__CRONOLOGIA DI STORIA
MATEMATICA (30.000 a.C.-1500)__

**http://www-groups.dcs.st-and.ac.uk/~history/Chronology/index.html**

**About 30000BC
Palaeolithic peoples in central Europe and France record numbers on bones.**

**About 25000BC
Early geometric designs used.**

**About 5000BC
A decimal number system is in use in Egypt.**

**About 4000BC
Babylonian and Egyptian calendars in use.**

**About 3400BC
The first symbols for numbers, simple straight lines, are used in Egypt.**

**About 3000BC
The abacus
is developed in the Middle East and in areas around the Mediterranean. A
somewhat different type of abacus is used in China.**

**About 3000BC
Hieroglyphic numerals in use in Egypt. **

**About 3000BC
Babylonians begin to use a sexagesimal
number system for recording financial transactions. It is a place-value system
without a zero place value. **

**About 2770BC
Egyptian calendar used.**

**About 2000BC
Harappans adopt a uniform decimal system of weights and measures.**

**About 1950BC
Babylonians solve quadratic
equations.**

**About 1900BC
The Moscow papyrus (also called the Golenishev papyrus) is written. It gives
details of Egyptian geometry.**

**About 1850BC
Babylonians know Pythagoras's
Theorem. **

**About 1800BC
Babylonians use multiplication tables.**

**About 1750BC
The Babylonians solve linear and quadratic algebraic equations, compile tables
of square and cube roots. They use Pythagoras's
theorem and use mathematics to extend knowledge of astronomy.**

**About 1700BC
The Rhind papyrus (sometimes called the Ahmes
papyrus) is written. It shows that Egyptian mathematics has developed many
techniques to solve problems. Multiplication is based on repeated doubling, and
division uses successive halving. **

**About 1360BC
A decimal number system with no zero starts to be used in China.**

**About 1000BC
Chinese use counting boards for calculation.**

**About 800BC
Baudhayana
is the author of one of the earliest of the Indian Sulbasutras. **

**About 750BC
Manava
writes a Sulbasutra. **

**About 600BC
Apastamba
writes the most interesting Indian Sulbasutra from a mathematical point of view. **

**575BC
Thales
brings Babylonian mathematical knowledge to Greece. He uses geometry to solve
problems such as calculating the height of pyramids and the distance of ships
from the shore.**

**About 540BC
Counting rods used in China.**

**530BC
Pythagoras
of Samos moves to Croton in Italy and teaches mathematics, geometry, music,
and reincarnation.**

**About 500BC
Panini's
work on Sanskrit grammar is the forerunner of the modern formal language theory.**

**About 500BC
The Babylonian sexagesimal
number system is used to record and predict the positions of the Sun, Moon and
planets. **

**About 500BC
Panini's
work on Sanskrit grammar is the forerunner of the modern formal language theory.**

**About 465BC
Hippasus writes of a "sphere of 12 pentagons", which must refer to a dodecahedron.**

**About 450BC
Greeks begin to use written numerals. **

**About 450BC
Zeno
of Elea presents his paradoxes.**

**About 440BC
Hippocrates
of Chios writes the Elements which is the first compilation of the
elements of geometry.**

**About 430BC
Hippias
of Elis invents the quadratrix which may have been used by him for trisecting
an angle and squaring
the circle.**

**About 425BC
Theodorus
of Cyrene shows that certain square roots are irrational.
This had been shown earlier but it is not known by whom.**

**About 400BC
Babylonians use a symbol to indicate an empty place in their numbers recorded in
cuneiform writing. There is no indication that this was in any way thought of as
a number. **

**387BC
Plato
founds his Academy in Athens**

**About 375BC
Archytas
of Tarentum develops mechanics. He studies the "classical problem"
of doubling
the cube and applies mathematical theory to music. He also constructs
the first automaton.**

**About 360BC
Eudoxus
of Cnidus develops the theory of proportion, and the method of exhaustion.**

**About 340BC
Aristaeus
writes Five Books concerning Conic
Sections.**

**About 330BC
Autolycus
of Pitane writes On the Moving Sphere which studies the geometry of
the sphere. It is written as an astronomy text.**

