Index of Persons

Prosopographical Register of Mathematicians, Patrons, Printers & Commentators

Biographical register of ancient, Islamic, medieval scholastic, Renaissance abbaco, Venetian patrician, and early modern figures connected to Pacioli’s 1494 Summa.

Alberti, Leon Battista (1404 – 1472)

Florentine Humanist, Architect, and Theorist

Hosted young Pacioli in Rome; cited on fol. 68v alongside Vitruvius and Piero della Francesca on architectural and pictorial symmetry.

Principal Works: De Re Aedificatoria, De Pictura, Ludi Rerum Mathematicarum

Archimedes of Syracuse (c. 287 – 212 BC)

Greek Geometer and Hydrostatician

Cited in Summa Part II, Dist. III (fol. 31r) for the 96-gon bounds 3 10/71 < pi < 3 1/7, Dist. V for sphere-and-cylinder mensuration, and Dist. VIII (fol. 70r, prob. 20) for hydrostatic volume measurement by displaced fluid.

Principal Works: Dimensio Circuli, De Sphaera et Cylindro, On Floating Bodies

Barbarigo, Agostino (1419 – 1501)

Doge of the Republic of Venice (1486 – 1501)

Doge of Venice under whose signory Paganino de’ Paganini and Fra Luca Pacioli were granted a ten-year printing privilege recorded in the colophon of Part II, fol. 76r.

Beldomandi, Prosdocimo de’ (c. 1380 – 1428)

Paduan Mathematician, Astronomer, and Music Theorist

Cited by Pacioli on Part I, fol. 1v among his foremost Italian predecessors in algorism and musical proportion.

Principal Works: Algorismus de integris (1410)

Boethius, Anicius Manlius Severinus (c. 480 – 524 AD)

Roman Philosopher and Codifier of the Quadrivium

Transmitted Nicomachus’s arithmetic and musical ratio nomenclature (multiplex, superparticularis, superpartiens) into the Latin scholastic curriculum expounded in Summa Part I, Dist. I & VI.

Principal Works: De Institutione Arithmetica, De Institutione Musica

Campanus of Novara (c. 1220 – 1296)

Medieval Commentator and Editor of the Latin Euclid

Papal chaplain whose Latin edition and scholia on Euclid’s Elements (printed at Venice by Erhard Ratdolt in 1482 and revised by Pacioli in 1509) supplied Pacioli’s proposition numbering and proportion commentary.

Principal Works: Euclidis Elementa cum commentariis Campani (1482)

Cardano, Gerolamo (1501 – 1576)

Milanese Physician and Algebraist; Author of the Ars Magna (1545)

Opened Chapter I of his Ars Magna (1545) by recalling Fra Luca Pacioli’s 1494 declaration that cubics were as impossible as squaring the circle before publishing the general cubic and quartic solutions of del Ferro, Tartaglia, and Ferrari.

Principal Works: Artis Magnae, sive de Regulis Algebraicis (1545), Liber de Ludo Aleae

Euclid of Alexandria (fl. c. 300 BC)

Greek Geometer; Author of the Elements

Revered throughout the Summa as the supreme deductive authority across arithmetic (Books VII–IX), proportion (Book V), irrational binomials and apotomes (Book X), plane geometry (Books I–VI), and the regular solids (Books XI–XIII).

Principal Works: Elements (Books I–XIII), On Divisions of Figures

Fermat, Pierre de (1607 – 1665)

French Mathematician and Co-Founder of Probability and Number Theory

Resolved both two-player and multi-player cases of Pacioli’s Problem of Points in 1654 via equiprobable completion sequences and discovered Fermat’s Little Theorem governing Mersenne primes (cf. Summa fol. 8r).

Principal Works: Correspondence with Blaise Pascal (1654)

Ferro, Scipione del (1465 – 1526)

Bolognese Mathematician; Discoverer of the Depressed Cubic Formula

Colleague of Pacioli at the University of Bologna (1501–1502) who, inspired directly by Pacioli’s 1494 challenge on fol. 150r, discovered the radical solution to x^3 + px = q around 1515.

Francesca, Piero della (c. 1412 – 1492)

Master Painter and Mathematician of Borgo Sansepolcro

Fellow townsman and mathematical mentor of Pacioli; praised on fol. 68v as ‘el monarca a li tempi nostri de la pictura’ and author of the Trattato d’abaco, De prospectiva pingendi, and Libellus de quinque corporibus regularibus.

Principal Works: Trattato d’abaco, De prospectiva pingendi, Libellus de quinque corporibus regularibus

Heron of Alexandria (fl. 1st century AD)

Alexandrian Geometer and Engineer

Discoverer of the semiperimeter area formula sqrt(s(s-a)(s-b)(s-c)) transmitted via Arabic intermediaries and Leonardo Pisano into Summa Part II, Dist. I, Cap. 8 (fol. 9v).

Principal Works: Metrica, Dioptra

Jordanus de Nemore (Jordanus Nemorarius) (fl. early 13th century)

Medieval Mathematician and Statician

Cited by Pacioli on Part I, fol. 1v and throughout Distinctio VI for speculative arithmetic and proportion theory (De elementis arismetice artis, De numeris datis).

Principal Works: De elementis arismetice artis, De numeris datis

Leonardo Pisano (Fibonacci) (c. 1170 – c. 1250)

Pisan Mathematician; Principal Medieval Source of the Summa

Explicitly acknowledged by Pacioli on Part I, fol. 1v as his foremost authority: wherever no other author is named in the Summa, the reader is to understand the doctrine derives from Leonardo Pisano’s Liber Abaci (1202/1228) and Practica Geometriae (1220).

