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Journal ArticleDOI

Anatomy of a Dispute: Leonardo, Pacioli and Scientific Courtly Entertainment in Renaissance Milan

01 Jan 2004-Early Science and Medicine (BRILL)-Vol. 9, Iss: 2, pp 115-135
Abstract: Historians have recently paid increasing attention to the role of the disputation in Italian universities and humanist circles. By contrast, the role of disputations as forms of entertainment at fifteenth-century Italian courts has been somewhat overlooked. In this article, the Milanese "scientific duel" (a courtly disputation) described in Luca Pacioli's De divina proportione is taken as a vantage point for the study of the dynamics of scientific patronage and social advancement as reflected in Renaissance courtly disputes. Pacioli names Leonardo da Vinci as one of the participants in the Milanese dispute. In this paper I argue that Leonardo's Paragone and Pacioli's De divina proportione are likewise the outcome of the Milanese "scientific duel." By challenging the traditional hierarchy of the arts, they both exemplify the dynamics of social and intellectual promotion of mathematicians and artists in the privileged setting of Renaissance courts, where courtly patronage could subvert the traditional disciplinary rankings.

Summary (2 min read)

The Battle of the Books: Social Status and the Nobility of Scientific Disciplines at Court

  • De divina proportione is far from being the book of technical mathematics and sophisticated calculations of the golden ratio that one might expect at first from a teacher of abacus.
  • 18 Letters by Gabriele Pirovano, Aloisio Marliani, and Nicolò Cusano appear often in the correspondence of Duke of Milan.19 I have found a wealth of letters signed by each of these physicians in the Milanese archives, most relating to the health of various members of the Duke’s extended family.
  • Not only were these learned physicians trusted members of the court but—at least in the case of Varesi and Pirovano—they were also the representatives of that class of “celestial” mathematicians practicing astrology and astronomy who considered themselves superior to scholars like Pacioli.
  • Be this as it may, the courtly scientific disputation presented the occasion for Pacioli to defend the nobility of mathematics as superior to all other arts and sciences, including astrology and astronomy, which—Pacioli argued—depended on the true principles of geometry.
  • VIIr; for its importance for natural philosophy, see fol.

Crossing Boundaries: The Dispute as Means of Social Advancement

  • Leonardo’s Paragone has been often identified as the first treatise to maintain the superiority of painting over the other liberal arts and as a significant testimony to the newly acquired status of the artist in society.
  • As Pacioli had done for mathematics, Leonardo defends the nobility of his discipline (which was generally associated with the mechanical arts), against the claims of another discipline.
  • It seems more likely that their function as spectators was to gave respectability and prominence to the event and, indirectly, to Leonardo’s and Pacioli’s performance.
  • Alberti, instead, explicitly adheres to the Horatian motto “ut pictura poesis.”.
  • In arguing for a higher social position for themselves and their disciplines, they attempted to gain new prestige and status outside the strict boundaries of university training and traditional education.

Science and Spectacle: The Scientific Courtly Dispute as Courtly Entertainment

  • As one looks closely at much of the intellectual production in fourteenth- and fifteenthcentury Italy, one cannot fail to notice that a large amount of this output revolves around intellectual disputes.
  • On Leoniceno’s medical disputes, see also Daniela Mugnai-Carrara, “Una polemica umanistico-scolastica circa l’interpretazione delle tre dottrine ordinate di Galeno,” Annali dell’Istituto e Museo di Storia della Scienza di Firenze 8 (1980), 31-57.
  • See also my comments on the importance of scholastic disputatio in late medieval and Renaissance culture in “In Praise of Art.” 56 Previous scholars had tended to concentrate on the academic dispute generated in Bologna following Leoniceno’s publication of his theories.

Conclusions

  • The academic disputation was a constant, statutory feature of Italian universities from the very moment of their foundation.
  • Almost unfailingly, these disputes seem to have resulted in the production of polemical texts.
  • Whereas scholastic, humanistic, and courtly disputes show common features, there are elements of the courtly dispute that seem to set it apart from the other two types.
  • Biagioli’s study of Galileo certainly provides positive evidence of Galileo’s crafty use of disputation for social and intellectual promotion at the Medici court in the sixteenth century.
  • In order to fully assess the role of esm9-2_2.pmd 4/21/2004, 3:58 PM134 patronage in science in the sixteenth-century, it seems essential to historicize these instances further by looking closely at the earlier period.

