Index of Persons, Dedicatees & Geometers

Ancient Authorities, Fifteenth-Century Interlocutors & Modern Mathematical Successors

Biographical register of 26 philosophers, humanists, dedicatees, geometers, astronomers, and critical editors connected with Nicholas of Cusa’s De Docta Ignorantia and mathematical treatises.

Nicholas of Cusa (Nicolaus Cusanus / Nikolaus Krebs von Kues) (1401 – August 11, 1464)

German Cardinal, Philosopher, Canonist & Speculative Geometer

Born at Kues on the Moselle, educated at Heidelberg, Padua (where he befriended Paolo dal Pozzo Toscanelli), and Cologne; author of De docta ignorantia (1440), De coniecturis (c. 1442), and eleven mathematical treatises (1445–1459) uniting coincidence of opposites, projective limits, and decentered cosmology.

Cardinal Julian Cesarini (Iulianus Caesarinus) (1398 – November 10, 1444)

Papal Legate, Teacher of Cusa at Padua & Dedicatee of De Docta Ignorantia

Humanist canonist who taught Cusa at Padua and presided at the Council of Basel; dedicated recipient of both De docta ignorantia (1440) and De coniecturis.

Paolo dal Pozzo Toscanelli (Paulus physicus Florentinus) (1397 – May 10, 1482)

Florentine Mathematician, Physician, Astronomer & Lifelong Friend of Cusa

Fellow student of Cusa at Padua, advisor to Brunelleschi and Columbus, dedicatory recipient of De geometricis transmutationibus (1445), and interlocutor of Cusa’s 1457 Dialogus de circuli quadratura; stood at Cusa’s deathbed at Todi in 1464.

Pope Nicholas V (Tommaso Parentucelli) (1397 – March 24, 1455)

Humanist Pope, Founder of the Vatican Library & Dedicatee of De Mathematicis Complementis

Commissioned Jacobus Cremonensis’s Latin translation of Archimedes’ Opera and presented it directly to Cardinal Nicholas of Cusa in 1453, inspiring De mathematicis complementis.

Cardinal Antonio Cerdá y Lloscos (1390 – September 12, 1459)

Cardinal Priest of S. Grisogono, Scholastic Theologian & Dedicatee of De Mathematica Perfectione

Majorcan theologian and friend of Cusa to whom Cusa dedicated De mathematica perfectione (1458) along with De beryllo.

Pythagoras of Samos (c. 570 – c. 495 BC)

Founder of Harmonic & Arithmetical Philosophy

Honored in De docta ignorantia I.1 and I.11 as ‘first philosopher in name and deed’ for grounding all comparative proportion and inquiry in number.

Socrates of Athens (469 – 399 BC)

Exemplar of Self-Critical Ignorance

Cited in De docta ignorantia I.1 as knowing nothing save that he did not know, anticipating Cusa’s methodological docta ignorantia.

Plato of Athens (428/427 – 348/347 BC)

Founder of the Academy & Author of Meno, Republic, Parmenides & Timaeus

Cited across I.11, I.17 (via Calcidius), and II.12; Cusa’s three-step mathematical transsumption transforms Republic VI–VII’s Divided Line and Parmenides 137e on straight and round (geometor/plato).

Aristotle of Stagira (384 – 322 BC)

Author of the Metaphysics, Physics, De Anima & De Caelo

Cited in I.1 (owl before the sun, Metaph. II.1), I.11 (species as numbers; triangle in quadrangle, De Anima II.3), I.17 (first as measure, Metaph. X.1), and I.18 (straight as measure of itself and the curved, De Anima I.5), while his fixed-center geocentrism is overturned in II.11–12 (geometor/aristotle).

Euclid of Alexandria (fl. c. 300 BC)

Author of the Elements

Supplies the geometric foundations of Cusa’s demonstrations: triangle inequality (I.20), angle sum of two right angles (I.32), greater side opposite greater angle (I.18–19), tangent perpendicularity (III.16, III.18), inscribed polygons (Book IV), and mean proportional quadrature (VI.13; Cusa cites Campanus’s numbering VI.9) (geometor/euclid, geometor/elements).

Archimedes of Syracuse (c. 287 – 212 BC)

Author of Measurement of a Circle & On Spirals

Studied intensely by Cusa in Jacobus Cremonensis’s 1450s Latin translation; De mathematicis complementis §§2–3 & §8 engage Dimensio circuli Prop. 1 and critique the kinematic postulate of De lineis spiralibus.

Proclus Diadochus (412 – 485 CE)

Neoplatonic Commentator on Euclid Book I & Plato’s Parmenides

Cusa owned and heavily annotated manuscripts of Proclus’s Commentary on the Parmenides and Elements; Proclus’s ontology of mathematicals in the imagination directly parallels De docta ignorantia I.11–12 (geometor/proclus).

