Page 244 - Art In The Age Of Exploration (Great Section on Chinese Art Ming Dynasty)

Although Pacioli was not a mathematician of
great originality on his own account, he was an
important author in terms of the early history of
mathematics in print. A member of the Franciscan
order, he spent a peripatetic career in a number of
the major Italian centers of learning, including
Venice, Urbino, Rome, Bologna, Milan, and Flor-
ence. Of particular significance for the production
of De divina proportione were his contacts with
Piero della Francesca in Urbino and with Leonardo
da Vinci in Milan. His treatment of the geomet-
rical solids is closely dependent upon Piero's trea-
tises, to the extent that Pacioli has been accused of
plagiarism, a charge hardly justified in light of the
standard techniques of copy and commentary in
the manuscript tradition of the late Middle Ages
and early Renaissance.
Pacioli arrived in Milan in 1496 and persuaded
Leonardo to draw the illustrations for his book on
the five regular or "Platonic" solids and some of
their semiregular variants. In his De viribus
quantitatis, Pacioli indicated that the illustrations
were "made and formed by the ineffable left
hand" of the "most worthy of painters, perspec-
tivists, architects and musicians, one endowed
with every perfection, Leonardo da Vinci the
Florentine, in Milan at the time when we were
both in the employ of the most illustrious Duke of
Milan, Ludovico Maria Sforza Anglo, in the years
of our Lord 1496 to 1499, whence we departed
together for various reasons and then shared
quarters at Florence."
The illustration of the geometrical solids in
previous geometrical treatises, including Luca's
own Summa de arithmetica of 1494, gave little
sense of the existence of real forms in measurable
space and were difficult to read coherently. Pacioli
142 stated that he had already constructed the Platonic
chapel in Masaccio's Trinity, though for the pur- bodies as actual solids, probably in various mate-
poses of this basic demonstration Piero does not After Leonardo da Vinci rials such as wood and glass (as depicted in his
use Masaccio's low viewpoint. Piero does not portrait in Naples [cat. 143]). He was later to be
intend this construction to be used as it stands for DODECAHEDRON paid by the Florentine government for a set of
a particular painting; rather he provides the geometrical solids (Kemp 1989). It is not known
student with the resources necessary to tackle from Luca Pacioli, De divina proportione, whether the brilliant idea of illustrating the poly-
such a construction when the need arises, as, for Venice, 1509 hedra perspectivally in both solid and skeletal
3
instance, when painting a sacra conversazione. 28.5 X 19.5 (llV4 X 7 /4J 1956; Rose 1975; forms should be credited to Pacioli or to Leonardo.
references:
Fontes Ambrosiani
The existence of four Latin manuscripts of Kemp 1989; Kemp igSya; Dalai Emiliani 1984 Although the solids are depicted very convinc-
Piero's treatise indicates that it was taken up in ingly in three dimensions, with carefully
learned circles outside the artists' studios. It was Library of Congress, Washington described cast shadows, their perspectival pro-
known to, among others, Luca Pacioli, who exten- jection is not mathematically precise in every
sively adopted ideas from Piero's other writings in Pacioli's treatise was produced in two manuscript respect. This suggests that they were not drawn
his publications, to Albrecht Diirer (either directly versions, the better of which was made for using the kind of point-by-point technique of
or via an intermediary), to the mathematician Galeazzo Sanseverino in Milan in 1498 and is now mathematical projection described by Piero della
Ignatio Danti, and probably also to Leonardo da in the Biblioteca Ambrosiana (MS S.P. 6) . The Francesca, but rather that Leonardo used a draw-
Vinci. Its most direct influence was on Daniele second manuscript, in the Bibliotheque Publique ing frame or "veil" or "glass," such as that he
Barbaro's La practica della perspettiva published et Universitaire in Geneva, has a fine frontispiece showed a draftsman using to depict an armillary
in Venice in 1569. Barbaro relied heavily upon dedicating it to Galeazzo's father-in-law, Duke sphere (Codice atlantico 51). The illustrations in
Piero's methods, although he avoided Piero's Ludovico Sforza, but it is otherwise a disorderly the treatises could have been produced by pricking
laborious line by line expositions, which he con- and inferior version and must be regarded as a through the corners of the facets of each body on
sidered to be addressed to "idiots." Through later compilation. The text and illustrations were the master drawing and transferring the prick
Barbaro's well-regarded treatise, Piero's lucid published in amplified form by the printer Paga- marks to the intended page. Prick marks, incised
methods entered the general currency of perspec- nini in Venice in 1509 and dedicated to the Gonfa- lines, and pentimenti in the Milan manuscript
tive theory during succeeding centuries. M.K. loniere of Florence, Piero Soderini. bear witness to the care that went into its produc-

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