**
About 320BC
Eudemus
of Rhodes writes the History of Geometry.**

**About 300BC
Euclid
gives a systematic development of geometry in his Stoicheion (The
Elements). He also gives the laws of reflection in Catoptrics.**

**About 290BC
Aristarchus
of Samos uses a geometric method to calculate the distance of the Sun and
the Moon from Earth. He also proposes that the Earth orbits the Sun.**

**About 250BC
In On the Sphere and the Cylinder, Archimedes
gives the formulae for calculating the volume of a sphere and a cylinder. In Measurement
of the Circle he gives an approximation of the value of p
with a method which will allow improved approximations. In Floating Bodies
he presents what is now called "Archimedes' principle" and begins the
study of hydrostatics. He writes works on two- and three-dimensional geometry,
studying circles, spheres and spirals. His ideas are far ahead of his
contemporaries and include applications of an early form of integration.**

**About 235BC
Eratosthenes
of Cyrene estimates the Earth's circumference with remarkable accuracy
finding a value which is about 15% too big.**

**About 230BC
Nicomedes
writes his treatise On conchoid lines which contain his discovery of the
curve known as the "Conchoid of Nicomedes".**

**About 225BC
Apollonius
of Perga writes Conics in which he introduces the terms "parabola",
"ellipse"
and "hyperbola".**

**About 230BC
Eratosthenes
of Cyrene develops his sieve method for finding all prime
numbers. **

**About 200BC
Diocles
writes On burning mirrors, a collection of sixteen propositions in
geometry mostly proving results on conics.**

**About 200BC
Possible earliest date for the classic Chinese work Jiuzhang suanshu or Nine
Chapters on the Mathematical Art. **

**About 180BC
Date of earliest Chinese document Suanshu shu (A Book on Arithmetic).**

**127BC
Hipparchus
discovers the precession of the equinoxes and calculates the length of the year
to within 6.5 minutes of the correct value. His astronomical work uses an early
form of trigonometry.**

**About 150BC
Hypsicles
writes On the Ascension of Stars. In this work he is the first to divide
the Zodiac into 360 degrees.**

**About 20
Geminus
writes a number of astronomy texts and The Theory of Mathematics. He
tries to prove the parallel
postulate. **

**About 60
Heron
of Alexandria writes Metrica (Measurements). It contains
formulas for calculating areas and volumes.**

**About 90
Nicomachus
of Gerasa writes Arithmetike eisagoge (Introduction to Arithmetic)
which is the first work to treat arithmetic as a separate topic from geometry.**

**About 110
Menelaus
of Alexandria writes Sphaerica which deals with spherical triangles
and their application to astronomy.**

**About 150
Ptolemy
produces many important geometrical results with applications in astronomy. His
version of astronomy will be the accepted one for well over one thousand years.**

**About 250
The Maya civilization of Central America uses an almost place-value number
system to base 20. **

**250
Diophantus
of Alexandria writes Arithmetica, a study of number theory problems
in which only rational
numbers are allowed as solutions.**

**263
By using a regular polygon with 192 sides Liu Hui calculates the value of p
as 3.14159 which is correct to five decimal places. **

**301
Iamblichus
writes on astrology and mysticism. His Life of Pythagoras is a
fascinating account.**

**340
Pappus
of Alexandria writes Synagoge (Collections) which is a guide
to Greek geometry.**

**390
Theon
of Alexandria produces a version of Euclid's
Elements (with textual changes and some additions) on which almost all
subsequent editions are based.**

**About 400
Hypatia
writes commentaries on Diophantus
and Apollonius.
She is the first recorded female mathematician and she distinguishes herself
with remarkable scholarship. She becomes head of the Neo-Platonist school at
Alexandria.**

**450
Proclus,
a mathematician and Neo-Platonist, is one of the last philosophers at Plato's
Academy at Athens.**

**About 460
Zu
Chongzhi gives the approximation ^{355}/_{113} to p
which is correct to 6 decimal places. **

**499
Aryabhata
I calculates p to be 3.1416. He produces his Aryabhatiya,
a treatise on quadratic equations, the value of p,
and other scientific problems.**

