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| Cronologia della matematica |
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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. (See this History
Topic.)
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. (See this History
Topic.)
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. (See this History
Topic.)
About 1850BC
Babylonians know Pythagoras's
Theorem. (See this History
Topic.)
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. (See this
History
Topic.)
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. (See this History
Topic.)
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. (See this
History
Topic.)
About 750BC
Manava
writes a Sulbasutra. (See this History
Topic.)
About 600BC
Apastamba
writes the most interesting Indian Sulbasutra from a mathematical point
of view. (See this History
Topic.)
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
The Babylonian sexagesimal number system is used to record and predict
the positions of the Sun, Moon and planets. (See this History
Topic.)
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. (See this History
Topic.)
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. (See this History
Topic.)
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 290BC
The Chinese classic Chou pei suan ching is written.
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 
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. (See this History
Topic.)
About 200BC
Diocles
writes On burning mirrors, a collection of sixteen propositions
in geometry mostly proving results on conics.
About 190BC
Chinese mathematicians use powers of 10 to express magnitudes.
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 100BC
Chinese mathematicians are the first to introduce negative numbers.
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. (See
this History
Topic.)
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. (See this History
Topic.)
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 as 3.14159 which is correct to five
decimal places. (See this History
Topic.)
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
Tsu
Ch'ung Chi gives the approximation 355/113 to
which is correct to 6 decimal
places. (See this History
Topic.)
499
Aryabhata
I calculates
to be 3.1416. He produces his Aryabhatiya, a treatise on quadratic
equations, the value of ,
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. (See this History
Topic.)
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. (See this History
Topic.)
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. (See this History
Topic.)
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.
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.
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
Ch'in
Chiu-Shao 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
Chu
Shih-Chieh 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 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 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.
1514
Vander Hoecke uses the + and - signs.
1515
Del
Ferro discovers a formula to solve cubic equations. (See this History
Topic.)
1522
Tunstall
publishes De arte supputandi libri quattuor (On the Art of Computation),
an arithmetic book based on Pacioli's
Summa.
1525
Rudolff
introduces a symbol resembling 
for square roots in his Die Coss
the first German algebra book. He understands that x0
= 1.
1525
Dürer
publishes Unterweisung der Messung mit dem Zirkel und Richtscheit,
the first mathematics book published in German. It is a work on geometric
constructions.
1533
Frisius
publishes a method for accurate surveying using trigonometry. He is the
first to propose the triangulation method.
1535
Tartaglia
solves the cubic equation independently of del
Ferro. (See this History
Topic.)
1536
Hudalrichus Regius finds the fifth perfect number. The number 212(213
- 1) = 33550336 is the first perfect number to be discovered since ancient
times. (See this History
Topic.)
1540
Ferrari
discovers a formula to solve quartic equations. (See this
History
Topic.)
1541
Rheticus
publishes his trigonometric tables and the trigonometrical parts of Copernicus's
work.
1543
Copernicus
publishes De revolutionibus orbium coelestium (On the revolutions
of the heavenly spheres). It gives a full account of the Copernican
theory, namely that the Sun (not the Earth) is at rest in the centre of
the Universe.
1544
Stifel
publishes Arithmetica integra which contains binomial coefficients and
the notation +, -, .
1545
Cardan
publishes Ars Magna giving the formula that will solve any cubic equation based on Tartaglia's
work and the formula for quartics discovered by Ferrari.
(See this History
Topic.)
1550
Ries
publishes his famous arithmetic book Rechenung nach der lenge, auff
den Linihen vnd Feder. It taught arithmetic both by the old abacus method and the new Indian method.
1551
Recorde
translates and abridges the ancient Greek mathematician Euclid's
Elements as The Pathewaie to Knowledge.
1555
J Scheybl gives the sixth perfect number 216(217 - 1) = 8589869056
but his work remains unknown until 1977. (See this History
Topic.)
1557
Recorde
publishes The Whetstone of Witte which introduces = (the equals
sign) into mathematics. He uses the symbol "bicause noe 2 thynges can
be moare equalle".
1563
Cardan
writes his book Liber de Ludo Aleae on games of chance but it would
not be published until 1663.
1571
Viète
begins publishing the Canon Mathematicus which he intends as a
mathematical introduction to his astronomy treatise. It covers trigonometry,
containing trigonometric tables and the theory behind their construction.
1572
Bombelli
publishes the first three parts of his Algebra. He is the first
to gives the rules for calculating with complex numbers.
1575
Maurolico
publishes Arithmeticorum libri duo which contains examples of inductive
proofs.
1585
Stevin
publishes De Thiende in which he presents an elementary and thorough
account of decimal fractions.
1586
Stevin
publishes De Beghinselen der Weeghconst containing the theorem
of the triangle of forces.
1590
Cataldi
uses continued fractions in finding
square roots.
1591
Viète
writes In artem analyticam isagoge (Introduction to the analytical
art), using letters as symbols for quantities, both known and unknown.
