ca. 600
Hindu scholars invent
DECIMAL REPRESENTATION
, the
method of numeration we use today to represent
numbers.
ca. 640
Hindu mathematician and astronomer B
RAHMAGUPTA
(ca. 598–665) introduces
NEGATIVE NUMBERS
and the
concept of
ZERO
as a number into
ARITHMETIC
.
641
The Library of Alexandria is burned.
ca. 775
Arabic scholars begin translating the great Greek and
Indian works into Arabic.
ca. 830
M
UHAMMAD IBN
M–
USS
–
AAL
-K
HW
–
ARIZM
–
ı (ca. 780–850)
writes two influential texts founding the field of
ALGE
-
BRA
. Al-Khw–
arizm–
ı also promotes the use of the Hindu
base-10 system of
ARITHMETIC
.
850
Indian mathematician Mahavira writes the Ganita
Sera Samgraha (The compendium of the arithmetic),
the first Indian text devoted solely to the topic of
mathematics.
1079
Persian scholar O
MAR
K
HAYYAM
(ca. 1048–1131) cal-
culates the length of the year to be 365.24219858156
days, correct to the sixth decimal place.
1202
Italian number theorist F
IBONACCI
(ca. 1170–1250)
writes Liber abaci (The book of the abacus), introduc-
ing H
INDU
-A
RABIC NUMERALS
to western Europe.
Fibonacci also discovers the sequence 1, 1, 2, 3, 5, 8,
13, 21, 34,…
1360
French mathematician N
ICOLE
O
RESME
(ca. 1323–82)
discovers that the area under a velocity curve corre-
sponds to the distance traveled.
1482
The first printed edition of Euclid’s text T
HE
E
LE
-
MENTS
is produced in Venice, Italy. It becomes the most
translated and published textbook of all time.
1498
German scholar Johannes Widmann (1462–98) writes
Mercantile arithmetic in which the symbols “+” and
“–” appear in printed form for the first time.
1533
German scholar R
EGIOMONTANUS
(1436–76) publishes
the first comprehensive modern treatise on the topic of
TRIGONOMETRY
.
ca. 1541
Italian mathematician N
ICCOLÒ
T
ARTAGLIA
(ca.
1499–1557) discovers a general method for solving
CUBIC EQUATION
s. He tells his method, in confidence,
to G
IROLAMO
C
ARDANO
(1501–76) and L
UDOVICO
F
ERRARI
(1522–65), who publish the details without
his consent. Ferrari discovers a method for solving
QUARTIC EQUATION
s.
1557
Welsh mathematician R
OBERT
R
ECORDE
(ca. 1510–58)
introduces the symbol “=” for equality in the world’s
first algebra text printed in English.
1585
Dutch mathematician S
IMON
S
TEVIN
(1548–1620)
introduces decimal notation for fractions.
1591
French mathematician F
RANÇOIS
V
IÈTE
(1540–1603)
writes In artem analyticam isagoge (Introduction to the
analytical arts), establishing the principles of modern
ALGEBRA
and modern algebraic notation.
1594
Scottish mathematician J
OHN
N
APIER
(1550–1617)
begins his work on arithmetical techniques that eventu-
ally led to the discovery of
LOGARITHM
s. He publishes
his work in 1614.
1609
German astronomer and mathematician J
OHANNES
K
EPLER
(1571–1630) observes that the planets move in
elliptical orbits. Italian scientist G
ALILEO
G
ALILEI
(1564–1642) improves upon the invention of the tele-
scope and begins his own astronomical observations.
1622
British mathematician W
ILLIAM
O
UGHTRED
(1574–1660)
invents the slide rule. He introduces the symbol “×” for
multiplication and the abbreviations “sin” and “cos” for
sine and cosine, respectively.
Appendix I 541