**About 500
Metrodorus assembles the Greek Anthology consisting of 46 mathematical
problems.**

**510
Eutocius
of Ascalon writes commentaries on Archimedes'
work.**

**510
Boethius
writes geometry and arithmetic texts which are widely used for a long time.**

**About 530
Eutocius
writes commentaries on the works of Archimedes
and Apollonius.**

**532
Anthemius
of Tralles, a mathematician of note, is the architect for the Hagia Sophia
at Constantinople.**

**534
Chinese mathematics is introduced into Japan.**

**575
Varahamihira
produces Pancasiddhantika (The Five Astronomical Canons). He makes
important contributions to trigonometry.**

**594
Decimal notation is used for numbers in India. This is the system on which our
current notation is based. **

**628
Brahmagupta
writes Brahmasphutasiddanta (The Opening of the Universe), a work
on astronomy; on mathematics. He uses zero and negative numbers, gives methods
to solve quadratic equations, sum series, and compute square roots.**

**644
Li
Chunfeng starts to assemble the Chinese Ten Mathematical Classics. **

**About 700
Mathematicians in the Mayan civilization introduce a symbol for zero into their
number system. **

**About 775
Alcuin
of York writes elementary texts on arithmetic, geometry and astronomy.**

**About 810
House of Wisdom set up in Baghdad. There Greek and Indian mathematical and
astronomy works are translated into Arabic.**

**About 810
Al-Khwarizmi
writes important works on arithmetic, algebra, geography, and astronomy. In
particular Hisab al-jabr w'al-muqabala (Calculation by Completion and
Balancing), gives us the word "algebra", from "al-jabr".
From al-Khwarizmi's name, as a consequence of his arithmetic book, comes the
word "algorithm".**

**About 850
Thabit
ibn Qurra makes important mathematical discoveries such as the extension of
the concept of number to (positive) real numbers, integral calculus, theorems in
spherical trigonometry, analytic geometry, and non-euclidean
geometry.**

**About 850
Thabit
ibn Qurra writes Book on the determination of amicable numbers which
contains general methods to construct amicable
numbers. He knows the pair of amicable numbers 17296, 18416.**

**850
Mahavira
writes Ganita Sara Samgraha. It consists of nine chapters and includes
all mathematical knowledge of mid-ninth century India.**

**900
Sridhara
writes the Trisatika (sometimes called the Patiganitasara) and the
Patiganita. In these he solves quadratic equations, sums series, studies combinations,
and gives methods of finding the areas of polygons.**

**About 900
Abu
Kamil writes Book on algebra which studies applications of algebra to
geometrical problems. It will be the book on which Fibonacci
will base his works.**

**920
Al-Battani
writes Kitab al-Zij a major work on astronomy in 57 chapters. It contains
advances in trigonometry.**

**950
Gerbert of Aurillac (later Pope Sylvester II) reintroduces the abacus into
Europe. He uses Indian/Arabic numerals without having a zero.**

**About 960
Al-Uqlidisi
writes Kitab al-fusul fi al-hisab al-Hindi which is the earliest
surviving book that presents the Hindu system.**

**About 970
Abu'l-Wafa
invents the wall quadrant for the accurate measurement of the declination
of stars in the sky. He writes important books on arithmetic and geometric
constructions. He introduces the tangent function and produces improved methods
of calculating trigonometric tables.**

**976
Codex Vigilanus copied in Spain. Contains the first evidence of decimal
numbers in Europe.**

**About 990
Al-Karaji
writes Al-Fakhri in Baghdad which develops algebra. He gives Pascal's
triangle.**

**About 1000
Ibn
al-Haytham (often called Alhazen) writes works on optics, including a theory
of light and a theory of vision, astronomy, and mathematics, including geometry
and number theory. He gives Alhazen's problem: Given a light source and a
spherical mirror, find the point on the mirror were the light will be reflected
to the eye of an observer.**