He uses vowels for the unknowns and consonants for known quantities. Descartes,
later, introduces the use of letters x, y ... at the end
of the alphabet for unknowns.
1593
Van
Roomen calculates
to 16 decimal places. (See this History
Topic.)
1595
Pitiscus
becomes the first to employ the term trigonometry in a printed publication.
1595
Clavius
writes Novi calendarii romani apologia justifying calendar reforms.
1603
Cataldi
finds the sixth and seventh perfect numbers, 216(217 - 1) =8589869056
and 218(219 - 1) = 137438691328.
1603
Accademia dei Lincei founded in Rome.
1606
Snell
makes the first attempt to measure a degree of the meridian arc on the
Earth's surface, and so determine the size of the Earth. He publishes
Hypomnemata mathematica (Mathematical Memoranda) which is
a Latin translation of Stevin's
work on mechanics.
1609
Kepler
publishes Astronomia nova (New Astronomy). The work contains
Kepler's first and second law on elliptical orbits, but only verified
for the planet Mars.
1610
Galileo
publishes Sidereus Nuncius (Message from the stars) which
describes the astronomical discoveries he has made with his telescopes.
Harriot
also observes the moons of Jupiter but does not publish his work.
1612
Bachet
publishes a work on mathematical puzzles and tricks which will form the
basis for almost all later books on mathematical recreations. He devises
a method of constructing magic squares.
1613
Cataldi
publishes Trattato del modo brevissimo di trovar la radice quadra delli
numeri in which he finds square roots using continued fractions.
1614
Napier
publishes his work on logarithms in Mirifici logarithmorum canonis
descriptio (Description of the Marvellous Rule of Logarithms).
1615
Kepler
publishes Nova stereometria doliorum vinarorum (Solid Geometry
of a Wine Barrel), an investigation of the capacity of casks, surface
areas, and conic sections. He first had the idea at his marriage celebrations
in 1613. His methods are early uses of the calculus.
1615
Mersenne
encourages mathematicians to study the cycloid. (See this Famous
curve.)
1617
Snell
publishes his technique of trigonometrical triangulation which improves
the accuracy of cartographic measurements.
1617
Briggs
publishes Logarithmorum chilias prima (Logarithms of Numbers
from 1 to 1,000) which introduces logarithms to the base 10.
1617
Napier
invents Napier's bones, consisting of numbered sticks, as a mechanical
calculator. He explains their function in Rabdologiae (Study
of Divining Rods) published in the year of his death.
1620
Bürgi
publishes Arithmetische und geometrische progress-tabulen which
contains his version of logarithms discovered independently of Napier.
1620
Gunter
makes a mechanical device, Gunter's scale, to multiply numbers
based on logarithms using a single scale and a pair of dividers.
1620
Guldin
gives Guldin's Centroid Theorem which was already known to Pappus.
1621
Bachet
publishes his Latin translation of Diophantus's
Greek text Arithmetica.
1623
Schickard
makes a "mechanical clock", a wooden calculating machine that add and
subtract and aid with multiplication and division. He writes to Kepler
suggesting using mechanical means to calculate ephemeredes.
1624
Briggs
publishes Arithmetica logarithmica (The Arithmetic of Logarithms)
which introduces the terms "mantissa" and "characteristic". It gives the
logarithms of the natural numbers from 1 to 20,000 and 90,000 to 100,000
computed to 14 decimal places as well as tables of the sine function to
15 decimal places, and the tangent and secant functions to 10 decimal
places.
1626
Albert
Girard publishes a treatise on trigonometry containing the first use
of the abbreviations sin, cos, tan. He also gives formulas for the area
of a spherical triangle.
1629
Fermat
works on maxima and minima. This work is an early contribution to the
differential calculus.
1630
Oughtred
invents an early form of circular slide rule. It uses two Gunter
rulers.
1630
Mydorge
works on optics and geometry. He gives an extremely accurate measurement
of the latitude of Paris.
1631
Harriot's
contributions are published ten years after his death in Artis analyticae
praxis (Practice of the Analytic Art). The book introduces
the symbols > and < for "greater than" and "less than" but these
symbols are due to the editors of the work and not Harriot himself. His
work on algebra is very impressive but the editors of the book do not
present it well.
1631
Oughtred
publishes Clavis Mathematicae which includes a description of Hindu-Arabic
notation and decimal fractions. It has a considerable section on algebra.
1634
Roberval
finds the area under the cycloid curve. (See this Famous
curve.)
1635
Descartes
discovers Euler's
theorem for polyhedra, V - E + F = 2.
1635
Cavalieri
presents his development of Archimedes'
method of exhaustion in his Geometria indivisibilis continuorum nova.
The method incorporates Kepler's
theory of infinitesimally small geometric quantities.
1636
Fermat
discovers the pair of amicable numbers 17296, 18416
which were known to Thabit
ibn Qurra 800 years earlier.
1637
Descartes
publishes La Géométrie which describes his application of algebra
to geometry.