Principal Works: Liber Abaci (1202/1228), Practica Geometriae (1220), Liber Quadratorum (1225)

Montefeltro, Federico da (1422 – 1482)

Duke of Urbino, Condottiero, and Builder of the Palazzo Ducale

Father of Guidobaldo da Montefeltro; patron of Piero della Francesca, Francesco di Giorgio Martini, and Luciano Laurana, celebrated by Pacioli on prelim. fol. 2v for the architectural proportion of the Ducal Palace of Urbino.

Montefeltro, Guidobaldo da (1472 – 1508)

Duke of Urbino; Dedicatee of Pacioli’s Summa (1494)

Son of Federico da Montefeltro and Battista Sforza; humanist prince of Urbino to whom Pacioli dedicated both the Italian and Latin dedicatory epistles of the 1494 Summa and fashioned wooden models of the regular and dependent polyhedra.

Pacioli, Fra Luca (c. 1447 – 1517)

Franciscan Mathematician of Borgo Sansepolcro; Author of the Summa (1494) and De Divina Proportione (1509)

Born at Borgo Sansepolcro, educated in the workshop of Piero della Francesca and hosted in Rome by Leon Battista Alberti; lectured on Euclid and practical mathematics across Perugia, Zara, Naples, Rome, Milan (alongside Leonardo da Vinci), Florence, Pisa, Bologna, and Venice, seeing his encyclopedic Summa through Paganino de’ Paganini’s press in November 1494.

Principal Works: Summa de arithmetica, geometria, proportioni et proportionalita (Venice, 1494), De Divina Proportione (Venice, 1509), Euclidis Opera (Latin edition, Venice, 1509), De Viribus Quantitatis (Bologna MS, c. 1508)

Paganini, Paganino de’ (fl. 1483 – 1538)

Master Printer from Brescia in Venice

Master typographer from Brescia operating in Venice who cut the marginal mathematical woodblocks and printed both Pacioli’s Summa (Nov. 10–20, 1494) and De Divina Proportione plus Euclidis Opera (1509).

Pascal, Blaise (1623 – 1662)

French Geometer and Co-Founder of Mathematical Probability

In his July–October 1654 correspondence with Pierre de Fermat, resolved the interrupted-game Problem of Points first printed in Pacioli’s 1494 Summa (fol. 197r–197v) via backward expectation and the arithmetic triangle.

Principal Works: Traité du triangle arithmétique (1654)

Pelacani da Parma, Biagio (Blasius of Parma) (c. 1347 – 1416)

Scholastic Natural Philosopher and Theorist of Proportions

Cited on Part I, fol. 1v and in Distinctio VI on kinematic and geometric proportions.

Principal Works: Quaestiones de proportionibus

Pompilio, Paolo (c. 1455 – 1491)

Roman Humanist Poet

Author of the Latin elegiac epigram in praise of Fra Luca Pacioli printed on prelim. fol. 1v of the 1494 Summa.

Principal Works: Epigramma ad Lucam Paciolum (Summa, prelim. fol. 1v)

Ptolemy, Claudius (c. 100 – c. 170 AD)

Greco-Egyptian Astronomer and Geometer

Cited in Summa Part II, Dist. III for chord tables and cyclic quadrilaterals from Book I of the Almagest.

Principal Works: Almagest (Syntaxis Mathematica)

Sacrobosco, Johannes de (John of Hollywood) (c. 1195 – c. 1256)

Scholastic Astronomer and Algorist at Paris

Acknowledged on Part I, fol. 1v as a standard authority on Hindu-Arabic algorism and spherical astronomy.

Principal Works: Algorismus Vulgaris, Tractatus de Sphaera

Sanudo, Marco (fl. 1490 – 1505)

Venetian Patrician, Mathematician, and Financial Patron of the 1494 Summa

Learned Venetian nobleman praised by Pacioli on prelim. fol. 1v as ‘astrologiae, geometriae, arithmeticaeque cultor exquisitissimus’, whose financial patronage underwrote the printing of the 1494 Summa in Venice.

Sommaripa, Giorgio (c. 1435 – 1504)

Veronese Patrician and Vernacular Poet

Author of the Italian caudate sonnet celebrating Pacioli’s universal synthesis of arithmetic, geometry, and Venetian double-entry ledger craft on prelim. fol. 1v.

Principal Works: Sonetto a Fra Luca Pacioli (Summa, prelim. fol. 1v)

Tartaglia, Niccolò Fontana (1499 – 1557)

Venetian Mathematician and Translator of Euclid and Archimedes

Rediscovered the cubic solution in Venice (1535), criticized Pacioli’s Problem of Points rule in his General Trattato (1556), and published the first Italian translation of Euclid (1543).

Principal Works: Quesiti et inventioni diverse (1546), General Trattato di numeri et misure (1556)

Vitruvius Pollio, Marcus (c. 80 – c. 15 BC)

Roman Architect and Engineer

Cited on Summa Part I, fol. 68v on architectural proportion and human symmetry.

Principal Works: De Architectura Libri Decem

al-Khwārizmī, Muḥammad ibn Mūsā (c. 780 – c. 850)

Founder of Hisāb al-jabr wa’l-muqābala in Baghdad

Established the six canonical positive-coefficient linear and quadratic equations and their geometric gnomon demonstrations inherited by Leonardo Pisano and expounded in Summa Part I, Dist. VIII (fols. 145r–146r).

Principal Works: Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa’l-muqābala