**About 1010
Al-Biruni
writes on many scientific topics. His work on mathematics covers arithmetic,
summation of series, combinatorial analysis, the rule of three, irrational
numbers, ratio theory, algebraic definitions, method of solving algebraic
equations, geometry, Archimedes' theorems, trisection
of the angle and other problems which cannot be solved with ruler
and compass alone, conic sections, stereometry, stereographic
projection, trigonometry, the sine theorem in the plane, and solving
spherical triangles.**

**About 1020
Ibn
Sina (usually called Avicenna) writes on philosophy, medicine, psychology,
geology, mathematics, astronomy, and logic. His important mathematical work Kitab
al-Shifa' (The Book of Healing) divides mathematics into four major
topics, geometry, astronomy, arithmetic, and music.**

**1040
Ahmad
al-Nasawi writes al-Muqni'fi al-Hisab al-Hindi which studies four
different number systems. He explains the operations of arithmetic, particularly
taking square and cube roots in each system.**

**About 1050
Hermann
of Reichenau (sometimes called Hermann the Lame or Hermann Contractus)
writes treatises on the abacus
and the astrolabe.
He introduces into Europe the astrolabe, a portable sundial and a quadrant with
a cursor.**

**1072
Al-Khayyami
(usually known as Omar Khayyam) writes Treatise on Demonstration of Problems
of Algebra which contains a complete classification of cubic equations with
geometric solutions found by means of intersecting conic sections. He measures
the length of the year to be 365.24219858156 days, a remarkably accurate result.**

**1093
Shen
Kua writes Meng ch'i pi t'an (Dream Pool Essays), which is a
work on mathematics, astronomy, cartography, optics and medicine. It contains
the earliest mention of a magnetic compass.**

**About 1AD
Chinese mathematician Liu Hsin uses decimal fractions.**

**About 20
Geminus
writes a number of astronomy texts and The Theory of Mathematics. He
tries to prove the parallel
postulate. **

**About 50
Chinese mathematician Sun-tzi presents the first known example of an
indeterminate equation.**

**About 60
Heron
of Alexandria writes Metrica (Measurements). It contains
formulas for calculating areas and volumes.**

**About 90
The Chinese invent magic
squares.**

**About 90
Nicomachus
of Gerasa writes Arithmetike eisagoge (Introduction to Arithmetic)
which is the first work to treat arithmetic as a separate topic from geometry.**

**About 100
The classical Chinese mathematics text Jiuzhang Suanshu (Nine Chapters
on the Mathematical Art) begins to be assembled.**

**About 110
Menelaus
of Alexandria writes Sphaerica which deals with spherical triangles
and their application to astronomy.**

**About 150
Ptolemy
produces many important geometrical results with applications in astronomy. His
version of astronomy will be the accepted one for well over one thousand years.**

**About 250
The Maya civilization of Central America uses an almost place-value number
system to base 20. **

**250
Diophantus
of Alexandria writes Arithmetica, a study of number theory problems
in which only rational
numbers are allowed as solutions.**

**263
By using a regular polygon with 192 sides Liu Hui calculates the value of p
as 3.14159 which is correct to five decimal places. **

**301
Iamblichus
writes on astrology and mysticism. His Life of Pythagoras is a
fascinating account.**

**340
Pappus
of Alexandria writes Synagoge (Collections) which is a guide
to Greek geometry.**

**390
Theon
of Alexandria produces a version of Euclid's
Elements (with textual changes and some additions) on which almost all
subsequent editions are based.**

**About 400
Hypatia
writes commentaries on Diophantus
and Apollonius.
She is the first recorded female mathematician and she distinguishes herself
with remarkable scholarship. She becomes head of the Neo-Platonist school at
Alexandria.**

**450
Proclus,
a mathematician and Neo-Platonist, is one of the last philosophers at Plato's
Academy at Athens.**

**About 460
Zu
Chongzhi gives the approximation ^{355}/_{113} to p
which is correct to 6 decimal places. **

**499
Aryabhata
I calculates p to be 3.1416. He produces his Aryabhatiya,
a treatise on quadratic equations, the value of p,
and other scientific problems.**

