THE RENAISSANCES OF THE TWELFTH CENTURY 245
since these organs happen to be in, as it were, a recessed location, women’s
modesty, not to mention the delicacy and sensitivity of these organs, com-
monly prevents them from bringing their troubles to male doctors. For that
reason I, out of sympathy for their situation and at the urging of a certain
prominent lady, began to study in earnest the maladies and complaints that
women are vulnerable to.
Trotula writes of diet, hygiene, skin care, menstruation, and pregnancy. Also how
to avoid the latter—and it is in some of her precise recommendations that we
perceive the survival of folk medicine within the broader Galenic theory.
Galen notes that “women with narrow vulvas and small wombs ought not to
marry, for they risk death if they become pregnant.” But since not all women
can avoid [marriage and pregnancy], they need help. If a woman fears death
and so seeks not to conceive, she should wear next to her naked flesh the
womb of a virgin she-goat....Shemight also try removing the testicles from
a weasel—without killing it—and wear them upon her bosom wrapped in
the skin of a goose or some other animal skin. Then she will not conceive.
Despite such passages, The Diseases of Women is filled with much valuable infor-
mation, especially on the use of medical herbs and ointments, and it became the
standard text on women’s health at Salerno. By the thirteenth century, however, a
new medical school opened up at Montpellier in southern France, and as it rose
to prominence Salerno and Trotula declined in influence.
More solid achievements were made in mathematics, geometry, and astron-
omy. Translators from England were especially important here. In the 1120s Ade-
lard of Bath, who learned Arabic in Sicily, translated an Arabized version of Eu-
clid’s work on geometry and ’al-Khwarizmi’s treatise on trigonometry.
’Al-Khwarizmi (800–847) is usually credited with having introduced “Arabic nu-
merals”—which actually originated in India—to the west. That might seem at first
like a relatively modest development; but European mathematics had long been
hampered by the use of Roman numerals, whose inherent limitations become ob-
vious if one tries to multiply mccxlviii by dcciv instead of 1248 by 704. Al-
Khwarizmi also wrote a book called The Restoration and Opposition of Numbers that
was translated by another Englishman, Robert of Chester, around 1150. So signif-
icant was this work that later Arab mathematicians referred to it simply as “The
Book,” which in Arabic is al-jibra—now the bane of many a Western adolescent.
The greatest Latin mathematician of the Middle Ages was Leonardo Fibonacci
(1170–1230), sometimes known as Leonardo Pisanus or Leonardo of Pisa. He made
his mark in 1202 when he published his Book on the Abacus, in which he explored
the possibilities of decimal-based mathematics. He developed a sequence of num-
bers known as the Fibonacci sequence that was to have important implications. It
goes like this:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...
In the sequence, each number is the sum of the two numbers that precede it.
Fibonacci developed the algebraic formula to express this sequence; it is called a
recursion relation. The significance of the formula, for our purposes at least, is that
it describes a surprising number of natural phenomena. The formula, when
mapped on a graph, corresponds exactly with the spiral arrangement of petals on
flowers, the curve of snail shells, the twisting array of branches around the trunk
of a tree. The ratio of pine leaves on opposed spirals of a pine cone is always 5:
8; of bumps on a mature pineapple 8:13; of seeds in the center of a sunflower 21: