← pacioli / De Divina Proportione

Index of Persons¶

Prosopographical Register of Mathematicians, Architects, Patrons & Philosophers

Biographical register of ancient, medieval, and Renaissance authorities and contemporaries referenced in Fra Luca Pacioli’s De Divina Proportione (1509).

Alberti, Leon Battista (1404 – 1472)¶

Florentine Humanist, Architect, and Theorist

Hosted young Luca Pacioli for several months in his own home in Rome during the pontificate of Pope Paul II (Pietro Barbo); author of De Re Aedificatoria, De Pictura, and De Statua.

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

Occurrences: Arch. Cap. 2 (Notes), Arch. Cap. 8 (DE), Arch. Cap. 8 (EN), Arch. Cap. 8 (Notes), Arch. index, Comp. Cap. 3 (Notes), Winterberg Intro (DE), Winterberg Intro (EN)

Albumasar (Abū Maʿshar al-Balkhī) (787 – 886 AD)¶

Persian Astronomer and Astrologer in Baghdad

Author of the Introductorium in Astronomiam, cited by Pacioli in Compendio Chapter II among the foremost authorities in astronomy.

Principal Works: Introductorium in Astronomiam

Occurrences: Comp. Cap. 2 (EN), Comp. Cap. 2 (IT)

Alexander III of Macedon (Alexander the Great) (356 – 323 BC)¶

King of Macedon

Patron of the architect Dinocrates in the founding of Alexandria (Architectura Prohemio).

Alfonso X of Castile (‘El Sabio’) (1221 – 1284)¶

King of Castile and León, Patron of the Alfonsine Tables

Royal patron of the Alfonsine Tables (Tabulae Alfonsinae), cited by Pacioli in Compendio Chapter II among the great astronomical authorities.

Principal Works: Tabulae Alfonsinae

Alfraganus (Aḥmad ibn Muḥammad ibn Kathīr al-Farghānī) (fl. 9th century AD)¶

Abbasid Astronomer

Author of the Elements of Astronomy (Liber de Aggregationibus Scientiae Stellarum), cited by Pacioli in Compendio Chapter II.

Principal Works: Liber de Aggregationibus Scientiae Stellarum

Occurrences: Comp. Cap. 2 (EN)

Ambrogio Varese da Rosate (c. 1437 – 1522)¶

Ducal Physician and Court Astrologer to Ludovico Sforza

Professor at Pavia and chief physician and astrologer at the Sforza court; participant in the 1498 scientific duel in the Castello Sforzesco.

Occurrences: Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Andrea da Novara (fl. 1498)¶

Physician and Astronomer at the Sforza Court

Participant in the February 9, 1498 scientific disputation at the Castello Sforzesco in Milan.

Occurrences: Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Apelles of Kos (fl. 4th century BC)¶

Classical Greek Painter

Court painter to Alexander the Great; Pacioli declares in Chapters I and XXIII that Apelles, Myron, and Polykleitos must yield before Leonardo da Vinci’s Last Supper.

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT)

Apuleius of Madaura (c. 124 – after 170 AD)¶

Middle Platonic Philosopher and Rhetorician

Author of De Platone et eius Dogmate, cited with Chalcidius and Macrobius in Compendio Chapter LV on Platonic natural philosophy.

Principal Works: De Platone et eius Dogmate

Occurrences: Comp. Cap. 55 (EN), Comp. Cap. 55 (IT), Comp. Cap. 55 (Notes)

Archimedes of Syracuse (c. 287 – 212 BC)¶

Greek Geometer, Physicist, and Military Engineer

Celebrated by Pacioli both for his defense of Syracuse against Marcus Claudius Marcellus using geometrical war machines and for his measurement of the circle (3 10/71 < π < 3 1/7), sphere, and cylinder, as well as the semi-regular (Archimedean) polyhedra.

Principal Works: Dimensio Circuli, De Sphaera et Cylindro

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 2 (Notes), Comp. Cap. 62 (DE), Comp. Cap. 62 (EN), Comp. Cap. 62 (IT), Comp. Cap. 62 (Notes), Comp. Cap. 64 (Notes), Comp. Cap. 66 (DE), Comp. Cap. 66 (EN), Comp. Cap. 66 (IT)

Aristotle of Stagira (384 – 322 BC)¶

Greek Philosopher (‘El Philosopho’ / ‘Il Maestro di color che sanno’)

Cited throughout De Divina Proportione on the primacy of mathematical certainty (‘in primo gradu certitudinis’), sense perception (‘nihil est in intellectu quin prius fuerit in sensu’), philosophical wonder (‘propter admirari’), and the rejection of the void (De Caelo).

Principal Works: Analytica Posteriora, Physica, De Caelo et Mundo, Metaphysica, De Anima, Meteorologica, Ethica Nicomachea

Occurrences: Arch. Cap. 3 (EN), Arch. Cap. 9 (EN), Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (Notes), Comp. Cap. 2 (EN), Comp. Cap. 2 (Notes), Comp. Cap. 3 (DE), Comp. Cap. 3 (EN), Comp. Cap. 3 (IT), Comp. Cap. 5 (Notes), Comp. Cap. 54 (DE)

Augustine of Hippo, St. (Aurelius Augustinus) (354 – 430 AD)¶

Bishop of Hippo and Doctor of the Church

Author of De Civitate Dei, cited by Pacioli in Compendio Chapter II on the supreme Artisan who created all things in number, weight, and measure.

Principal Works: De Civitate Dei, De Genesi ad Litteram

Occurrences: Comp. Cap. 2 (EN)

Augustus, Caesar (Octavian) (63 BC – 14 AD)¶

First Roman Emperor

Cited in Compendio Chapter LXIX alongside the Temple of Universal Peace in Rome as a classical parallel to Ludovico Sforza’s patronage of Santa Maria delle Grazie.

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 69 (Notes)

Averroes (Ibn Rushd) (1126 – 1198)¶

Andalusian Philosopher and Commentator on Aristotle

Cited with Aristotle in Compendio Chapter I (from Metaphysics II comm. 16) for the maxim that the mathematical sciences stand in the first degree of certainty (‘in primo gradu certitudinis’).

Principal Works: Commentaria Magna in Aristotelem

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes), Comp. Cap. 2 (IT)

Avicenna (Ibn Sīnā) (980 – 1037)¶

Persian Physician, Astronomer, and Philosopher

Author of the Canon Medicinae; cited in Compendio Chapter I both among the authorities expounded by Ambrogio da Rosate and alongside Galen and Hippocrates on the seat of vital spirit.

Principal Works: Canon Medicinae

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Bartolus of Sassoferrato (Bartolo da Sassoferrato) (1313 – 1357)¶

Medieval Italian Jurist and Commentator on Roman Law

Cited by Pacioli in Compendio Chapter II for his geometric treatise De Fluminibus seu Tyberiadis (‘la Teberina’), which used Euclidean compass-and-straightedge constructions to divide alluvial river deposits.

Principal Works: Tractatus de Fluminibus seu Tyberiadis

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 2 (Notes)

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

Paduan Mathematician, Astronomer, and Music Theorist

Professor of Astrology and Mathematics at the University of Padua, cited by Pacioli (‘Prodocimo’) in Compendio Chapter II alongside Ptolemy, Albumasar, and Bianchini.