**About 500
Metrodorus assembles the Greek Anthology consisting of 46 mathematical
problems.**

**510
Eutocius
of Ascalon writes commentaries on Archimedes'
work.**

**510
Boethius
writes geometry and arithmetic texts which are widely used for a long time.**

**About 530
Eutocius
writes commentaries on the works of Archimedes
and Apollonius.**

**532
Anthemius
of Tralles, a mathematician of note, is the architect for the Hagia Sophia
at Constantinople. **

**534
Chinese mathematics is introduced into Japan.**

**575
Varahamihira
produces Pancasiddhantika (The Five Astronomical Canons). He makes
important contributions to trigonometry.**

**594
Decimal notation is used for numbers in India. This is the system on which our
current notation is based. **

**628
Brahmagupta
writes Brahmasphutasiddanta (The Opening of the Universe), a work
on astronomy; on mathematics. He uses zero and negative numbers, gives methods
to solve quadratic equations, sum series, and compute square roots.**

**About 700
Mathematicians in the Mayan civilization introduce a symbol for zero into their
number system. **

**729
Hsing introduces a new calendar into China, correcting many errors in earlier
calendars.**

**732
Qutan Zhuan accuses Hsing of copying an Indian calendar in producing his own.
However Hsing's Chinese calendar is far more accurate than the Indian one.**

**About 775
Alcuin
of York writes elementary texts on arithmetic, geometry and astronomy.**

**About 790
Chinese begin to use finite difference methods.**

**About 810
House of Wisdom set up in Baghdad. There Greek and Indian mathematical and
astronomy works are translated into Arabic.**

**About 810
Al-Khwarizmi
writes important works on arithmetic, algebra, geography, and astronomy. In
particular Hisab al-jabr w'al-muqabala (Calculation by Completion and
Balancing), gives us the word "algebra", from "al-jabr".
From al-Khwarizmi's name, as a consequence of his arithmetic book, comes the
word "algorithm".**

**About 850
Thabit
ibn Qurra makes important mathematical discoveries such as the extension of
the concept of number to (positive) real numbers, integral calculus, theorems in
spherical trigonometry, analytic geometry, and non-euclidean
geometry.**

**About 850
Thabit
ibn Qurra writes Book on the determination of amicable numbers which
contains general methods to construct amicable
numbers. He knows the pair of amicable numbers 17296, 18416.**

**850
Mahavira
writes Ganita Sara Samgraha. It consists of nine chapters and includes
all mathematical knowledge of mid-ninth century India.**

**About 900
Abu
Kamil writes Book on algebra which studies applications of algebra to
geometrical problems. It will be the book on which Fibonacci
will base his works.**

**900
Sridhara
writes the Trisatika (sometimes called the Patiganitasara) and the
Patiganita. In these he solves quadratic equations, sums series, studies combinations,
and gives methods of finding the areas of polygons.**

**About 900
Abu
Kamil writes Book on algebra which studies applications of algebra to
geometrical problems. It will be the book on which Fibonacci
will base his works.**

**920
Al-Battani
writes Kitab al-Zij a major work on astronomy in 57 chapters. It contains
advances in trigonometry.**

**950
Gerbert of Aurillac (later Pope Sylvester II) reintroduces the abacus into
Europe. He uses Indian/Arabic numerals without having a zero.**

**About 960
Al-Uqlidisi
writes Kitab al-fusul fi al-hisab al-Hindi which is the earliest
surviving book that presents the Hindu system.**

**About 970
Abu'l-Wafa
invents the wall quadrant for the accurate measurement of the declination
of stars in the sky. He writes important books on arithmetic and geometric
constructions. He introduces the tangent function and produces improved methods
of calculating trigonometric tables.**

**976
Codex Vigilanus copied in Spain. Contains the first evidence of decimal
numbers in Europe.**

**About 990
Al-Karaji
writes Al-Fakhri in Baghdad which develops algebra. He gives Pascal's
triangle.**

**About 1000
Ibn
al-Haytham (often called Alhazen) writes works on optics, including a theory
of light and a theory of vision, astronomy, and mathematics, including geometry
and number theory. He gives Alhazen's problem: Given a light source and a
spherical mirror, find the point on the mirror were the light will be reflected
to the eye of an observer.**