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Anatomy of a Dispute
Citation for published version:
Azzolini, M 2004, 'Anatomy of a Dispute: Leonardo, Pacioli, and Scientific Entertainment in Renaissance
Milan.', Early Science and Medicine, vol. 9, no. 2, pp. 115 -135. https://doi.org/10.1163/1573382041154088
Digital Object Identifier (DOI):
10.1163/1573382041154088
Link:
Link to publication record in Edinburgh Research Explorer
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Early Science and Medicine
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© Azzolini, M. (2004). Anatomy of a Dispute: Leonardo, Pacioli, and Scientific Entertainment in Renaissance
Milan.Early Science and Medicine, 9(2), 115 -135doi: 10.1163/1573382041154088
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anatomy of a dispute 115
© Koninklijke Brill NV, Leiden, 2004 Early Science and Medicine 9, 2
Also available online – www.brill.nl
ANATOMY OF A DISPUTE:
LEONARDO, PACIOLI AND SCIENTIFIC COURTLY
ENTERTAINMENT IN RENAISSANCE MILAN
*
MONICA AZZOLINI
University of New South Wales
Abstract
Historians have recently paid increasing attention to the role of the disputation
in Italian universities and humanist circles. By contrast, the role of disputations
as forms of entertainment at fifteenth-century Italian courts has been somewhat
overlooked. In this article, the Milanese “scientific duel” (a courtly disputation)
described in Luca Pacioli’s De divina proportione is taken as a vantage point for the
study of the dynamics of scientific patronage and social advancement as reflected
in Renaissance courtly disputes. Pacioli names Leonardo da Vinci as one of the
participants in the Milanese dispute. In this paper I argue that Leonardo’s Para-
gone and Pacioli’s De divina proportione are likewise the outcome of the Milanese
“scientific duel.” By challenging the traditional hierarchy of the arts, they both
exemplify the dynamics of social and intellectual promotion of mathematicians
and artists in the privileged setting of Renaissance courts, where courtly patron-
age could subvert the traditional disciplinary rankings.
In 1496 the Dominican friar and mathematician Luca Pacioli was
called to Milan by Duke Ludovico il Moro to offer public lectures
on mathematics in the city.
1
In taking up his job Pacioli performed
one of the roles assigned to mathematicians in the late fifteenth
century. Italian Renaissance mathematical practitioners could be
divided essentially into two disciplinary and professional catego-
ries: those who taught arithmetic and geometry, and those who
taught astrology and astronomy. While in some cases universities
offered chairs in arithmetic and geometry (“ad arithmeticam et
geometriam”), more often these subjects were taught in the city’s
public schools. This seems to have been the case in Milan, where
figures like Pacioli—but also Fazio Cardano, father of the more
*
I wish to thank Mark Byron, Sachiko Kusukawa, Nancy Siraisi, Katharine
Park, Paul Grendler and Christoph Lüthy for their very insightful comments and
criticisms on earlier drafts of this paper.
1
On Luca Pacioli, see S. A. Jayawardene, “Pacioli, Luca,” in Dictionary of Scien-
tific Biography, X (1974), 269-272.
esm9-2_2.pmd 4/21/2004, 3:58 PM115

monica azzolini116
famous Girolamo—were hired to teach arithmetic and basic geo-
metry.
2
As Mario Biagioli noted in his study of Italian mathematicians,
in the first half of the Quattrocento this disciplinary division trans-
lated into a marked difference in professional, social, and intel-
lectual status. While the teaching of arithmetic and geometry
was generally associated with the lower mechanical arts, the teach-
ing of astrology and astronomy was related to the study and prac-
tice of medicine and natural philosophy.
3
Within the hierarchy
of knowledge, the mathematician-astronomer-astrologer was thus
close to the top.
4
The perceived difference in the nobility of their
disciplines created a noticeable social, economical and profes-
sional disparity between the “celestial” mathematicians who engag-
ed in astronomical studies, astrological prediction and astrological
medicine, and the “terrestrial” mathematicians who dealt with
book-keeping, land surveying and engineering.
5
Although by the
2
The Duchy’s Studio was located in the neighbouring city of Pavia. The Duke
of Milan exerted direct control over the appointment and the salaries of the pro-
fessors teaching at the Studio. Ludovico, however, maintained a separate school
for rhetoric, poetry, Greek and mathematics in Milan. The salaries of those teach-
ing in Milan were generally higher than those of the scholars teaching in Pavia.
On the relationship between the Duke and the Studio, see Agostino Sottili “L’Uni-
versità di Pavia nella politica culturale sforzesca,” in Gli Sforza a Milano e in Lom-
bardia e i loro rapporti con gli stati italiani ed europei (1450-1535) (Milan, 1982),
519-581. On the Studio, see also Paul F. Grendler, The Universities of the Italian
Renaissance (Baltimore-London, 2002), 82-93. On the Milanese teaching of Pacioli
and Cardano, see Alfonso Corradi, Memorie e documenti per la Storia dell’Università
di Pavia e degli uomini più illustri che v’insegnarono, 2 vols. (Pavia, 1877-1878), I: 162-
165; and Sottili, “L’Universita di Pavia,” 540-42. Sottili mistakenly speaks of a
Francesco Cardano instead of Fazio Cardano.
3
For a concise introduction to classical, medieval, and Renaissance astrology
see Charles Burnett’s excellent entry in F.A.C. Mantello and A.G. Rigg (eds.),
Medieval Latin: An Introduction and Bibliographical Guide (Washington, D.C., 1996),
369-382.
4
On the hierarchy of knowledge in the Renaissance, see the classic articles by
Paul O. Kristeller, “The Modern System of the Arts. A Study in the History of
Aesthetics,” Journal of the History of Ideas 12 (1944), 496-527; 13 (1945) 17-46.
5
In what follows I use the terms “celestial” and “terrestrial” mathematician to
indicate, respectively, those mathematicians who teach astrology and astronomy,
and those who teach arithmetic and geometry. I borrow these expressions from
Mario Biagioli’s “The Social Status of Italian Mathematicians: 1450-1600,” History
of Science 27 (1989), 42-43. The terms “astrologia” and “astronomia” were often
used interchangeably in the Renaissance. For a discussion as to the origin and
nature of such terms, see S. J. Tester, A History of Western Astrology (Woodbridge,
Suffolk, 1987), 187; and Steven Vanden Broecke, The Limits of Influence: Pico,
Louvain, and the Crisis of Renaissance Astrology (Louvain, 2003), ch. 1.
esm9-2_2.pmd 4/21/2004, 3:58 PM116

