to question the value assigned to final causes. “Research
into final causes,” Bacon asserted, “like a virgin dedicated
to God is barren and produces nothing.”
Although Bacon’s strictures found wide support
among a later generation of physicists, Renaissance biolo-
gists remained uncompromisingly Aristotelian. Conse-
quently, Aristotle’s classification of animals on the basis of
their modes of reproduction and development remained
without serious challenge until the 18th century. In the
field of generation, using concepts derived from his meta-
physics, Aristotle argued that the female parent con-
tributed the matter of the embryo and the male parent its
form. It was precisely this view that William HARVEYbegan
to consider in the opening chapter of his De generatione
animalium (1651).
As a final area of intellectual domination there re-
mains Aristotelian logic. Despite the objections of Ramus
and Bacon, the bulk of Renaissance logic textbooks
worked exclusively within the parameters set out by Aris-
totle in the Organon, as indeed did the textbooks of the
17th and 18th centuries. It should, however, be remem-
bered that traditions other than Aristotelianism were pre-
sent during the Renaissance, and that, in their own way,
NEOPLATONISM, skepticism, and atomism exercised a com-
parable influence.
See also: CRITICISM, LITERARY
Further reading: David A. Lines, Aristotle’s Ethics in
the Italian Renaissance (1300–1600): The Universities and
the Problem of Moral Education (Leyden, Netherlands:
Brill, 2002); Charles B. Schmitt, Aristotle and the Renais-
sance (Cambridge, Mass.: Harvard University Press,
1983).
Aristotle (384–322 BC) Greek philosopher
He was born at Stagira (hence allusions to him as “the Sta-
girite”) and studied philosophy at Athens under PLATOfor
20 years from 367. After short spells teaching at Assos in
the Troad and Mytilene he became (342) tutor to Alexan-
der the Great. In 335 he returned to Athens to found his
own philosophical school, the disciples of which were
known as Peripatetics on account of the master’s habit of
walking to and fro while teaching.
The huge quantity of Aristotle’s surviving works cover
a vast range of subjects: logic, physics, biology, psychol-
ogy, metaphysics, politics, ethics, rhetoric, and poetry.
Many of the treatises were known to medieval scholars in
the West only through Latin translations of Arabic ver-
sions. Nonetheless his works were the basis of the pre-
dominant scholastic philosophy, and although there was
some reaction against him in the Renaissance, especially
in favor of PLATO, he continued to dominate philosophical
and scientific discourse well into the 17th century (see
ARISTOTELIANISM, RENAISSANCE). In the 16th century his
rediscovered Poetics became the basis of Renaissance liter-
ary theory (see CRITICISM, LITERARY), affecting the status
and composition of both EPICand TRAGEDY.arithmetic Both the Greeks and the Romans had repre-
sented numbers with letters of their alphabets, a custom
that mattered little as long as problems were presented
geometrically, and as long as calculations were performed
on an ABACUS. A more sophisticated arithmetic required a
more lucid symbolism, which was first provided by the
mathematicians of the Renaissance. Hindu numerals en-
tered Europe through Islam. They were picked up by Ger-
bert in 10th-century Spain and later used by Leonardo of
Pisa in his influential Liber abaci (1202). Consequently, by
the time of the Renaissance, there was a growing need to
develop appropriate algorithms in the new symbolism for
the basic arithmetical operations of multiplication, divi-
sion, subtraction, addition, exponentiation, and the ex-
traction of roots. The result was a number of elementary
textbooks appearing throughout Europe, all designed to
convey the secrets of the new arithmetic to a public be-
coming increasingly concerned with numerical problems
arising in commerce. Such works as PACIOLI’s Somma
(1494), Robert Recorde’s Grounde of Artes (1540), and
Michael Stifel’s Arithmetica integra (1544) performed this
task in France, Italy, England, and Germany respectively.
A bewildering variety of methods was presented, suffi-
ciently complex to engender the belief that long division
could be performed only by a professional mathematician.
The Renaissance also saw extensions to the concept of
number. CARDANO, for example, in his Ars magna (1545),
accepted into mathematics the long-suspected negative
and complex numbers. Later in the century decimals were
introduced by Simon STEVIN, and in 1614 John NAPIER
successfully introduced the notion of a logarithm. He had
not, however, expressed his logarithms in terms of a deci-
mal base. This latter innovation was carried through by
Henry BRIGGSwho published in 1617 a table of logarithms
to the base 10 of the numbers 1 to 1000.Armada See SPANISH ARMADAarmillary spheres Astronomical instruments consisting
of linked adjustable rings (the name derives from Latin
armilla: bracelet) representing the circles of the celestial
sphere such as the ecliptic and equator. A sphere in the
center represents the earth. Used by Hipparchus (second
century BCE) they were described by Ptolemy in his Al-
magest (see PTOLEMAIC SYSTEM) and later became an indis-
pensable tool of Renaissance astronomers. Fitted with
sights (alidades), they could be used to make quite precise
measurements. One of the most accurate of such instru-
ments, with a diameter of nearly nine feet, was built by
Tycho BRAHEat his Uraniborg observatory.3300 AArriissttoottllee