Bibliography & Critical Editions

Primary Latin Witnesses, Renaissance Printings, Critical Editions & Geometric Studies

Authoritative Latin editions, classical mathematical treatises, and modern studies (28 entries) cited across geometor-cusa.

Nicolaus Cusanus — De Docta Ignorantia Libri Tres (completed at Kues, February 12, 1440)

  • Citation Key: cusa:ddi:1440 | Locus: Dedicatio; Lib. I, Caps. 1–26; Lib. II, Caps. 1–13; Lib. III, Caps. 1–12; Epistola auctoris

  • Significance: Foundational treatise introducing learned ignorance, coincidence of opposites, infinite geometric figures, and the decentered moving Earth.

Nicolaus Cusanus — De Geometricis Transmutationibus, ad Paulum Dominici Florentinum (1445)

  • Citation Key: cusa:transmut:1445 | Locus: §§1–36 (esp. §§1–11)

  • Significance: Introduces Cusa’s compass-and-straightedge quarter-side sesquiquarta (5:4) rectification of the inscribed equilateral triangle, yielding pi_Cusa = 24*sqrt(21)/35.

Nicolaus Cusanus — De Mathematicis Complementis, ad Nicolaum V Pontificem Maximum (1453–1454)

  • Citation Key: cusa:compl:1453 | Locus: Lib. I–II (esp. Dedicatio §§1–3 & §§4–10)

  • Significance: Written upon receiving Archimedes’ Opera in Latin from Pope Nicholas V; develops the theory of prima linea (inradius) and secunda linea (circumradius) across isoperimetric polygons.

Nicolaus Cusanus — De Mathematica Perfectione, ad Antonium Cardinalem S. Chrysogoni (1458)

  • Citation Key: cusa:perf:1458 | Locus: Dedicatio & §§1–24

  • Significance: Derives from the coincidence of minimal chord and minimal arc the fifth-order harmonic rectification hc : bc ~= 3*ac : (2*ac + ab).

Nicolaus Cusanus — R. D. N. Cardinalis S. Petri in Mathematicis Aurea Propositio (Rome, August 8, 1459)

  • Citation Key: cusa:aurea:1459 | Locus: §§1–7 & Colophon

  • Significance: Cusa’s crowning three-ray formulation equating endpoint ascent and midpoint descent (theta ~= 3 sin theta / (2 + cos theta), residual theta^5/180).

Nicolaus Cusanus (ed. Jacques Lefèvre d’Étaples / Faber Stapulensis) — Haec accurata recognitio trium voluminum operum Clariss. P. Nicolai Cusae Cardinalis (Paris: Jodocus Badius Ascensius, 1514)

  • Citation Key: cusa:paris:1514 | Locus: Vol. I (De docta ignorantia); Vol. II, fols. 33r–114v (Mathematica)

  • Significance: Monumental Renaissance humanist edition preserving full mathematical woodcuts and text witnesses prior to Rotta’s 1913 omissions.

Nicolaus Cusanus — Nicolai de Cusa Cardinalis, utriusque iuris doctoris, in omnique philosophia incomparabilis viri, Opera, 3 vols. (Basel: Ex Officina Henricpetrina, August 1565)

  • Citation Key: cusa:basel:1565 | Locus: pp. 1–75 (DDI), pp. 939–966 (Transmut.), pp. 1005–1090 (Compl.), pp. 1120–1136 (Perf.)

  • Significance: Standard early modern Basel edition read by Giordano Bruno, Johannes Kepler, and Willebrord Snellius.

Nicolaus Cusanus (ed. Paolo Rotta) — Nicolai Cusani De Docta Ignorantia Libri Tres (Bari: Gius. Laterza & Figli, Classici della Filosofia Moderna 19, 1913)

  • Citation Key: cusa:rotta:1913 | Locus: pp. 1–189

  • Significance: Early twentieth-century critical edition; McGill Library holds Raymond Klibansky’s annotated copy recording Rotta’s homeoteleuton omissions at p. 28 (I.13) and p. 31 (I.14).