Principal Works: Algorismus de integris, Canones de motibus corporum supercoelestium

Occurrences: Comp. Cap. 2 (EN)

Bianchini, Giovanni (c. 1410 – after 1469)¶

Italian Mathematician and Astronomer at the Court of Ferrara

Professor at the University of Ferrara and author of astronomical and trigonometric tables (Tabulae astronomicae), cited by Pacioli in Compendio Chapter II.

Principal Works: Tabulae astronomicae

Occurrences: Comp. Cap. 2 (EN)

Boethius, Anicius Manlius Severinus (c. 477 – 524 AD)¶

Roman Philosopher and Theorist of the Quadrivium

Author of De Institutione Arithmetica and De Institutione Musica; cited by Pacioli on the fourfold classification of the mathematical disciplines (Quadrivium) and on equality as the principle of all proportions (Musica II.15).

Principal Works: De Institutione Arithmetica, De Institutione Musica

Occurrences: Comp. Cap. 3 (DE), Comp. Cap. 3 (EN), Comp. Cap. 3 (IT), Comp. Cap. 3 (Notes), Comp. Cap. 7 (EN), Comp. Cap. 7 (Notes), Plates: Architectural (DE), Plates: Architectural (EN)

Bramante, Donato (1444 – 1514)¶

Renaissance Architect

Active alongside Leonardo da Vinci and Luca Pacioli at the Sforza court in Milan; designed the tribune of Santa Maria delle Grazie and the sacristy of Santa Maria presso San Satiro, whose perspective domes Pacioli relates to the 72-base body in Chapter LIV.

Occurrences: Comp. Cap. 54 (EN), Comp. Cap. 54 (Notes), Comp. Cap. 69 (Notes)

Brocheneck (fl. mid-19th century)¶

German Writer on Human Proportions

Author of Die männliche und weibliche Normalgestalt, cited by Winterberg in the Einleitung (fn. 4) among the nineteenth-century followers of the Golden Section canon.

Principal Works: Die männliche und weibliche Normalgestalt

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Busti, Fra Francesco, O.F.M. (fl. 1498)¶

Franciscan Theologian and Regent of San Francesco Grande in Milan

Regent Master of the Franciscan Studium in Milan at the time of the February 9, 1498 disputation.

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Caesar, Gaius Julius (100 – 44 BC)¶

Roman General, Statesman, and Author

Cited in Compendio Chapter II for his geometric timber bridge across the Rhine (Pacioli writes Rhone) described in Commentarii de Bello Gallico IV.17.

Principal Works: Commentarii de Bello Gallico

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN)

Callimachus (Catatechnos) (fl. late 5th century BC)¶

Athenian Sculptor and Architect

Recounted in Architectura Chapter VII (from Vitruvius IV.1.9–10) as the inventor of the Corinthian capital after seeing acanthus leaves growing around a basket on the grave of a maiden of Corinth.

Occurrences: Arch. Cap. 7 (DE), Arch. Cap. 7 (EN), Arch. Cap. 7 (IT), Arch. Cap. 7 (Notes), Arch. index

Campanus of Novara (Giovanni Campano) (c. 1220 – 1296)¶

Medieval Mathematician, Astronomer, and Commentator on Euclid

Chaplain to Pope Urban IV and author of the standard medieval Latin redaction and commentary on Euclid’s Fifteen Books (printed by Ratdolt in 1482 and revised by Pacioli in 1509), praised by Pacioli for his remarks on IX.16 and XIV.10.

Principal Works: Elementa Euclidis cum Commentariis Campani

Canozi, Giovan Marco (da Lendinara) (d. 1525)¶

Italian Architect and Perspective Master

Son of Lorenzo Canozi da Lendinara; praised by Pacioli in the Dedication of the Tractato de l’Architectura among the disciples with whom he discussed Vitruvian architecture.

Occurrences: Arch. Prohemio (EN), Arch. Prohemio (Notes)

Canozi, Lorenzo (Lorenzo da Lendinara) (1425 – 1477)¶

Italian Master of Perspective, Intarsia, and Architecture

Intarsia master in Padua and Modena and close friend of Piero della Francesca; praised by Pacioli in the Dedication of the Tractato de l’Architectura.

Occurrences: Arch. Prohemio (Notes)

Capella, Marcantonio (M. Ant. Capella) (fl. 1509)¶

Franciscan Scholar and Editorial Reviewer of the 1509 Venice Edition

Credited on the 1509 title page (‘M. Ant. Capella eruditiss. recensente’) as editorial reviser of De Divina Proportione.

Caro, Annibale (1507 – 1566)¶

Italian Humanist, Poet, and Translator of the Aeneid

Cited by Winterberg in the Einleitung for coining the famous satirical epithet ‘Ceneraccio’ (‘bundle of ash-lye’) to characterize Pacioli’s hybrid Latin-Tuscan-Lombard prose style.

Principal Works: Apologia degli Accademici di Banchi di Roma (1558)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Carus, Carl Gustav (1789 – 1869)¶

German Physician, Natural Philosopher, Anatomist, and Painter

Author of Die Proportionslehre der menschlichen Gestalt (1854) and Symbolik der menschlichen Gestalt (1853), proposing the vertebral column length (divided into thirds, the ‘module’) as the organic unit of bodily proportion; cited by Winterberg in the Einleitung.

Principal Works: Die Proportionslehre der menschlichen Gestalt (1854)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Catani, Catano (da Borgo Sansepolcro) (fl. late 15th century)¶

Merchant of Borgo Sansepolcro in Florence

Compatriot of Luca Pacioli with whom Pacioli visited the Villa del Tovaglia outside Florence (Architectura Cap. VIII).

Occurrences: Arch. Cap. 8 (DE), Arch. Cap. 8 (EN)

Chalcidius (Calcidio) (fl. 4th century AD)¶

Late Antique Translator and Commentator on Plato’s Timaeus

Cited by Pacioli in Compendio Chapter LV alongside Apuleius and Macrobius as a principal Latin authority on Plato’s Timaeus and the five cosmic solids.

Principal Works: Timaeus Platonis translatus et Commentarius

Occurrences: Comp. Cap. 55 (EN), Comp. Cap. 55 (IT)

Cicero, Marcus Tullius (106 – 43 BC)¶

Roman Orator, Statesman, and Philosopher

Author of De Natura Deorum, cited by Pacioli in Compendio Chapter LVII for the anecdote of Hiero and Simonides.

Principal Works: De Natura Deorum

Occurrences: Comp. Cap. 57 (DE), Comp. Cap. 57 (EN), Comp. Cap. 57 (IT), Comp. Cap. 57 (Notes), Comp. Cap. 69 (DE), Comp. Cap. 69 (EN), Comp. Cap. 69 (IT)

Cusano, Nicolò (Milanese Physician) (fl. 1498)¶

Milanese Physician and Astronomer

Senior physician and natural philosopher at the court of Ludovico Sforza admired by Rosate, Marliani, and Pirovano at the 1498 disputation.

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Dinocrates of Rhodes (fl. late 4th century BC)¶

Greek Architect and Urban Planner to Alexander the Great

Recounted in the Dedication of the Tractato de l’Architectura (from Vitruvius Book II Preface) for presenting himself before Alexander the Great and designing the city of Alexandria in Egypt.

Dionysius (Historian and Geometer) (fl. 1st century BC)¶

Greek Historian and Geometer

Cited in Compendio Chapter II (Dionysius of Halicarnassus, Roman Antiquities) and Chapter LVI (Dionysius the Geometer / Dionysodorus on the definition of the sphere).

