (1974), pp. 266–271.
Hales (2005) — Thomas C. Hales, A Proof of the Kepler Conjecture, Annals of Mathematics 162(3) (2005), pp. 1065–1185 (Flyspeck formal verification, 2014/2017).