Nicolaus Cusanus (eds. Ernst Hoffmann & Raymond Klibansky) — Nicolai de Cusa Opera Omnia, iussu et auctoritate Academiae Litterarum Heidelbergensis, Vol. I: De Docta Ignorantia (Leipzig: Felix Meiner, 1932)

  • Citation Key: cusa:heidelberg:1932 | Locus: h I, pp. 1–163

  • Significance: Reference critical apparatus establishing the manuscript stemma (Codex Cusanus 218 et al.).

Nicolaus Cusanus (ed. Menso Folkerts) — Nicolai de Cusa Opera Omnia, Vol. XX: Scripta Mathematica (Hamburg: Felix Meiner, 2010)

  • Citation Key: cusa:folkerts:2010 | Locus: h XX

  • Significance: Definitive philological edition and mathematical analysis of Cusa’s eleven mathematical treatises (1445–1459).

De Felice, Federica (ed.) — Niccolò Cusano: Scritti matematici (Berlin: Max Planck Institute for the History of Science, Edition Open Sources 13, 2020)

  • Citation Key: defelice:eos:2020 | Locus: Chs. 7, 11, 16, 17

  • Significance: Open-access edition preserving digital transcriptions and figures of Cusa’s mathematical corpus.

Hofmann, Joseph Ehrenfried (trans. Josepha Hofmann) — Nikolaus von Cues: Die mathematischen Schriften (Hamburg: Felix Meiner, 1952; 2nd ed. 1979)

  • Citation Key: hofmann:cusa:1952 | Locus: Introduction & Notes

  • Significance: Landmark modern mathematical reconstruction of Cusa’s algebraic approximations and series expansions.

Plato — Meno (82b–85d), Republic VI–VII (509d–534e), Parmenides (137e, 145b), & Timaeus (31b–36d)

  • Citation Key: plato:opera | Locus: Stephanus pagination

  • Significance: Platonic foundations of recollection, mathematical dianoia vs. noesis, straight vs. round, and World-Soul harmony (geometor/plato).

Aristotle — Metaphysics II.1 (993b9), X.1 (1052b18); Physics VII.4 (248a10–b7); De Anima I.5 (411a5), II.3 (414b29); De Caelo II.13–14

  • Citation Key: aristotle:opera | Locus: Bekker pagination

  • Significance: Aristotelian doctrines on the incomparability of straight and curved, unity as measure, and geocentric rest engaged and transformed by Cusa (geometor/aristotle).

Euclid — Elements, Books I, III, IV, VI & XII (ed. Heiberg; trans. Heath 1926)

  • Citation Key: euclid:elements | Locus: I.18–20, I.32, III.16, III.18, IV.2–15, VI.13, XII.2

  • Significance: Classical axiomatic baseline for Cusa’s triangle, tangent, polygon-exhaustion, and quadrature arguments (geometor/euclid, geometor/elements).

Archimedes — Dimensio Circuli (Measurement of a Circle) & De Lineis Spiralibus (On Spirals)

  • Citation Key: archimedes:dimensio | Locus: Dim. circ. Props. 1–3 (3+10/71 < pi < 3+1/7); Spir. Defs. & Prop. 18

  • Significance: Primary ancient foil for Cusa’s polygon bounds and critique of kinematic spiral rectification.

Proclus Diadochus — In Primum Euclidis Elementorum Librum Commentarii (ed. Friedlein 1873)

  • Citation Key: proclus:in-euclidem | Locus: Prologues I–II (pp. 3–70) & on Defs. 2–4, 15–17 (pp. 97–113, 153–162)

  • Significance: Neoplatonic philosophy of limit/unlimited, circular simplicity, and imaginative projection studied by Cusa (geometor/proclus).

Pseudo-Dionysius the Areopagite — De Mystica Theologia, De Divinis Nominibus, & Epistola I ad Gaium

  • Citation Key: dionysius:mystica | Locus: MT I.1–3, V; DN I, V, XIII

  • Significance: Apophatic theological source explicitly cited in De docta ignorantia I.16–18.