Pseudo-Dionysius the Areopagite (fl. c. 500 CE)

Author of Mystical Theology & On Divine Names

Cited repeatedly in I.16–18 for apophatic theology (‘theology is simultaneously maximal and minimal’) and supersubstantiality above affirmation and negation.

Aurelius Augustinus (St. Augustine of Hippo) (354 – 430 CE)

Patristic Philosopher of Divine Number & Trinity

Cited in I.11 for De quantitate animae’s geometric method and in I.19 for ‘When you begin to number the Trinity, you depart from the truth.’

Anicius Manlius Severinus Boethius (c. 477 – 524 CE)

Author of De Institutione Arithmetica & De Trinitate

Praised in I.11 as ‘most learned of the Romans’ for teaching that all truth is comprehended in multitude and magnitude (Quadrivium).

St. Anselm of Canterbury (1033 – 1109)

Author of the Proslogion & De Veritate

Inspires both I.2’s formula of the Maximum (quo nihil maius esse potest) and I.12’s comparison of supreme Truth to infinite rectitude (rectitudo infinita).

St. Thomas Aquinas (1225 – 1274)

Scholastic Philosopher of Mathematical Abstraction & Judgment

Articulated the threefold degree of abstraction and intelligible matter (In Boethium de Trinitate q. 5–6), against whose strict Aristotelian non-contradiction in finite ratio Cusa distinguishes higher intellectus (geometor/aquinas).

Johannes Müller von Königsberg (Regiomontanus) (1436 – 1476)

Renaissance Trigonometrician & Critic of Cusa’s Quadratures

In De triangulis et quadratura circuli (composed 1464, printed 1533), subjected Cusa’s algebraic rectifications to rigorous trigonometric error bounds using Archimedes’ 96-gon inequalities, proving their non-exactness while confirming their remarkable numerical accuracy.

Fra Luca Pacioli (c. 1447 – 1517)

Author of Summa de Arithmetica & De Divina Proportione (1509)

Shared Cusa’s mathematical-theological conviction that irrational geometric proportion reveals divine unity, trinity, and incommensurability (geometor/pacioli).

Albrecht Dürer (1471 – 1528)

Author of Underweysung der Messung (1525)

Transmitted Renaissance constructive transmutations of curved and rectilinear magnitudes into German workshop geometry within a decade of Faber Stapulensis’s 1514 edition of Cusa.

Johannes Kepler (1571 – 1630)

Imperial Mathematician & Author of Mysterium Cosmographicum (1596)

Hailed Nicholas of Cusa in Mysterium Cosmographicum Chapter II as ‘divinus mihi Cusanus’ explicitly for Cusa’s transsumption of curved and straight as the archetypal symbol of Creator and created cosmos, and adopted Cusa’s Principle of Continuity in Ad Vitellionem Paralipomena (1604) on conic foci at infinity.

Willebrord Snellius & Christiaan Huygens (1580–1626 / 1629–1695)

Seventeenth-Century Provers of the Cusa–Snellius–Huygens Inequality

Snellius rediscovered Cusa’s 1458–1459 formula theta ~= 3 sin(theta)/(2 + cos theta) in Cyclometricus (1621), and Huygens rigorously proved in De circuli magnitudine inventa (1654) that it forms a strict fifth-order lower bound on arc length.

Jean-Victor Poncelet, John Casey & Felix Klein (1788–1867 / 1820–1891 / 1849–1925)

Architects of Projective Continuity, Circle Inversion & Erlangen Geometry

Provided the modern synthetic and analytic realization of Cusa’s I.13–14 theorems through points at infinity, Möbius circle inversion, and projective degeneration of conics and triangles.

Norman J. Wildberger (b. 1955)

Founder of Rational Trigonometry (Divine Proportions, 2005)

Replaces transcendental distance and angle by algebraic quadrance Q and spread s; under Rational Trigonometry, Cusa’s I.14 flattening triangle exhibits pure rational spread s_A = 4n^2/(n^2+1)^2 -> 0 and Triple Quad residual 16/n^2 -> 0 (geometor/wildberger).

Petrus H. J. Hoenen, S.J. (1880 – 1961)

Author of De Noetica Geometriae (1954)

Analyzed geometric abstraction and intellectual judgment of necessity from singular phantasmata, illuminating Cusa’s contrast between sensible imagination and visio intellectualis (geometor/hoenen).

Jacques Lefèvre d’Étaples, Paolo Rotta & Raymond Klibansky (c. 1455–1536 / 1873–1962 / 1905–2005)

Critical Editors of De Docta Ignorantia (Paris 1514, Bari 1913, Leipzig 1932)

Lefèvre d’Étaples (Faber Stapulensis) edited the monumental 1514 Paris Opera; Rotta produced the 1913 Laterza text; Klibansky’s handwritten collations in his personal copy of Rotta (now at McGill Library) prepared the 1932 Heidelberg Academy edition (h I) and restored Rotta’s eye-skip omissions in I.13 and I.14.