anatomy of a dispute 117
mid-sixteenth century one could trace a distinctive rise in the sta-
tus of the teacher of arithmetic and geometry, in Pacioli’s time we
can assume that this social distinction was still relatively clear.
6
Despite the fact that Pacioli’s teaching took place in the city, his
appointment and his remuneration were granted by the Duke. As
a consequence, Pacioli was the beneficiary of courtly patronage
and subject to the courtly dynamics of gift-giving and exchange
that have been explored by social anthropologists, cultural histori-
ans and, more recently, historians of science.
7
As a way to celebrate
and honor his new patron, a few years after his arrival in Milan
Pacioli offered his next book, De divina proportione, to the Duke.
Pacioli’s token of gratitude to Ludovico was produced only in a
small number of preciously illuminated presentation copies which
were adorned with sixty geometric figures thought to have origi-
nally been drawn by Leonardo. Of the three presentation copies
produced only two survive: a copy, dedicated to the Duke of Mi-
lan, is now preserved at the civic library of Geneva, and a second
one, which Pacioli donated to Gian Galeazzo Sanseverino, is now
at the Ambrosiana Library.
8
The Battle of the Books: Social Status and the Nobility of Scientific
Disciplines at Court
Pacioli’s De divina proportione is far from being the book of techni-
cal mathematics and sophisticated calculations of the golden ratio
that one might expect at first from a teacher of abacus. The beau-
6
Biagioli ascribes this change to the professionalization of military engineer-
ing and the demand of professional mathematicians who could teach applied
mathematics within Italian courts. See Biagioli, “The Social Status,” esp. 44-46.
7
The bibliography on court etiquette and courtly patronage is far too exten-
sive to be summed up effectively here. On Italian courts besides the classic study
by Lauro Martinez, Power and Imagination: City-States in Renaissance Italy (New York,
1979), esp. 218-240, see the bibliography indicated in the articles by Paula Findlen
and William Eamon in Bruce T. Moran (ed.), Patronage and Institutions: Science,
Technology, and Medicine at the European Court 1500-1750 (Rochester, NY, 1991), 5-
24, esp. n. 6; and 25-50, esp. n. 17; as well as in Mario Biagioli, “Galileo’s System
of Patronage,” History of Science 28 (1990), 1-62; and idem, Galileo, Courtier (Chi-
cago, 1993).
8
A third one, now lost, was offered to Pietro Soderini. See Luca Pacioli, De
divina proportione, introd. by Augusto Marinoni (Milan, 1982; facsimile edition of
the ms at the Ambrosiana Library, Milan), esp. the prefatory note to the intro-
duction. The manuscript was concluded by 1498. The first printed edition was
published in Venice in 1509. See Marinoni’s introduction, 5-18.
esm9-2_2.pmd 4/21/2004, 3:58 PM117