Thomas Aquinas — Expositio super Librum Boethii de Trinitate, qq. 5–6

  • Citation Key: aquinas:boethius | Locus: q. 5 a. 3; q. 6 a. 1–2

  • Significance: Scholastic account of mathematical abstraction and terminatio ad imaginationem (geometor/aquinas).

Regiomontanus (Johannes Müller) — De Quadratura Circuli Dialogus, Secundum Nicolaum Cusensem (composed 1464; Nuremberg: Johannes Petreius, 1533)

  • Citation Key: regiomontanus:quadratura:1533 | Locus: Appendix to De Triangulis Omnimodis

  • Significance: Demonstrated by Archimedean bounds that Cusa’s 1450s rectifications slightly miss exact transcendental pi while honoring their ingenuity.

Pacioli, Fra Luca — De Divina Proportione (Venice: Paganino Paganini, 1509)

  • Citation Key: pacioli:divina:1509 | Locus: Compendio Caps. V–VII

  • Significance: Parallels Cusa in treating irrational geometric proportion as an emblem of the incommensurable, triune Divine (geometor/pacioli).

Dürer, Albrecht — Underweysung der Messung, mit dem Zirckel und Richtscheyt (Nuremberg, 1525)

  • Citation Key: durer:underweysung:1525 | Locus: Books I–II

  • Significance: Applies constructive circle-quadrature and polygon transmutations in Northern Renaissance craft geometry.

Kepler, Johannes — Prodromus Dissertationum Cosmographicarum, continens Mysterium Cosmographicum (Tübingen, 1596) & Ad Vitellionem Paralipomena (1604)

  • Citation Key: kepler:mysterium:1596 | Locus: Myst. Cosm. Cap. II; Paralipomena Cap. IV.4

  • Significance: Celebrates ‘divinus mihi Cusanus’ on curved/straight symbolism and extends Cusa’s coincidence into the projective continuity of conic sections.

Snellius, Willebrord & Huygens, Christiaan — Cyclometricus (Leiden, 1621) & De Circuli Magnitudine Inventa (Leiden: Elzevier, 1654)

  • Citation Key: snellius:huygens:1654 | Locus: Huygens Props. 10–16

  • Significance: Rediscovers and rigorously proves the fifth-order Cusa–Snellius inequality 3 sin(theta)/(2 + cos theta) < theta.

Casey, John — A Sequel to the First Six Books of the Elements of Euclid, 4th ed. (Dublin: Hodges, Figgis & Co., 1886)

  • Citation Key: casey:sequel:1886 | Locus: Book VI, Section V (Theory of Inversion & Coaxal Circles)

  • Significance: Synthetic theory of circle inversion and parabolic coaxial pencils formalizing Cusa’s I.13 circle-line unity.

Klein, Felix — Elementarmathematik vom höheren Standpunkte aus, Bd. II: Geometrie (Leipzig: Teubner, 1908)

  • Citation Key: klein:elementary:1908 | Locus: Part II (Projective & Möbius Transformations)

  • Significance: Erlangen group-theoretic unification of lines and circles on the Riemann/Möbius sphere.

Hoenen, Petrus H. J., S.J. — De Noetica Geometriae: Origine Theoriae Cognitionis (Rome: Analecta Gregoriana 63, 1954)

  • Citation Key: hoenen:noetica:1954 | Locus: Caps. I–IV, IX

  • Significance: Epistemological study of insight into geometric necessity in concrete diagrams (geometor/hoenen).

Wildberger, Norman J. — Divine Proportions: Rational Trigonometry to Universal Geometry (Sydney: Wild Egg, 2005)

  • Citation Key: wildberger:divine:2005 | Locus: Chs. 3–6 (Quadrance, Spread, Triple Quad & Triple Spread Formulas)

  • Significance: Algebraic trigonometry proving pure rational convergence of Cusa’s I.14 flattening triangle to collinearity (geometor/wildberger).