**About 1010
Al-Biruni
writes on many scientific topics. His work on mathematics covers arithmetic,
summation of series, combinatorial analysis, the rule of three, irrational
numbers, ratio theory, algebraic definitions, method of solving algebraic
equations, geometry, Archimedes' theorems, trisection
of the angle and other problems which cannot be solved with ruler
and compass alone, conic sections, stereometry, stereographic
projection, trigonometry, the sine theorem in the plane, and solving
spherical triangles.**

**About 1020
Ibn
Sina (usually called Avicenna) writes on philosophy, medicine, psychology,
geology, mathematics, astronomy, and logic. His important mathematical work Kitab
al-Shifa' (The Book of Healing) divides mathematics into four major
topics, geometry, astronomy, arithmetic, and music.**

**1040
Ahmad
al-Nasawi writes al-Muqni'fi al-Hisab al-Hindi which studies four
different number systems. He explains the operations of arithmetic, particularly
taking square and cube roots in each system.**

**About 1050
Hermann
of Reichenau (sometimes called Hermann the Lame or Hermann Contractus)
writes treatises on the abacus
and the astrolabe.
He introduces into Europe the astrolabe, a portable sundial and a quadrant with
a cursor.**

**1072
Al-Khayyami
(usually known as Omar Khayyam) writes Treatise on Demonstration of Problems
of Algebra which contains a complete classification of cubic equations with
geometric solutions found by means of intersecting conic sections. He measures
the length of the year to be 365.24219858156 days, a remarkably accurate result.**

**1093
Shen
Kua writes Meng ch'i pi t'an (Dream Pool Essays), which is a
work on mathematics, astronomy, cartography, optics and medicine. It contains
the earliest mention of a magnetic compass.**

**Anno 1130
Jabir
ibn Aflah writes works on mathematics which, although not as good as many
other Arabic works, are important since they will be translated into Latin and
become available to European mathematicians.**

**About 1140
Bhaskara
II (sometimes known as Bhaskaracharya) writes Lilavati (The
Beautiful) on arithmetic and geometry, and Bijaganita (Seed
Arithmetic), on algebra.**

**1142
Adelard
of Bath produces two or three translations of Euclid's
Elements from Arabic.**

**1144
Gherard
of Cremona begins translating Arabic works (and Arabic translations of Greek
works) into Latin.**

**1149
Al-Samawal
writes al-Bahir fi'l-jabr (The brilliant in algebra). He develops
algebra with polynomials using negative powers and zero. He solves quadratic
equations, sums the squares of the first n natural numbers, and looks at
combinatorial problems.**

**1150
Arabic numerals are introduced into Europe with Gherard
of Cremona's translation of Ptolemy's
Almagest. The name of the "sine" function comes from this
translation.**

**About 1200
Chinese start to use a symbol for zero. (See this History
Topic.)**

**1202
Fibonacci
writes Liber abaci (The Book of the Abacus), which sets out the
arithmetic and algebra he had learnt in Arab countries. It also introduces the
famous sequence of numbers now called the "Fibonacci
sequence".**

**1225
Fibonacci
writes Liber quadratorum (The Book of the Square), his most
impressive work. It is the first major European advance in number theory since
the work of Diophantus
a thousand years earlier.**

**About 1225
Jordanus
Nemorarius writes on astronomy. In mathematics he uses letters in an early
form of algebraic notation.**

**About 1230
John
of Holywood (sometimes called Johannes de Sacrobosco) writes on arithmetic,
astronomy and calendar reform.**

**1247
Qin
Jinshao writes Mathematical Treatise in Nine Sections. It contains
simultaneous integer congruences and the Chinese Remainder Theorem. It considers
indeterminate equations, Horner's
method, areas of geometrical figures and linear simultaneous equations.**

**1248
Li Yeh writes a book which contains negative numbers, denoted by putting a
diagonal stroke through the last digit.**

**About 1260
Campanus
of Novara, chaplain to Pope Urban IV, writes on astronomy and publishes a
Latin edition of Euclid's
Elements which became the standard Euclid for the next 200 years.**

**1275
Yang
Hui writes Cheng Chu Tong Bian Ben Mo (Alpha and omega of
variations on multiplication and division). It uses decimal fractions (in
the modern form) and gives the first account of Pascal's
triangle.**