Principal Works: Antiquitates Romanae

Occurrences: Arch. Cap. 1 (DE), Arch. Cap. 1 (EN), Arch. Cap. 1 (IT), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 56 (DE), Comp. Cap. 56 (EN), Comp. Cap. 56 (IT), Comp. Cap. 56 (Notes)

Duns Scotus, John, O.F.M. (‘Il Dottor Sottile’) (c. 1266 – 1308)¶

Franciscan Scholastic Philosopher and Theologian

Praised by Pacioli in Compendio Chapter II for attaining the loftiest speculations of theology through his mastery of Euclid’s Elements, particularly in Book II of his Commentary on the Sentences on the definitive location of angels and indivisibles.

Principal Works: Ordinatio / Quaestiones in Quattuor Libros Sententiarum

Eitelberger von Edelberg, Rudolf (1817 – 1885)¶

Austrian Art Historian and Founder of Quellenschriften für Kunstgeschichte

First Professor of Art History at the University of Vienna and founding Director of the k. k. Österreichisches Museum für Kunst und Industrie; founded the Quellenschriften für Kunstgeschichte und Kunsttechnik des Mittelalters und der Neuzeit series and personally commissioned Constantin Winterberg’s edition of Pacioli’s Divina Proportione.

Principal Works: Quellenschriften für Kunstgeschichte und Kunsttechnik des Mittelalters und der Neuzeit

Occurrences: DE DIVINA PROPORTIONE, Winterberg Intro (DE), Winterberg Intro (EN)

Este, Cardinal Ippolito I d’ (1479 – 1520)¶

Cardinal-Deacon of Santa Lucia in Selci and Archbishop of Milan

Brother-in-law of Ludovico Sforza (brother of Beatrice d’Este); witnessed the presentation of De Divina Proportione in Milan, attended the 1498 Franciscan General Chapter, and participated in the Vitruvian architectural discussion on Milan Cathedral.

Occurrences: Comp. Cap. 69 (Notes)

Euclid of Alexandria (identified by Pacioli as Euclid of Megara) (fl. c. 300 BC)¶

Greek Geometer and Author of the Elements

Revered by Pacioli as ‘nostra guida’ and ‘archimandrita’ of the mathematical disciplines; Books II, V, VI, X–XIII (and Books XIV–XV of Hypsicles/Campanus) form the demonstrative backbone of De Divina Proportione.

Principal Works: Elementa (Libri XV, ed. Campanus / Pacioli 1509)

Occurrences: Arch. Cap. 1 (DE), Arch. Cap. 1 (EN), Arch. Cap. 1 (IT), Arch. Cap. 3 (DE), Arch. Cap. 3 (EN), Arch. Cap. 3 (IT), Arch. Cap. 10 (DE), Arch. Cap. 10 (EN), Arch. Cap. 10 (IT), Arch. Cap. 11 (DE), Arch. Cap. 11 (EN), Arch. Cap. 11 (IT), Arch. Cap. 11 (Notes), Arch. Cap. 17 (Notes), Arch. Cap. 19 (DE), Arch. Cap. 19 (EN), Arch. Cap. 19 (IT), Arch. Prohemio (DE), Arch. Prohemio (IT), Arch. Prohemio (Notes), Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 2 (Notes), …and 67 more

Euclid of Megara (c. 435 – c. 365 BC)¶

Greek Socratic Philosopher and Founder of the Megarian School

Disciple of Socrates from Megara whom medieval and Renaissance writers—including Campanus and Luca Pacioli (‘Euclide Megarense’)—habitually conflated with the Alexandrian geometer Euclid; glossed by Winterberg in Compendio Chapter II, fn. 2.

Occurrences: Comp. Cap. 2 (Notes), Comp. Cap. 67 (EN), Comp. Cap. 71 (EN)

Ferrante I (Ferdinand I of Naples) (1423 – 1494)¶

Aragonese King of Naples (r. 1458–1494)

Royal patron under whom Luca Pacioli taught mathematics and Euclid at the University of Naples; glossed by Winterberg in the Dedication of the Tractato de l’Architectura (fn. 2).

Occurrences: Arch. Cap. 8 (Notes), Arch. Prohemio (Notes)

Fibonacci (Leonardo Pisano) (c. 1170 – c. 1240/50)¶

Italian Mathematician

Author of the Liber Abaci (1202) and Practica Geometriae (1220), primary medieval sources for Pacioli’s Summa de Arithmetica and abacus algebra.

Principal Works: Liber Abaci, Practica Geometriae

Francis of Assisi, St. (1181/1182 – 1226)¶

Founder of the Order of Friars Minor (Seraphic Order)

Founder of Pacioli’s Franciscan (‘Minorite’ / ‘Seraphic’) Order.

Occurrences: Arch. Prohemio (IT), Comp. Cap. 1 (Notes)

Fromme, Carl (k. k. Hofbuchdruckerei Carl Fromme) (1828 – 1884 (Firm active 1889))¶

Imperial-Royal Court Printer in Vienna

Viennese court printing house (k. k. Hofbuchdruckerei Carl Fromme) that printed Constantin Winterberg’s 1889 edition of Pacioli’s Divina Proportione.

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Frontinus, Sextus Julius (c. 40 – 103 AD)¶

Roman Senator, Engineer, and Military Writer

Author of Strategemata and De Aquaeductu, cited alongside Vegetius in Compendio Chapter II.

Principal Works: Strategemata, De Aquaeductu Urbis Romae

Occurrences: Arch. Prohemio (DE), Arch. Prohemio (EN), Arch. Prohemio (IT), Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 2 (Notes)

Gaetani, Daniele (Danielis Caietanus Cremonensis) (c. 1465 – 1528)¶

Humanist of Cremona and Author of the 1509 Prefatory Epistle and Epigram

Cremonese philologist and lecturer in Padua and Venice; composed the Latin title-page epigram (‘Natura omnipotens produxit corpora quinque’) and the laudatory epistle to Andrea Mocenigo styling Pacioli ‘a second Nicomachus of our age’.

Principal Works: Epigramma in De Divina Proportione (1509, A1r), Epistolium ad Andream Mocenicum (1509, A2v)

Galen of Pergamon (129 – c. 216 AD)¶

Greek Physician and Medical Philosopher

Cited in Compendio Chapter I alongside Avicenna and Hippocrates to illustrate the contrasting opinions of physicians versus the demonstrative certainty of mathematicians.

Principal Works: Opera Medica

Occurrences: Comp. Cap. 1 (EN), Comp. Cap. 1 (Notes)

Geber (Jābir ibn Aflaḥ of Seville) (c. 1100 – c. 1150)¶

Andalusian Mathematician and Astronomer

Author of the Flores Almagesti (Correction of the Almagest), translated into Latin by Gerard of Cremona and cited by Pacioli in Compendio Chapter II.

Principal Works: Flores Almagesti (De Astronomia Libri IX)

Occurrences: Comp. Cap. 2 (EN)

Giacomo Andrea da Ferrara (d. 1500)¶

Architect, Military Engineer, and Commentator on Vitruvius

Close friend of Leonardo da Vinci (‘suo quarto fratello’) and Luca Pacioli at the Sforza court in Milan; celebrated as the most accurate follower of the works of Vitruvius.

Occurrences: Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Giocondo, Fra Giovanni (da Verona) (c. 1433 – 1515)¶

Franciscan Friar, Architect, Antiquarian, and Classical Scholar

Editor of the first illustrated printed edition of Vitruvius (M. Vitruvii per Iocundum solito castigatior factus, Venice, 1511), lectured on Vitruvius in Paris, and succeeded Bramante as co-architect of St. Peter’s; cited by Winterberg in the Einleitung (fn. 8).

Principal Works: M. Vitruvii per Iocundum solito castigatior factus (Venice, 1511)

Occurrences: Arch. Cap. 14 (Notes)

Gometius Hispanus (Frei Gomes de Lisboa), O.F.M. (c. 1440 – 1513)¶

Franciscan Scholastic Theologian and Vicar General

Portuguese-born Franciscan Regent Master at Pavia and Vicar General of the Conventual Franciscans; participant in the 1498 Milan disputation.

Principal Works: Quaestio perutilis de cuiuscumque scientiae subiecto

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Graeser, Carl (1849 – 1899)¶

Viennese Publisher (Verlagsbuchhändler)

Publisher of the Neue Folge of Quellenschriften für Kunstgeschichte in Vienna (Verlag von Carl Graeser, 1889).

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Harless, Emil (1820 – 1862)¶

German Physiologist and Professor of Plastic Anatomy in Munich

Author of Lehrbuch der plastischen Anatomie (Stuttgart, 1856–1858), cited by Winterberg in the Einleitung (fn. 5) for empirically refuting Zeising’s Golden Section canon through anatomical measurement of the living body.

Principal Works: Lehrbuch der plastischen Anatomie (1856–1858)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Hiero I of Syracuse (d. 467 BC)¶

Tyrant of Syracuse

Cited in Compendio Chapter LVII (from Cicero’s De Natura Deorum I.60) for asking the poet Simonides to define the nature of God.

Occurrences: Comp. Cap. 57 (DE), Comp. Cap. 57 (EN), Comp. Cap. 57 (IT), Comp. Cap. 57 (Notes)

Hippocrates of Kos (c. 460 – c. 370 BC)¶

Greek Physician

Cited in Compendio Chapter I alongside Galen and Avicenna.

Principal Works: Corpus Hippocraticum

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT)

Hypsicles of Alexandria (c. 190 – c. 120 BC)¶

Greek Mathematician and Astronomer

Author of Book XIV of the Euclidean corpus on the comparison of the regular icosahedron and dodecahedron inscribed in the same sphere.

Principal Works: Elementa Liber XIV

Occurrences: Comp. Cap. 4 (Notes), Comp. Cap. 19 (Notes), Comp. Cap. 31 (EN), Comp. Cap. 32 (Notes), Comp. Cap. 46 (Notes), Winterberg Anmerkungen (EN)

Ilg, Albert (1847 – 1896)¶

Austrian Art Historian and Editor of Quellenschriften (Neue Folge)

Director at the Kunsthistorisches Museum in Vienna who succeeded Rudolf von Eitelberger as general editor of the Neue Folge of Quellenschriften für Kunstgeschichte und Kunsttechnik, in which Winterberg’s 1889 edition of Pacioli appeared as Band II.

Principal Works: Quellenschriften für Kunstgeschichte und Kunsttechnik (Neue Folge)

Occurrences: DE DIVINA PROPORTIONE, Winterberg Intro (DE), Winterberg Intro (EN)

Ion (Mythical Founder of Ionia) (Mythological)¶

Athenian Leader of the Ionian Colonists

Son of Xuthus and Creusa; cited in Architectura Chapter VII (from Vitruvius IV.1) as the founder of Ionia and eponym of the Ionic order.

Isidore of Seville, St. (c. 560 – 636 AD)¶

Archbishop of Seville and Encyclopedist

Author of the Etymologiae (Book III, De Mathematica); cited by Pacioli in Compendio Chapter III alongside Plato, Aristotle, and Boethius on the fourfold division of the mathematical sciences.

Principal Works: Etymologiae (Origines)

Occurrences: Comp. Cap. 3 (EN), Comp. Cap. 34 (Notes)

Jesus Christ (c. 4 BC – c. 30/33 AD)¶

Savior in Christian Theology

Invoked by Pacioli in Chapters I, V, and XXIII in connection with the sacred number thirteen (Christ and the twelve apostles in Leonardo da Vinci’s Last Supper at Santa Maria delle Grazie) and the theological analogies of the Divine Proportion.

Occurrences: Arch. Cap. 8 (EN)

Julius II, Pope (Giuliano della Rovere) (1443 – 1513)¶

Pope (1503–1513) and Formerly Cardinal of San Pietro in Vincoli

Uncle of Cardinal Galeotto Franciotti della Rovere and reigning pontiff named in the 1509 colophon (‘Pontificatus Iulii II. Anno VI’).

Occurrences: Arch. Cap. 11 (DE), Arch. Cap. 20 (DE)

Kepler, Johannes (1571 – 1630)¶

German Astronomer and Geometer

Author of Mysterium Cosmographicum (1596) and Harmonices Mundi (1619), who gave the name Stella Octangula to the elevated octahedron (Octahedron elevatum) first depicted by Leonardo da Vinci and Pacioli in Plates XIX–XX.

Principal Works: Harmonices Mundi (1619)

Occurrences: Comp. Cap. 50 (Notes), Comp. Cap. 52 (Notes)

Leonardo da Vinci (1452 – 1519)¶

Florentine Painter, Sculptor, Architect, and Engineer

Compatriot and close collaborator of Luca Pacioli in Milan and Florence; drew the sixty perspective polyhedra templates (‘schemata Vincii nostri Leonardi manibus scalpta’) for De Divina Proportione, sculpted the Sforza Equestrian Monument, and painted The Last Supper at Santa Maria delle Grazie.

Principal Works: Polyhedra Plates (Tabulae I–LIX) in De Divina Proportione (1498/1509), Libro di Pittura e Movimenti Humani, De Moto Locale, delle Percussioni e Pesi, Il Cenacolo (Santa Maria delle Grazie, Milan), Sforza Equestrian Colossus

Occurrences: Arch. Cap. 6 (DE), Arch. Cap. 6 (EN), Arch. Cap. 6 (IT), Arch. Cap. 6 (Notes), Arch. Cap. 9 (Notes), Arch. Cap. 10 (DE), Arch. Cap. 10 (IT), Arch. Cap. 18 (Notes), Arch. Cap. 20 (DE), Arch. Cap. 20 (EN), Arch. Cap. 20 (IT), Arch. Cap. 20 (Notes), Arch. index, Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes), Comp. Cap. 3 (DE), Comp. Cap. 3 (EN), Comp. Cap. 3 (IT), Comp. Cap. 3 (Notes), Comp. Cap. 23 (DE), Comp. Cap. 23 (EN), Comp. Cap. 23 (IT), …and 14 more

Libri, Guillaume (Guglielmo Libri Carucci dalla Sommaja) (1803 – 1869)¶

Franco-Italian Mathematician and Historian of Science

Author of Histoire des sciences mathématiques en Italie (4 vols., Paris, 1838–1841), cited by Winterberg in the Einleitung (fn. 1 & 8) on the printing history of Pacioli’s Summa and Divina Proportione and on Piero della Francesca’s manuscripts.

Principal Works: Histoire des sciences mathématiques en Italie (Vol. III, 1840)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Livy (Titus Livius) (59 BC – 17 AD)¶

Roman Historian

Author of Ab Urbe Condita, cited in Compendio Chapter II on Roman military engineering and siegecraft.

