ax^2 + bx + c = 0where x is the unknown, and a,b,c, stand for given num-
bers could not have been written before 1637. The equal-
ity sign (=) was introduced by Robert Recorde in 1537,
and the custom of equating the function to zero was es-
tablished by René Descartes in 1637.
Exponents proved more troublesome. In his In artem
analyticam isagoge (1591) François VIÈTEhad, following
the Greek custom, written A^2 , A^3 , as AQ, and AC, where
the Q and C stood for “quadratus” and “cubus” respec-
tively. The modern convention of A^2 and A^3 dates, once
more, from Descartes, as does the use of letters of the al-
phabet to stand systematically for the unknowns. The
16th-century Italian mathematicians TARTAGLIAand CAR-
DANOwould have written the equation
x^3 + 6x = 12
as
cubus p: 6 rebus aequilis 12
which translates as
a cube plus 6 things equals 12.Despite the opacity of their notation, Tartaglia and Car-
dano still managed to make the first major breakthrough
in modern algebra. Neither Greek nor medieval mathema-
ticians had worked out a suitable algorithm for the solu-
tion of cubic or higher equations. Algebra seemed stuck at
the level of quadratics. In this latter field BOMBELLIhad
shown how quadratics could be solved by completing the
square, while solution by factorization was first worked
out by Thomas HARRIOT. Linear equations, by contrast,
tended to be solved by a number of traditional rules.
Known by such names as “the rule of false position” and
“the method of scales,” they could be applied quite me-
chanically.
There remained the cubic equation. In 1535 Tartaglia
publicly solved 30 cubics in a competition with the Italian
mathematician Scipione del Ferro. Four years later he re-
vealed his algorithm to Cardano, who unhesitatingly pub-
lished his own variant of the solution in Ars magna
(1545). Cardano also reported on the solution of the
biquadratic or quartic discovered by his pupil Ludovico
Ferrari (1522–c. 1560). To advance further, however, re-
quired the possession of techniques unknown to Renais-
sance mathematicians.
Allen, William (1532–1594) English Roman Catholic
scholar and cardinal (1587)
Refusal to comply with the conditions of the Protestant
settlement under Elizabeth I obliged him to relinquish his
academic post at Oxford and in 1565 to go into permanent
exile. He devoted his life to the training of priests for mis-
sions to England to reclaim the country for the Roman
Catholic Church, establishing colleges for that purpose at
DOUAI(1568), Rome (1575), and Valladolid (1589), and
instigating the Douai–Reims translation of the Bible into
English. However, his backing for the attempted Spanish
invasion of England in 1588 alienated many English
Catholics. He died at the ENGLISH COLLEGE, his foundation
in Rome.Alleyn, Edward (1566–1626) English tragic actor and
theatrical impresario
Having made his reputation on the London stage in the
1590s, he went into partnership with Philip Henslowe
(died 1616) to build the Fortune Theatre (1600). In 1604
they became joint masters of the royal bear-baiting estab-
lishment. Alleyn’s performances in roles such as MAR-
LOWE’s Faustus earned him comparisons with the classical
Roman actor Roscius. A shrewd businessman, he amassed
a considerable fortune from his theatrical and other prop-
erties, using it to buy up the manor of Dulwich, southeast
of London, where he founded (1616–19) “the College of
God’s Gift,” now the public school Dulwich College.Allori, Alessandro (c. 1535–1607) Italian painter
Allori was active in Florence, where he studied under his
uncle BRONZINO, of whom he was a close follower. A visit
to Rome (1554–56) also brought him under the influence
of MICHELANGELO, which is visible in his frescoes from the
early 1560s in SS. Annunziata, Florence. He was patron-
ized by Francesco I de’ Medici and contributed paintings
in the manner of Bronzino to the duke’s Studiolo in the
Palazzo Vecchio. Other work for the Medici includes dec-
oration in the Salone of their villa at Poggio a Caiano. His
later works, among them a Birth of the Virgin (1602; SS.
Annunziata, Florence) and an Ascension (1603; San
Michele, Prato), are in a softer, more relaxed style. His son
Cristofano (1577–1621) followed the emerging baroque
tendency in Florentine art. Cristofano’s best-known pic-
ture, Judith (Palazzo Pitti, Florence), incorporates por-
traits of the artist and his wife.Altdorfer, Albrecht (c. 1480–1538) German painter,
print maker, and architect
The son of an illuminator, Altdorfer became a citizen of
his home town of Regensburg in 1505. A member of Re-
gensburg city council since 1519, he was appointed sur-
veyor of public buildings in 1526. In 1535 he was chosen
as an ambassador to Vienna, possibly because of his
knowledge of the region.
Together with Wolf HUBERand the young CRANACH,
Altdorfer was a chief exponent of the socalled “Danube
style”. Possibly influenced by the pastoral poetry of Kon-
rad CELTIS, these painters delighted in portraying the lush
vegetation and dreamy enchantment of the German
woods. This fascination with the luxuriance of nature is
strongly apparent in Altdorfer’s tiny Berlin Satyr Family
(1507). Despite the emphatically Germanic location of1122 AAlllleenn,, WWiilllliiaamm