148
Chapter 11
The Middle Ages
In mathematics as in other fields, to find one self lost in wonder at some
manifestation is frequently the half of a new discoveryDirichlet
As we prepare to enter the age of European Hegemony, an age which eventually gives
r
1
Chapter 1
Roots
I wish I knew as much as I thought I
knew 10 years agoNeugebauer
As one begins to contemplate the history of mathematics, one begins to appreciate the
vastness of its panorama. Mathematics, together with music and art, must be among the
61
Chapter 6
Early Alexandria
Geometry that held acquaintance with the stars,
And wedded soul to soul in purest bond
Of reason, undisturbed by space or time
Wordsworth
After Plato's Academy had lost some luster, the Museum in
Alexandria became the most re
103
Chapter 8
India
It is true that a mathematician, who is not somewhat of a poet,
will never be a perfect mathematicianWeierstrass
We now travel to the East to keep up with mathematical tradition. As we mentioned in
one of the disclaimers in the preface
44
Chapter 5
Athens
Let no one ignorant of geometry enter my doorPlatos Academy
It was perhaps the devastating discovery of the irrationality of the square root of 2 that
sent such quivers down the Greek mathematical spine that they are, for several centu
14
Chapter 2
Mesopotamia
What science can there be more noble, more excellent, more useful
for men, more admirably high and demonstrative, than this of the
mathematicsB. Franklin
The two oldest major civilizations, which are often referred to as the cradl
28
Chapter 4
Greek Beginnings
As
. there was far more imagination in the head of
Archimedes than in that of HomerVoltaire
we start discussing the truly wonderful and imaginative world of Greek
mathematics, there is a basic idea to keep in mind. The basic
182
Chapter 13
Gateway to Our Times
Number, place, and combinationthe three intersecting but distinct spheres of
thought to which all mathematical ideas admit of being referredSylvester
As we enter the seventeenth century, we enter an
age where present da
88
Chapter 7
Greek Twilight
In questions of science the authority of a thousand is not worth
the humble reasoning of a single individualGalileo
As we ended the last chapter, the Romans were about to conquer Cartage, and within
150 years of Archimedes' dea
216
Chapter 14
The Birth of Calculus
He who can digest a second or third fluxion, a second or third difference, need
not, methinks, be squeamish about any point in Divinity.
And what are these fluxions? The velocities of evanescent increments. And what
ar
116
Chapter 9
Islam
Algebra is generous, she often gives more than is asked of herDAlembert
Mohammed, the prophet died in
632 AD. By the year 750, his
influence, through both political
and religious conversion, had
spread from China to Spain.
Although the
131
Chapter 10
China
As the prerogative of Natural Science is to cultivate a taste for observation,
so that of Mathematics is, almost from the starting point,
to stimulate the faculty of inventionSylvester
We continue our journey to the East by visiting t
159
Chapter 12
The Renaissance
The miraculous powers of modern calculation are due to three inventions: the
Arabic Notation, Decimal Fractions and LogarithmsCajori
In the early stages of the Renaissance, Italy, due
to its privileged geographical, economic
21
Chapter 3
Egypt
The Nile is nothing else than the year, because the numbers expressed by
the letters , Nile, are in Greek arithmetic, = 50 , = 5 , = 10 ,
= 30 , = 70 , = 200 ; and these figures make up together 365
Heliodorus
The other major ancient