Principal Works: Ab Urbe Condita

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN)

Loredan, Leonardo, Doge of Venice (1436 – 1521)¶

Doge of the Republic of Venice (1501–1521)

Named in the 1509 colophon of De Divina Proportione (‘Leonardo Lauretano Ve. Rem. Pu. Gubernante’).

Ludwig, Heinrich (1829 – 1897)¶

German Painter and Leonardo da Vinci Scholar in Rome

Edited and translated Leonardo da Vinci’s Trattato della Pittura (Das Buch von der Malerei, Quellenschriften Band XV–XVIII, 1882) and inspired Rudolf von Eitelberger and Constantin Winterberg in Rome to undertake the critical edition of Pacioli’s Divina Proportione.

Principal Works: Lionardo da Vinci: Das Buch von der Malerei (Wien, 1882)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Macrobius, Ambrosius Theodosius (fl. c. 400 AD)¶

Late Roman Neoplatonic Writer

Author of Commentarii in Somnium Scipionis, cited with Chalcidius and Apuleius in Compendio Chapter LV on Platonic cosmology and numerical harmony.

Principal Works: Commentarii in Somnium Scipionis

Occurrences: Comp. Cap. 55 (DE), Comp. Cap. 55 (EN), Comp. Cap. 55 (IT), Comp. Cap. 55 (Notes)

Malatesta, Sigismondo Pandolfo (1417 – 1468)¶

Lord of Rimini and Condottiere

Patron of Leon Battista Alberti (Tempio Malatestiano) and Piero della Francesca, and dedicatee of Roberto Valturio’s military treatise De Re Militari cited by Pacioli in Compendio Chapter II.

Occurrences: Comp. Cap. 2 (Notes)

Marcellus, Marcus Claudius (c. 268 – 208 BC)¶

Roman Consul and General

Commander of the Roman siege of Syracuse (214–212 BC), whose assaults were long repelled by the geometrical engines of Archimedes (Compendio Cap. II).

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT)

Marinus of Tyre (fl. c. 100 – 130 AD)¶

Greek Geographer and Cartographer

Predecessor of Claudius Ptolemy in mathematical geography and map projections; cited by Pacioli alongside Ptolemy and Strabo among the masters of cosmography.

Occurrences: Arch. Prohemio (EN)

Marliani, Aloisio (Luigi Marliano) (c. 1460 – 1521)¶

Milanese Physician, Humanist, and Later Bishop of Tuy

Ducal physician to Ludovico Sforza (and later to Emperor Maximilian I and Charles V); participant in the 1498 Milan disputation.

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Mellini, Mario (Mario Melini) (fl. late 15th century)¶

Roman Patrician and Antiquarian

Roman baron in whose home on Monte Mario Pacioli read ancient Roman annals recording Phidias’s placement of an icosahedron in the Temple of Ceres (Architectura Cap. XVIII).

Occurrences: Arch. Cap. 18 (DE), Arch. Cap. 18 (Notes)

Melozzo da Forlì (Melozzo degli Ambrosi) (1438 – 1494)¶

Renaissance Painter and Master of Foreshortening and Perspective

Friend of Luca Pacioli; present at Count Girolamo Riario’s Roman palace when Pacioli challenged a boastful stonemason to carve the regular polyhedra (Compendio Cap. LVII).

Occurrences: Comp. Cap. 57 (DE), Comp. Cap. 57 (EN), Comp. Cap. 57 (IT), Comp. Cap. 57 (Notes), Comp. index

Mocenigo, Andrea (1473 – 1542)¶

Venetian Patrician, Philosopher, and Historian

Doctor of philosophy from the University of Padua, Venetian senator, and dedicatee of Daniele Gaetani’s 1509 prefatory epistle in De Divina Proportione.

Principal Works: Bellum Cameracense (1525)

Mocenigo, Leonardo (fl. 1509)¶

Venetian Patrician and Senator

Father of Andrea Mocenigo and son of Doge Giovanni Mocenigo, mentioned in Gaetani’s 1509 epistle.

Montefeltro, Federico da, Duke of Urbino (1422 – 1482)¶

Duke of Urbino, Condottiero, and Humanist Patron

Builder of the Palazzo Ducale in Urbino, around whose base he commissioned the carved stone frieze of ancient and modern military machines and mathematical instruments praised by Pacioli in Chapter II.

Occurrences: Comp. Cap. 2 (EN), Comp. Cap. 2 (Notes)

Montefeltro, Guidobaldo da, Duke of Urbino (1472 – 1508)¶

Duke of Urbino and Patron of Luca Pacioli

Son of Federico da Montefeltro and kinsman of Ludovico Sforza; dedicatee of Pacioli’s Summa de Arithmetica, Geometria, Proportioni et Proportionalita (1494) and recipient of a complete set of wooden polyhedra models.

Occurrences: Arch. Prohemio (DE), Arch. Prohemio (EN), Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 33 (EN), Winterberg Intro (DE), Winterberg Intro (EN)

Montucla, Jean-Étienne (1725 – 1799)¶

French Mathematician and Historian of Mathematics

Author of the monumental Histoire des mathématiques (1758; 2nd ed. 1799–1802), cited by Winterberg in the Einleitung (fn. 2) on Pacioli’s biography and role as commercial tutor in Venice.

Principal Works: Histoire des mathématiques

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Myron of Eleutherae (fl. mid-5th century BC)¶

Classical Greek Bronze Sculptor

Classical master named alongside Apelles and Polykleitos in Chapters I and XXIII in praise of Leonardo da Vinci.

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT)

Nero Claudius Caesar (37 – 68 AD)¶

Roman Emperor

Cited in Architectura Chapter XIX for the ancient bronze-inlaid monumental inscriptions surviving in the ruins of the Palace of Nero (Domus Aurea) and on the Capitol in Rome.

Occurrences: Arch. Cap. 19 (DE)

Nicomachus of Gerasa (c. 60 – c. 120 AD)¶

Neopythagorean Mathematician

Author of Introductio Arithmetica; Daniele Gaetani’s 1509 prefatory epistle hails Luca Pacioli as ‘alterum nostrae aetatis Nicomachum’ (‘a second Nicomachus of our age’).

Principal Works: Introductio Arithmetica

Pacioli, Fra Luca, O.F.M. (c. 1447 – 1517)¶

Franciscan Mathematician and Professor of Sacred Theology

Born in Borgo Sansepolcro; disciple of Piero della Francesca, collaborator of Leonardo da Vinci at the Sforza court in Milan (1496–1499), and author of the Summa de Arithmetica (1494), De Divina Proportione (1509), and the 1509 Latin edition of Euclid’s Elements.

Principal Works: Summa de Arithmetica, Geometria, Proportioni et Proportionalita (1494), De Divina Proportione (1498 MS / 1509 Venice print), Tractato de l’Architectura (1509), Libellus in tres partiales tractatus divisus (1509), Euclidis Megarensis Opera (1509), De Viribus Quantitatis (MS, c. 1500–1508)

Paganini, Paganino de’ (de Brixia) (c. 1450 – 1538)¶

Venetian Master Printer from Brescia

Printer of Pacioli’s Summa de Arithmetica (1494), Euclidis Opera (1509), and De Divina Proportione (June 1, 1509) in Venice under a fifteen-year Dogal privilege.

Occurrences: Arch. Cap. 20 (EN), Arch. Prohemio (Notes), Comp. index, DE DIVINA PROPORTIONE, Winterberg Intro (DE), Winterberg Intro (EN)

Palamides, Messer Ciriaco (da Borgo Sansepolcro) (fl. 1500)¶

Knight of the Golden Spur from Borgo Sansepolcro

Fellow townsman of Pacioli honored by Duke Guidobaldo da Montefeltro of Urbino, praised in the Dedication of the Tractato de l’Architectura.

Occurrences: Arch. Prohemio (DE)

Pappus of Alexandria (c. 290 – c. 350 AD)¶

Late Antique Greek Geometer

Author of the Synagoge (Mathematical Collection), Book V of which preserves the classical account of the thirteen Archimedean semi-regular solids.

Principal Works: Synagoge (Mathematical Collection)

Occurrences: Comp. Cap. 46 (Notes), Winterberg Anmerkungen (EN)

Parrhasius of Ephesus (fl. late 5th century BC)¶

Classical Greek Painter

Celebrated in Compendio Chapter III for painting an illusionistic curtain that deceived Zeuxis himself, proving that perspective painting deceives both irrational and rational animals.

Occurrences: Comp. Cap. 3 (EN), Comp. Cap. 3 (IT)

Paul II, Pope (Pietro Barbo) (1417 – 1471)¶

Venetian Pope (1464–1471)

Reigning pontiff when Luca Pacioli resided for several months in Rome in the household of Leon Battista Alberti (Architectura Cap. VIII).

Pepi, Francesco (1450 – 1513)¶

Florentine Ambassador to Milan and Statesman

Florentine orator and diplomat who served alongside Francesco Soderini in Milan and witnessed Pacioli’s presentation of De Divina Proportione to Ludovico Sforza.

Phidias of Athens (c. 480 – c. 430 BC)¶

Classical Greek Sculptor

Cited by Pacioli both for the colossal Horse Tamers on the Quirinal Hill (Monte Cavallo) in Rome and for placing a bronze icosahedron (figure of water) in the Temple of Ceres near Rome (Architectura Cap. XVIII).

Occurrences: Arch. Cap. 18 (DE), Arch. Cap. 18 (EN), Arch. Cap. 18 (IT), Arch. Prohemio (DE), Arch. Prohemio (EN), Arch. index, Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Winterberg Intro (DE), Winterberg Intro (EN)

Piero della Francesca (Maestro Pietro de li Franceschi) (c. 1415 – 1492)¶

Painter and Mathematician of Borgo Sansepolcro

Pacioli’s fellow townsman and teacher in Borgo Sansepolcro (‘monarca a li tempi nostri de la pictura e architectura’); author of De Prospectiva Pingendi and the Latin Libellus de Quinque Corporibus Regularibus translated into the vernacular in Part III.

Principal Works: Libellus de Quinque Corporibus Regularibus, De Prospectiva Pingendi, Trattato d’Abaco

Occurrences: Arch. Cap. 2 (Notes), Arch. Cap. 11 (DE), Arch. Cap. 11 (IT), Arch. Cap. 19 (EN), Arch. Cap. 19 (Notes), Arch. Prohemio (IT), Arch. Prohemio (Notes), Arch. index, Comp. Cap. 3 (Notes), Comp. Cap. 22 (Notes), Comp. Cap. 35 (Notes), Comp. Cap. 46 (Notes), Comp. Cap. 54 (Notes), Comp. Cap. 57 (Notes), DE DIVINA PROPORTIONE, Winterberg Intro (DE), Winterberg Intro (EN), Winterberg Anmerkungen (DE), Winterberg Anmerkungen (EN)

Pirovano, Gabriele (d. 1512)¶

Milanese Physician and Astrologer

Ducal physician at the Sforza court and author of De Astronomiae Veritate; participant in the February 9, 1498 disputation.

Principal Works: Defensio Astronomiae (1507)

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

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

Greek Philosopher and Founder of the Academy

Placed the inscription ‘Let no one ignorant of geometry enter here’ over the portal of the Academy; in the Timaeus (53c–56c), assigned the five regular polyhedra to the four elements (fire, earth, air, water) and the cosmos (fifth essence).

Principal Works: Timaeus, Respublica

Occurrences: Arch. Cap. 1 (DE), Arch. Cap. 1 (EN), Arch. Cap. 3 (DE), Arch. Cap. 3 (EN), Arch. Cap. 3 (IT), Arch. Cap. 12 (DE), Arch. Cap. 12 (EN), Arch. Cap. 12 (IT), Arch. Cap. 20 (DE), Arch. Cap. 20 (EN), Arch. Cap. 20 (IT), Arch. Cap. 20 (Notes), Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 3 (DE), Comp. Cap. 3 (EN), Comp. Cap. 3 (IT), Comp. Cap. 5 (DE), Comp. Cap. 5 (EN), Comp. Cap. 5 (IT), Comp. Cap. 5 (Notes), Comp. Cap. 22 (DE), Comp. Cap. 22 (EN), …and 13 more

Pliny the Elder (Gaius Plinius Secundus) (23/24 – 79 AD)¶

Roman Natural Philosopher and Encyclopedist

Author of the Naturalis Historia; cited by Pacioli in Chapter II and source of the Zeuxis and Parrhasius account in Chapter III.

Principal Works: Naturalis Historia

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 3 (DE), Comp. Cap. 3 (EN), Comp. Cap. 3 (IT)

Polykleitos of Argos (fl. 5th century BC)¶

Classical Greek Sculptor and Author of the Canon

Author of the classical Canon of human proportions and sculptor named alongside Apelles and Myron in Chapters I and XXIII.

Principal Works: Canon

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT)

Pontano, Giovanni Gioviano (1429 – 1503)¶

Neapolitan Humanist, Poet, and Royal Secretary

Head of the Accademia Pontaniana and chief minister to King Ferrante of Naples; cited by Pacioli in the Dedication of the Tractato de l’Architectura.

Occurrences: Arch. Prohemio (EN), Arch. Prohemio (IT), Arch. Prohemio (Notes)

Ponzone, Fra Domenico, O.F.M. (fl. 1498)¶

Franciscan Preacher and Theologian

Celebrated Franciscan herald of Sacred Scripture present at the February 9, 1498 disputation in Milan.

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes)

Praxiteles of Athens (fl. 4th century BC)¶

Classical Greek Sculptor

Paired with Phidias on the Quirinal Horse Tamers (Monte Cavallo) in Rome, which Pacioli declares surpassed by Leonardo da Vinci’s Sforza equestrian colossus.

Occurrences: Arch. Prohemio (DE), Arch. Prohemio (EN), Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT)

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

Greco-Roman Astronomer, Mathematician, and Geographer

Author of the Almagest and Cosmographia (Geography); cited by Pacioli on the chord of the pentagon and hexadecagon, spherical astronomy, and cartographic scaling.

Principal Works: Almagest (Syntaxis Mathematica), Cosmographia (Geographia)

Occurrences: Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 3 (IT), Comp. Cap. 17 (DE), Comp. Cap. 17 (EN), Comp. Cap. 17 (IT), Comp. Cap. 17 (Notes)

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

Greek Philosopher and Mathematician

Cited by Pacioli (via Vitruvius Book IX) for sacrificing a hecatomb of one hundred oxen to the gods upon discovering the theorem of the right-angled triangle (‘angolo dela iustitia’, Euclid I.47).

Principal Works: Pythagorean Theorem (Euclid I.47)

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 54 (DE), Comp. Cap. 54 (EN), Comp. Cap. 54 (Notes), Winterberg Intro (DE), Winterberg Intro (EN)

Quetelet, Adolphe (1796 – 1874)¶

Belgian Astronomer, Mathematician, and Founder of Anthropometry

Author of Sur l’homme (1835) and Anthropométrie, ou Mesure des différentes facultés de l’homme (1870); cited by Winterberg in the Einleitung for establishing statistical anthropometry.

