Page 245 - Art In The Age Of Exploration (Great Section on Chinese Art Ming Dynasty)

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Jacopo de' Barbari (?)
Venetian, active before 1495 -died by 1516
PORTRAIT OF FRA LUCA PACIOLI
WITH A YOUNG MAN
1494?
oil on panel
2
99 x 120 (39 x 47 /4J
references: Pacioli 1494; Pacioli 1509; Gronau 1905,
28; Servolini 1944, 105-106; Rose 1975; Daly Davis
1977; Levenson 1978; Naples and Rome 1983, no.
79; Dalai Emiliani 1984; Kemp 1989, 1:237-242
Museo e Gallerie Nazionali di Capodimonte, Naples

The identity of the main figure as the Franciscan
mathematician Luca Pacioli and the nature of the
mathematical allusions are the only indisputable
aspects of this remarkable picture. The inscription
on the large volume to the right, "Li\be]r R[e-
verendi] Luc[a] Bur[gensis] ," indicates almost
certainly that the book is Pacioli's Summa de
arithmetica, geometria, proportione et proportio-
nalita, the large compendium of pure and practical
mathematics that was published in Venice in
1494. The open book is a printed edition of
Euclid's Elements, of which Pacioli was to publish
an Italian translation in 1509. The geometrical
solids — the dodecahedron perched on the cover of
the Summa and the semiregular polyhedron com-
posed of squares and triangles (a rhombicuboc-
tahedron) hanging in the upper left — allude to his
special interest in the regular (Platonic) and semi-
Dodeacdron Abfdfiim Eicwtoia "Vacuum regular geometrical bodies. This interest had been
fired by his contacts with Piero della Francesca
and was to result in his most attractive book, the
treatise De divina proportione, illustrated by Leo-
nardo da Vinci and published in 1509. Pacioli is
known to have constructed actual models of the
polyhedra (Kemp 1989). The "crystal" polyhedron
tion, whereas the illustrations in the Geneva identify the elements literally with the Platonic in the present picture, suspended from a cord that
manuscript are drawn far more casually. It is pos- solids, he was wholly convinced of the mathe- runs through the upper vertex to a point of
sible that the Milan illustrations were laid in by matical base of harmonic beauty and accepted the attachment at the bottom of the solid, appears to
Leonardo himself, although the attractive and idea that the underlying organization of nature have been constructed from glass faces, with a
skillfully disposed shading in colored washes conformed to proportional principles. glass plane running horizontally across its center
seems not to be by his hand. The folio reproduced shows plate xxxn, the to stabilize the structure. The dodecahedron, an
For Pacioli the interest of the solids extended truncated and stellated dodecahedron in its skeletal apparently humbler object for everyday teaching,
far beyond the realms of pure geometry. Plato had form. This solid is assembled from a regular body is made from wood. The geometrical diagram on
regarded the five regular bodies—the tetrahedron of twelve pentagonal faces, the corners of which the writing tablet takes up the analysis of an equi-
(four equilateral triangles), the hexahedron or have been truncated to produce equilateral trian- lateral triangle inscribed in a circle from book xm
cube (six squares), the octahedron (eight equilat- gles. Stellations with equilateral faces have been of Euclid's Elements, open in front of the mathe-
eral triangles), the dodecahedron (twelve penta- built out from each of the pentagonal and triangu- matician, while the lines and figures deal with the
gons), and the icosahedron (twenty equilateral lar faces of the truncated body. Following the proportional ratios and sums that occupied a good
triangles) — as the archetypal forms of the ele- publication of Pacioli's treatise in 1509, such com- deal of attention in Pacioli's Summa (Daly Davis
ments and the quintessence from which the plex bodies became popular motifs in intarsia 1977)-
cosmos was constructed. Pacioli allied this cosmo- designs and provided generations of authors on Other historical aspects of the portrait are far
logical geometry with the "divine" harmony of perspective with one of their greatest challenges. more problematic, including the identities of the
the golden section (i.e., the division of a line AB M.K. author of the painting and of the young man
at C such that ACiCB as AB:AC), which can be beside Pacioli. Taken at face value, the signature
used to construct the /2-degree angle of the pen- on the cartellino beside the book— jaco[po] bar-
tagon. Although Leonardo was not disposed to [bari] vigennis p[inxit] 149.— would appear to

244 CIRCA 1492