render a contemporary event, was com-
pleted by 1425 but since that time has been
destroyed.
Very few other works of Masaccio’s
have survived into modern times, but on
these paintings rests his reputation as a
highly skilled and original painter. He col-
laborated with Tommaso Masolino on a
polyptych, or multipaneled altarpiece, for
the church of Santa Maria del Carmine in
Pisa. This work was broken apart and
found its way to several museums. The
central panel, theMadonna and Child En-
throned, was flanked by portraits of Saint
Paul and Saint Andrew.
Masaccio also completed an important
series of frescoes in the Brancacci chapel
of the Church of Santa Maria del Carmine
in Florence, as well as a fresco of the Trin-
ity in the church of Santa Maria Novella.
The Brancacci chapel fresco was commis-
sioned by Felice Brancacci to Masaccio and
his collaborator Masolino da Panicale. The
paintings include depictions of biblical
events, set in a classical world: theExpul-
sion from the Garden of Eden, Tribute
Money, St. Peter Baptizing, Miracle of the
Shadow, andSt. Peter and St. John Distrib-
uting Alms. Inspired by the new sculpture
of Donatello’s, Masaccio composed power-
fully expressive and monumental figures,
an important change from the slender,
ethereal figures of the saints that were a
tradition in European Gothic art. He de-
picted a wide range of emotional expres-
sion and more realistic human emotion,
skillfully used light to sharpen and define
contours, and incorporated classical archi-
tecture to reflect the new respect artists
were showing for the works of the ancient
Romans. The invention of artificial per-
spective by Brunelleschi also had an im-
portant impact on Masaccio. The painter
used foreshortening of the figures and per-
spective as a means of guiding the specta-
tor of the paintings to certain elements of
the work, and of setting the figures in a
more dramatic, natural world. This ap-
proach revolutionized painting and set the
stage for the monumental and powerfully
realistic paintings of the Renaissance.
The Brancacci chapel frescoes became
a place of pilgrimage and study for many
major Italian artists, including Michelan-
gelo Buonarroti, Leonardo da Vinci, San-
dro Botticelli, Andrea del Verrocchio, An-
drea del Sartro, and many others. Before
completing this work, however, Masaccio
left for Rome, where he died at the young
age of twenty-six.SEEALSO: Brunelleschi, Filippo; Donatello;
Florence; paintingmathematics .....................................
Mathematical knowledge in medieval Eu-
rope was strongly influenced by treatises
of Arabic scholars that were imported to
the continent from Sicily and Moorish-
controlled Iberia (modern Spain and
Portugal), and by the works of ancient
Greeks such as Ptolemy, Erastothenes, and
Euclid that had survived in Arabic ver-
sions and were later translated into Latin.
The Italian scientist Leonardo Fibonacci
had revived original research in the thir-
teenth century. The calculation of speed
and uniform motion were problems tack-
led by a school of mathematicians known
as the Oxford Calculators of the fourteenth
century. Everyday calculation, however, was
still a difficult process. It involved the use
of cumbersome Roman numerals and
complex methods of doing division and
multiplication—without the use of alge-
braic symbols and mathematical signs.
The study of mathematics was spurred
by growing trade and international bank-
ing, which followed an earlier period of
localized trade and the barter system. Themathematics