Principal Works: Anthropométrie, ou Mesure des différentes facultés de l’homme (1870)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Riario, Count Girolamo, Lord of Imola and Forlì (1443 – 1488)¶

Captain General of the Church and Nephew of Pope Sixtus IV

Host of the architectural gathering at his palace construction in Rome (now Palazzo Altemps) with Melozzo da Forlì and Luca Pacioli recounted in Compendio Cap. LVII.

Occurrences: Comp. Cap. 57 (Notes), Comp. index

Roch, St. (San Rocco) (c. 1348 – 1376/1379)¶

Christian Confessor and Patron Saint against the Plague

Venerated in Venice at the Church and Scuola Grande di San Rocco; glossed by Winterberg in the Dedication of the Tractato de l’Architectura (fn. 1).

Occurrences: Arch. Prohemio (DE), Arch. Prohemio (Notes)

Rovere, Cardinal Galeotto Franciotti della (1471 – 1507)¶

Cardinal of San Pietro in Vincoli and Vice-Chancellor of the Roman Church

Nephew of Pope Julius II and patron of Luca Pacioli (Architectura Cap. XI), whose premature death in 1507 Pacioli laments.

Occurrences: Arch. Cap. 18 (Notes), Arch. index

Sanseverino, Galeazzo da (c. 1458 – 1525)¶

Captain General of the Sforza Armies and Patron of Pacioli

Son-in-law of Ludovico Sforza, close friend of Leonardo da Vinci, and ‘peculiar patrone’ of Luca Pacioli in Milan; recipient of one of the three presentation manuscripts of De Divina Proportione (now in the Biblioteca Ambrosiana).

Occurrences: Arch. Cap. 6 (DE), Arch. Cap. 6 (IT), Arch. Cap. 6 (Notes), Arch. Cap. 20 (DE), Arch. Cap. 20 (Notes), Arch. Prohemio (DE), Arch. Prohemio (IT), Arch. Prohemio (Notes), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT), Comp. Cap. 1 (Notes), Comp. Cap. 70 (Notes)

Sansone, Fra Francesco (Nanni) da Brescia, O.F.M. (1414 – 1499)¶

Minister General of the Franciscan Order (1475–1499)

Presided over the General Chapter of the Franciscan Order celebrated in Milan in 1498 under the patronage of Ludovico Sforza.

Occurrences: Comp. Cap. 69 (DE), Comp. Cap. 69 (Notes)

Schmidt, Carl (fl. 1849)¶

German Art Theorist and Anatomist

Author of Proportionsschlüssel: Neues System der Verhältnisse des menschlichen Körpers (Stuttgart, 1849), which modified Carus’s vertebral module to include the cranial bones for measuring the extremities; cited by Winterberg in the Einleitung.

Principal Works: Proportionsschlüssel: Neues System der Verhältnisse des menschlichen Körpers (1849)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Serapion (Yahya ibn Sarafyun / Ibn Sarabi) (fl. 9th / 12th century)¶

Medical Authority

Medical authority paired with Avicenna in Compendio Chapter I in Pacioli’s praise of the court physician Ambrogio da Rosate.

Principal Works: Practica / Liber Aggregatus in Medicinis Simplicibus

Occurrences: Comp. Cap. 1 (DE), Comp. Cap. 1 (EN), Comp. Cap. 1 (IT)

Serlio, Sebastiano (1475 – c. 1554)¶

Italian Mannerist Architect and Architectural Theorist

Author of I Sette Libri dell’Architettura (1537–1551), cited by Winterberg in the Einleitung alongside Vitruvius and Alberti on Renaissance architectural proportion.

Principal Works: I Sette Libri dell’Architettura

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Sforza, Francesco I, Duke of Milan (1401 – 1466)¶

Founder of the Sforza Dynasty of Milan and Condottiero

Father of Ludovico Sforza; honored by Leonardo da Vinci’s bronze equestrian colossus and remembered by Pacioli for the massive bridge cables hung as votive trophies in San Fortunato at Todi.

Occurrences: Comp. Cap. 1 (Notes), Comp. Cap. 2 (EN), Winterberg Intro (DE), Winterberg Intro (EN)

Sforza, Ludovico Maria (‘Il Moro’), Duke of Milan (1452 – 1508)¶

Duke of Milan and Patron of Pacioli and Leonardo da Vinci

Dedicatee of the 1498 Compendio de Divina Proportione; established the public chair of mathematics in Milan for Luca Pacioli (1496–1499) and hosted the scientific disputation of February 9, 1498 in the Castello Sforzesco.

Occurrences: Arch. Cap. 6 (EN), Arch. Cap. 6 (IT), Arch. Cap. 6 (Notes), Arch. Cap. 20 (EN), Arch. Cap. 20 (Notes), Arch. Prohemio (IT), Arch. Prohemio (Notes), Comp. Cap. 1 (Notes), Comp. Cap. 2 (Notes), Comp. Cap. 54 (Notes), Comp. Cap. 69 (Notes), Comp. Cap. 70 (Notes), Comp. index, DE DIVINA PROPORTIONE, Winterberg Intro (DE), Winterberg Intro (EN)

Simonides of Ceos (c. 556 – 468 BC)¶

Greek Lyric Poet

Cited in Compendio Chapter LVII for repeatedly doubling the time requested of Hiero of Syracuse to define God, illustrating the folly of rash boasters.

Occurrences: Comp. Cap. 57 (DE), Comp. Cap. 57 (EN), Comp. Cap. 57 (IT), Comp. Cap. 57 (Notes)

Soderini, Cardinal Francesco, Bishop of Volterra (1453 – 1524)¶

Cardinal of Volterra, Florentine Ambassador, and Patron of Pacioli

Brother of Gonfaloniere Piero Soderini; served as Florentine ambassador to the court of Milan when Pacioli presented De Divina Proportione to Ludovico Sforza, and praised by Pacioli as ‘my singular patron, to whom I owe my very life’.

Soderini, Giovan Battista (fl. 1509)¶

Florentine Patrician

Nephew of Piero Soderini mentioned in Pacioli’s 1509 dedicatory epistle.

Soderini, Giovan Vittorio (1460 – 1528)¶

Florentine Jurist (Doctor of Both Laws) and Statesman

Brother of Piero and Cardinal Francesco Soderini, praised in Pacioli’s 1509 dedicatory epistle for his legal and mathematical learning.

Soderini, Piero (1452 – 1522)¶

Gonfaloniere a Vita (Perpetual Prince) of the Florentine Republic

Dedicatee of the 1509 printed Venice edition of De Divina Proportione and of Part III (Libellus); recovered Pacioli’s manuscript after the fall of Ludovico Sforza and housed Pacioli’s hand-built polyhedra models in Florence.

Occurrences: Arch. Cap. 6 (EN), Arch. Cap. 18 (EN), Comp. Cap. 70 (Notes)

Soderini, Tommaso (fl. 1509)¶

Florentine Patrician

Nephew of Piero Soderini mentioned in Pacioli’s 1509 dedicatory epistle.

Solomon, King (fl. 10th century BC)¶

King of Israel and Builder of the Temple of Jerusalem

Builder of the Temple in Jerusalem whose Gate Called Beautiful (‘Porta Templi Domini dicta Speciosa’) Pacioli reconstructs geometrically in Architectura Chapter VI and Folio 0185.