monica azzolini118
tiful illuminations that adorn its dedication page and the large
folio size, together with the geometric figures designed by Leo-
nardo, betray a much more ambitious scope. The first chapter of
the work opens with a commendatio of the court of Milan and its
illustrious members, which is followed by the praise of the court-
sponsored projects of the horse monument in honor of Francesco
Sforza and the fresco decoration of Santa Maria delle Grazie com-
missioned to Leonardo da Vinci, and it concludes with the com-
mendatio of Pacioli’s own work to the Duke.
9
For its form and content, the opening chapter that constitutes
Pacioli’s dedicatory letter to the Duke warrants special attention.
There, Pacioli recalls how in February 1498, Duke Ludovico as-
sisted, at his Milanese residence in the Castle of Porta Giovia, at
the performance of a laudable scientific duel (“scientifico duello”).
Presumably the duel was staged as a disputation on the nobility of
geometry and mathematics, a topic that features prominently in
the opening chapters. Both lay and ecclesiastical personalities who
tended to frequent his court accompanied the Duke.
From Pacioli’s account it seems clear that this was a large-scale
event that gathered together the most influential personalities of
the time. After having reverentially mentioned some of the most
prominent ecclesiastical figures, Pacioli quickly moves on to praise
his “secular patron,” Gian Galeazzo Sanseverino, condottiere of Lu-
dovico’s army, as a man “second to none in military prowess and a
keen imitator of our own disciplines.”
10
From this passage we can
evince that although Pacioli received the patronage of the Duke
of Milan, his broker at the time was Gian Galeazzo Sanseverino,
who had probably acted as intermediary with the Duke to procure
Pacioli his teaching job in Milan. It seems plausible also to infer
that Sanseverino had a professional interest in mathematics and
geometry and that he had personally pursued the study of these
disciplines, possibly under the guidance of Pacioli himself.
11
9
Pacioli, De divina proportione, n. p.: “Commendatione dela sua Magnifica
corte.” The commendatio was a rhetorical form of praise that was widely used both
in humanistic and scholastic writings. On the use of the commendatio in scholastic
writings and university orations, see Jole Agrimi and Chiara Crisciani, Edocere
Medicos (Naples, 1988), esp. 238-253.
10
Pacioli, De divina proportione, fol. Iv: “[…] el R.
do
p. M. Francesco Busti al
presente nel degno convento vostro de Milano regente deputato e de seculari
prima el mio peculiare patrone S. Galeazo Sf. V. S. Severino fortissimo e generale de
V. Cel.
ne
Capitano nellarmi hoggi aniuno secondo e de nostre discipline solerto
immitatore.” Emphasis mine.
11
Pacioli’s case thus constitutes an early instance of a tutor of mathematics
esm9-2_2.pmd 4/21/2004, 3:58 PM118

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  • ...(Azzolini, 2004, pp. 115, 123) This debate formed the catalyst for De Divina Proportione, which he completed in December 1498 and published in print in 1509.25 The argument he presented during the disputation was also included by Pacioli in the dedicatory letters in both Summa Arithmetica and De…...

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Frequently Asked Questions (9)
Q1. What are the contributions in "Anatomy of a dispute: leonardo, pacioli and scientific courtly entertainment in renaissance milan*" ?

In this article, the Milanese “ scientific duel ” ( a courtly disputation ) described in Luca Pacioli ’ s De divina proportione is taken as a vantage point for the study of the dynamics of scientific patronage and social advancement as reflected in Renaissance courtly disputes. In this paper I argue that Leonardo ’ s Paragone and Pacioli ’ s This seems to have been the case in Milan, where figures like Pacioli—but also Fazio Cardano, father of the more * I wish to thank Mark Byron, Sachiko Kusukawa, Nancy Siraisi, Katharine Park, Paul Grendler and Christoph Lüthy for their very insightful comments and criticisms on earlier drafts of this paper. 

The court, with its emphasis on spectacle and entertainment, represented a privileged space in which to wage such intellectual battles. 

He rapidly ascended to power and prestige: by 1480 Ludovico il Moro assigned Varesi an annual salary of a hundred golden duc-15 Ibid., fol. 

as in the case of Pacioli and the Ferrarese physicians, the letters of dedication of some of their writings allow us to infer that they were written and produced for courtly consumption and geared towards the acquisition of privileges and the consolidation of patronage relationships. 

As such, it involves courtiers and intellectuals, academicians and craftsmen, subtly crossing the conventional boundaries of fifteenth century Italian court hierarchies, and allowing for the subversion, permissible only by the Duke’s willingness to grant patronage, of the social order of Renaissance society. 

Biagioli’s study of Galileo certainly provides positive evidence of Galileo’s crafty use of disputation for social and intellectual promotion at the Medici court in the sixteenth century. 

41 Within Italian universities the scholastic disputation was an integral part of the educational curriculum, sanctioned by the university statutes. 

29teaching of music at the university level was at Milan between 1494-1499, when Franchino Gaffurio was appointed by Ludovico “ad lecturam musicae” in the Milanese studio. 

As the passing of time has relegated most of this figures to oblivion, it is only through an accurate reconstruction of their role at court that historians can assess fully the importance of the duel and the roles played in it by Pacioli and Leonardo. 

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In this paper I argue that Leonardo's Paragone and Pacioli's De divina proportione are likewise the outcome of the Milanese "scientific duel."