be an integral part of a formal education elevates the
status of mathematics within the Western world.
ca. 386 B.C.E.
The oracle of Delos tells the people of Athens that in
order to end a plague they must double the size of the
cube-shaped altar to the god Apollo. This establishes
the problem of DUPLICATING THE CUBE.
ca. 370 B.C.E.
EUDOXUS OF CNIDUS (ca. 400–350 B.C.E.) develops a
“method of exhaustion” to determine the areas of simple curved figures. The method is a precursor to the
notion of LIMIT developed in 18th-century CALCULUS.
ca. 350 B.C.E.
ARISTOTLE (ca. 384–322 B.C.E.) analyzes the structure
of ARGUMENTs and logical reasoning to develop ideas
seminal to the field of FORMAL LOGIC.
ca. 310 B.C.E.
Ruler Ptolemy Soter founds the Library of Alexandria.
It remains the center of intellectual learning for more
than 700 years.
ca. 300 B.C.E.
Greek geometer EUCLID summarizes all mathematical
knowledge known at his time in THE ELEMENTS. The
method of logical deduction and rigor he provides
remains the paradigm of mathematical thinking today.
ca. 240 B.C.E.
ARCHIMEDES OF SYRACUSE (ca. 287–212 B.C.E.) uses
the method of exhaustion to compute the area under a
section of a PARABOLA. He also makes fundamental
contributions to the fields of geometry, engineering,
astronomy, and hydrostatics. He discovers a method of
computing the value π to any degree of accuracy and
shows, in particular, that its values lies between 3
10/71 and 3 1/7.
ca. 230 B.C.E.
ERATOSTHENES OF CYRENE (ca. 275–195 B.C.E.) calculates the circumference of the EARTH to be 28,500
miles. He develops the SIEVE OF ERATOSTHENES for
computing PRIME numbers.
ca. 220 B.C.E.
APOLLONIUS OF PERGA (ca. 262–190 B.C.E.) develops
the study of CONIC SECTIONS. He also develops a theory of EPICYCLEs to model planetary motion.
ca. 214 B.C.E.
Construction begins on the Great Wall of China.
ca. 150 B.C.E.
Hipparchus of Nicaea (ca. 190–126 B.C.E.) develops
beginning ideas in the theory of TRIGONOMETRY. He
uses geometry to calculate the distances of the Sun and
the Moon from the Earth.
ca. 100 B.C.E.
Chinese scholars write JIUZHANG SUANSHU (Nine
chapters on the mathematical arts). The text includes
solutions to linear and QUADRATIC equations, the computation of areas and volumes, a statement of
PYTHAGORAS’S THEOREM, and the use of NEGATIVE
NUMBERS.
ca. 140
Greek astronomer CLAUDIUS PTOLEMY writes the
Almagest, the most influential work in mathematical
astronomy until the 16th century. It includes a table of
chord values equivalent to a modern-day table of sines.
He uses the value 377/120 for π.
ca. 250
Greek mathematician DIOPHANTUS OF ALEXANDRIA
writes Arithmetica. He is the first to use symbols to
represent unknown quantities.
ca. 320
PAPPUS OF ALEXANDRIA attempts to revive interest in
the classical Greek pursuit of mathematics. He writes
Synagoge (Collections) as a guide to the great Greek
works.
ca. 370
HYPATIA (ca. 370–415), the first woman named in the
history of mathematics, is born. She becomes head of
the Platonist school in Alexandria.
ca. 475
Indian astronomer and mathematician ARYABHATA
(ca. 476–550) is born. He develops methods for
extracting square roots, summing arithmetic series,
and computing chord values. He uses the value
3.1416 for π.
ca. 480
Chinese scholar ZU CHONGZHI (430–500) uses the
value 355/113 for π.
540 Appendix I
status of mathematics within the Western world.
ca. 386 B.C.E.
The oracle of Delos tells the people of Athens that in
order to end a plague they must double the size of the
cube-shaped altar to the god Apollo. This establishes
the problem of DUPLICATING THE CUBE.
ca. 370 B.C.E.
EUDOXUS OF CNIDUS (ca. 400–350 B.C.E.) develops a
“method of exhaustion” to determine the areas of simple curved figures. The method is a precursor to the
notion of LIMIT developed in 18th-century CALCULUS.
ca. 350 B.C.E.
ARISTOTLE (ca. 384–322 B.C.E.) analyzes the structure
of ARGUMENTs and logical reasoning to develop ideas
seminal to the field of FORMAL LOGIC.
ca. 310 B.C.E.
Ruler Ptolemy Soter founds the Library of Alexandria.
It remains the center of intellectual learning for more
than 700 years.
ca. 300 B.C.E.
Greek geometer EUCLID summarizes all mathematical
knowledge known at his time in THE ELEMENTS. The
method of logical deduction and rigor he provides
remains the paradigm of mathematical thinking today.
ca. 240 B.C.E.
ARCHIMEDES OF SYRACUSE (ca. 287–212 B.C.E.) uses
the method of exhaustion to compute the area under a
section of a PARABOLA. He also makes fundamental
contributions to the fields of geometry, engineering,
astronomy, and hydrostatics. He discovers a method of
computing the value π to any degree of accuracy and
shows, in particular, that its values lies between 3
10/71 and 3 1/7.
ca. 230 B.C.E.
ERATOSTHENES OF CYRENE (ca. 275–195 B.C.E.) calculates the circumference of the EARTH to be 28,500
miles. He develops the SIEVE OF ERATOSTHENES for
computing PRIME numbers.
ca. 220 B.C.E.
APOLLONIUS OF PERGA (ca. 262–190 B.C.E.) develops
the study of CONIC SECTIONS. He also develops a theory of EPICYCLEs to model planetary motion.
ca. 214 B.C.E.
Construction begins on the Great Wall of China.
ca. 150 B.C.E.
Hipparchus of Nicaea (ca. 190–126 B.C.E.) develops
beginning ideas in the theory of TRIGONOMETRY. He
uses geometry to calculate the distances of the Sun and
the Moon from the Earth.
ca. 100 B.C.E.
Chinese scholars write JIUZHANG SUANSHU (Nine
chapters on the mathematical arts). The text includes
solutions to linear and QUADRATIC equations, the computation of areas and volumes, a statement of
PYTHAGORAS’S THEOREM, and the use of NEGATIVE
NUMBERS.
ca. 140
Greek astronomer CLAUDIUS PTOLEMY writes the
Almagest, the most influential work in mathematical
astronomy until the 16th century. It includes a table of
chord values equivalent to a modern-day table of sines.
He uses the value 377/120 for π.
ca. 250
Greek mathematician DIOPHANTUS OF ALEXANDRIA
writes Arithmetica. He is the first to use symbols to
represent unknown quantities.
ca. 320
PAPPUS OF ALEXANDRIA attempts to revive interest in
the classical Greek pursuit of mathematics. He writes
Synagoge (Collections) as a guide to the great Greek
works.
ca. 370
HYPATIA (ca. 370–415), the first woman named in the
history of mathematics, is born. She becomes head of
the Platonist school in Alexandria.
ca. 475
Indian astronomer and mathematician ARYABHATA
(ca. 476–550) is born. He develops methods for
extracting square roots, summing arithmetic series,
and computing chord values. He uses the value
3.1416 for π.
ca. 480
Chinese scholar ZU CHONGZHI (430–500) uses the
value 355/113 for π.
540 Appendix I