Occurrences: Arch. Cap. 8 (Notes), Arch. Prohemio (DE), Arch. Prohemio (EN)

Tartaglia, Niccolò (Niccolò Fontana) (1499/1500 – 1557)¶

Venetian Mathematician and Engineer

Author of the General Trattato di Numeri et Misure (Venice, 1556–1560) and translator of the first Italian vernacular edition of Euclid (1543); cited by Winterberg in the Einleitung (fn. 7) on errors in Pacioli’s Latin Euclid of 1509.

Principal Works: General Trattato di Numeri et Misure (1556–1560)

Occurrences: Comp. Cap. 35 (Notes), Comp. Cap. 46 (Notes), Winterberg Intro (DE), Winterberg Intro (EN), Winterberg Anmerkungen (DE), Winterberg Anmerkungen (EN)

Theaetetus of Athens (c. 417 – c. 369 BC)¶

Greek Geometer of the Platonic Academy

Originated the classical theory of quadratic irrationals (Euclid Book X) and the constructions of the octahedron and icosahedron (Euclid Book XIII).

Thomas Aquinas, St., O.P. (1225 – 1274)¶

Dominican Scholastic Philosopher and Theologian

Scholastic authority on Aristotelian natural philosophy and epistemology.

Principal Works: Summa Theologiae, In Libros Physicorum et De Caelo

Tovaglia, Piero del (fl. late 15th century)¶

Florentine Patrician and Patron of Architecture

Owner of the suburban villa near Florence (Villa del Tovaglia) whose stone columns Pacioli praises as models of proportion in Architectura Chapter VIII.

Trivulzio, Gian Giacomo (1440/1441 – 1518)¶

Milanese Condottiere and Marshal of France

Celebrated military commander praised by Pacioli in the Dedication of the Tractato de l’Architectura for his discourse on military and Vitruvian architecture in Naples.

Occurrences: Arch. Prohemio (Notes)

Trost, Johann Jacob (fl. 1854 – 1866)¶

Austrian Art Theorist at the Vienna Academy of Fine Arts

Author of Die Proportionslehre Dürer’s nach ihren wesentlichen Bestimmungen in übersichtlicher Darstellung (Vienna, 1859), cited by Winterberg in the Einleitung.

Principal Works: Die Proportionslehre Dürer’s (1859)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Valturio, Roberto (1405 – 1475)¶

Humanist and Military Engineer of Rimini

Author of De Re Militari (printed in Verona, 1472), praised by Pacioli in Compendio Chapter II as ‘peritissimo Ariminese’ for his treatise on ancient and modern military machines dedicated to Sigismondo Pandolfo Malatesta.

Principal Works: De Re Militari (1472)

Occurrences: Comp. Cap. 2 (EN), Comp. Cap. 2 (Notes)

Vasari, Giorgio (1511 – 1574)¶

Renaissance Painter, Architect, and Biographer of Artists

Author of Le Vite de’ più eccellenti pittori, scultori, e architettori (1550/1568); cited critically by Winterberg in the Einleitung for accusing Pacioli of plagiarizing Piero della Francesca’s geometrical treatises.

Principal Works: Le Vite de’ più eccellenti pittori, scultori, e architettori

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Vegetius Renatus, Publius Flavius (fl. late 4th century AD)¶

Roman Military Theorist

Author of Epitoma Rei Militaris, cited in Compendio Chapter II on the mathematical foundations of Roman military engineering.

Principal Works: Epitoma Rei Militaris

Occurrences: Comp. Cap. 2 (DE), Comp. Cap. 2 (EN), Comp. Cap. 2 (IT), Comp. Cap. 2 (Notes)

Vettori, Pier (the Elder) (fl. late 15th century)¶

Florentine Statesman and Ambassador in Naples

Florentine ambassador at the Aragonese court in Naples and father of Francesco Vettori; cited by Pacioli in the Dedication of the Tractato de l’Architectura.

Occurrences: Arch. Prohemio (EN), Arch. Prohemio (Notes)

Vitelli, Camillo (c. 1459 – 1496)¶

Umbrian Condottiere of Città di Castello

Military commander to whom Pacioli expounded Euclid’s Elements for three years across campaigns in Naples and Rome (Architectura Prohemio).

Occurrences: Arch. Prohemio (DE), Arch. Prohemio (Notes)

Vitruvius Pollio, Marcus (c. 80–70 BC – after c. 15 BC)¶

Roman Architect and Military Engineer

Author of De Architectura Libri X, the primary classical authority for Pacioli’s Tractato de l’Architectura on human proportion (Homo ad circulum et quadratum), the Doric, Ionic, and Corinthian orders, and entablatures.

Principal Works: De Architectura Libri Decem

Occurrences: Arch. Cap. 1 (IT), Arch. Cap. 3 (DE), Arch. Cap. 3 (EN), Arch. Cap. 3 (IT), Arch. Cap. 4 (DE), Arch. Cap. 4 (EN), Arch. Cap. 4 (IT), Arch. Cap. 5 (DE), Arch. Cap. 5 (EN), Arch. Cap. 5 (IT), Arch. Cap. 5 (Notes), Arch. Cap. 7 (DE), Arch. Cap. 7 (EN), Arch. Cap. 7 (IT), Arch. Cap. 7 (Notes), Arch. Cap. 8 (DE), Arch. Cap. 8 (EN), Arch. Cap. 8 (IT), Arch. Cap. 12 (DE), Arch. Cap. 12 (EN), Arch. Cap. 12 (IT), Arch. Cap. 12 (Notes), Arch. Cap. 13 (Notes), Arch. Cap. 14 (DE), …and 35 more

Winterberg, Constantin (fl. 1887 – 1889)¶

German Art Historian, Editor and Translator of De Divina Proportione

Prepared the 1889 Vienna critical edition and German translation (Fra Luca Pacioli: Divina Proportione — Die Lehre vom Goldenen Schnitt, Quellenschriften für Kunstgeschichte, N. F. Band II), including the Vorwort, Einleitung, chapter footnotes, and 17 Sachliche Anmerkungen on the polyhedra plates; also authored ‘Das Malerbuch Lionardo da Vinci’s’ in the Jahrbücher der königlich preussischen Kunstsammlungen (1887).

Principal Works: Fra Luca Pacioli: Divina Proportione — Die Lehre vom Goldenen Schnitt (Wien: Carl Graeser, 1889), Das Malerbuch Lionardo da Vinci’s (Jahrbücher der königlich preussischen Kunstsammlungen, 1887)

Zeising, Adolf (1810 – 1876)¶

German Aesthetic Theorist and Morphologist

Author of Neue Lehre von den Proportionen des menschlichen Körpers (Leipzig, 1854), which sought to establish the Golden Section as the universal morphological law of the human body, nature, and classical art; discussed by Winterberg in the Einleitung (fn. 4).

Principal Works: Neue Lehre von den Proportionen des menschlichen Körpers (1854)

Occurrences: Winterberg Intro (DE), Winterberg Intro (EN)

Zeuxis of Heraclea (fl. late 5th century BC)¶

Classical Greek Painter

Celebrated with his rival Parrhasius in Compendio Chapter III (from Pliny’s Naturalis Historia XXXV.65) for painting grapes so lifelike that birds flew down to peck at them.

Occurrences: Comp. Cap. 3 (DE), Comp. Cap. 3 (EN), Comp. Cap. 3 (IT)