**1303
Zhu
Shijie writes Szu-yuen Yu-chien (The Precious Mirror of the Four
Elements), which contains a number of methods for solving equations up to
degree 14. He also defines what is now called Pascal's
triangle and shows how to sum certain sequences.**

**1321
Levi
ben Gerson (sometimes known as Gersonides) writes Book of Numbers
dealing with arithmetical operations, permutations
and combinations.**

**1328
Bradwardine
writes De proportionibus velocitatum in motibus which is an early work on
kinematics using algebra.**

**1335
Richard of Wallingford writes Quadripartitum de sinibus demonstratis, the
first original Latin treatise on trigonometry.**

**1336
Mathematics becomes a compulsory subject for a degree at the University of
Paris.**

**1342
Levi
ben Gerson (Gersonides) writes De sinibus, chordis et arcubus (Concerning
Sines, Chords and Arcs), a treatise on trigonometry which gives a proof of
the sine theorem for plane triangles and gives five figure sine tables.**

**1343
Jean de Meurs writes Quadripartitum numerorum (Four-fold Division of
Numbers), a treatise on mathematics, mechanics, and music.**

**1343
Levi
ben Gerson (Gersonides) writes De harmonicis numeris (Concerning
the Harmony of Numbers), which is a commentary on the first five books of Euclid.**

**1364
Nicole
d'Oresme writes Latitudes of Forms, an early work on coordinate
systems which may have influence Descartes.
Another work by Oresme contains the first use of a fractional exponent.**

**1382
Nicole
d'Oresme publishes Le Livre du ciel et du monde (The Book of
Heaven and Earth). It is a compilation of treatises on mathematics,
mechanics, and related areas. Oresme opposed the theory of a stationary Earth.**

**1400
Madhava
of Sangamagramma proves a number of results about infinite sums giving Taylor
expansions of trigonometric functions. He uses these to find an approximation
for p correct to 11 decimal places.**

**1411
Al-Kashi
writes Compendium of the Science of Astronomy.**

**1424
Al-Kashi
writes Treatise on the Circumference giving a remarkably good
approximation to p in both sexagesimal
and decimal forms.**

**1427
Al-Kashi
completes The Key to Arithmetic containing work of great depth on decimal
fractions. It applies arithmetical and algebraic methods to the solution of
various problems, including several geometric ones and is one of the best
textbooks in the whole of medieval literature.**

**1434
Alberti
studies the representation of 3-dimensional objects and writes the first general
treatise Della Pictura on the laws of perspective.**

**1437
Ulugh
Beg publishes his star catalogue Zij-i Sultani. It contains
trigonometric tables correct to eight decimal places based on Ulugh Beg's
calculation of the sine of one degree which he calculated correctly to 16
decimal places.**

**1450
Nicholas
of Cusa studies geometry and logic. He contributes to the study of infinity,
studying the infinitely large and the infinitely small. He looks at the circle
as the limit of regular polygons.**

**About 1470
Chuquet
writes Triparty en la science des nombres, the earliest French algebra
book.**

**1472
Peurbach
publishes Theoricae Novae Planetarum (New Theory of the Planets).
He uses Ptolemy's
epicycle
theory of the planets but believes they are controlled by the sun.**

**1474
Regiomontanus
publishes his Ephemerides, astronomical tables for the years 1475 to 1506
AD, and proposes a method for calculating longitude by using the moon.**

**1475
Regiomontanus
publishes De triangulis planis et sphaericis (Concerning Plane and
Spherical Triangles), which studies spherical trigonometry to apply it to
astronomy.**

**1482
Campanus
of Novara's edition of Euclid's
Elements becomes the first mathematics book to be printed.**

**1489
Widman
writes an arithmetic book in German which contains the first appearance of + and
- signs.**

**1494
Pacioli
publishes Summa de arithmetica, geometria, proportioni et proportionalita
which is a review of the whole of mathematics covering arithmetic, trigonometry,
algebra, tables of moneys, weights and measures, games of chance, double-entry
book-keeping and a summary of Euclid's
geometry.**