1639
Desargues
begins the study of projective geometry, which
considers what happens to shapes when they are projected on to a non-parallel
plane. He describes his ideas in Brouillon project d'une atteinte aux
evenemens des rencontres du Cone avec un Plan (Rough draft for
an essay on the results of taking plane sections of a cone).
1640
Pascal
publishes Essay pour les coniques (Essay on Conic Sections).
1641
Wilkins
publishes on codes and ciphers.
1642
Pascal
builds a calculating machine to help his father with tax calculations.
It performs only additions.
1644
Torricelli
publishes Opera geometrica which contains his results on projectiles.
He investigates the point which minimises the sum of its distances from
the vertices of a triangle.
1647
Fermat
claims to have proved a theorem, but leaves no details of his proof since
the margin in which he writes it is too small. Later known as Fermat's last theorem, it
states that the equation xn + yn
= zn has no non-zero solutions for x,
y and z when n > 2. This theorem is finally proved
to be true by Wiles
in 1994. (See this History
Topic.)
1647
Cavalieri
publishes Exercitationes geometricae sex (Six Geometrical Exercises)
which contains in print for the first time the integral from 0 to a
of xn.
1648
Wilkins
publishes Mathematical Magic giving an account of mechanical devices.
1648
Abraham Bosse publishes a work containing Desargues'
famous "perspective theorem" - that when two triangles are in perspective
the meets of corresponding sides are collinear.
1649
Van
Schooten publishes the first Latin version of Descartes'
La géométrie.
1649
De
Beaune writes Notes brièves which contains the many results
on "Cartesian geometry", in particular giving the now familiar equations
for hyperbolas, parabolas and ellipses.
1650
De
Witt completes writing Elementa curvarum linearum. It is the
first systematic development of the analytic geometry of the straight
line and conic. It is not published, however, until 1661 when it appears
as an appendix to van
Schooten's major work.
1651
Nicolaus
Mercator publishes three works on trigonometry and astronomy, Trigonometria
sphaericorum logarithmica, Cosmographia and Astronomica
sphaerica. He gives the well known series expansion of log(1 + x).
1653
Pascal
publishes Treatise on the Arithmetical Triangle on "Pascal's triangle". It had
been studied by many earlier mathematicians.
1654
Fermat
and Pascal
begin to work out the laws that govern chance and probability in five letters
which they exchange during the summer.
1654
Pascal
publishes his Treatise on the Equilibrium of Liquids on hydrostatics.
He recognizes that force is transmitted equally in all directions through
a fluid, and gives Pascal's law of pressure.
1655
Brouncker
gives a continued fraction expansion
of 4/. He also computes the quadrature of the hyperbola, a result he will publish three years later.
1656
Wallis
publishes Arithmetica infinitorum which uses interpolation methods
to evaluate integrals.
1656
Huygens
patents the first pendulum clock.
1657
Huygens
publishes De ratiociniis in ludi aleae (On Reasoning in Games
of Chance). It is the first published work on probability theory, outlining
for the first time the concept called mathematical expectation based on
the ideas in the letters of Fermat
and Pascal
from 1654.
1657
Neile
becomes the first to find the arc length of an algebraic curve when he
rectified the cubical parabola. (See this Famous curve.)
1657
Frenicle
de Bessy publishes Solutio duorm problematum ... which gives
solutions to some of Fermat's
number theory challenges.
1658
Wren
finds the length of an arc of the cycloid. (See this Famous
curve.)
1659
Rahn
publishes Teutsche algebra which contains 
(the division sign) probably invented
by Pell.
1660
De
Sluze discusses spirals, points of inflection and the finding of geometric
means in his works. He studies curves which Pascal
names the "pearls of Sluze". (See this Famous curve.)
1660
Hooke
discovers Hooke's law of elasticity.
1660
Viviani
measures the velocity of sound. He determines the tangent to a cycloid.
(See this Famous
curve.)
1661
Van
Schooten publishes the second and final volume of Geometria a Renato
Des Cartes. This work establishes analytic geometry as a major mathematical
topic. The book also contains appendices by three of his disciples, de
Witt, Hudde,
and Heuraet.
1662
The Royal Society of London is founded. Brouncker
becomes its first President. (See this Article.)
1662
Graunt and Petty publish Natural and Political Observations made upon
the Bills of Mortality. It is one of the first statistics books.
1663
Barrow
becomes the first Lucasian Professor of Mathematics at the University
of Cambridge in England. (See this Article.)
1665
Newton
discovers the binomial theorem and begins
work on the differential calculus.
1666
The Académie des Sciences in Paris is founded.
1667
James
Gregory publishes Vera circuli et hyperbolae quadratura which
lays down exact foundations for the infinitesimal geometry.
1668
James
Gregory publishes Geometriae pars universalis which is the
first attempt to write a calculus textbook.
1668
Pell
gives a table of factors of all integers up to 100000.
1669
Wren
publishes his result that a hyperboloid of revolution is a ruled surface.
1669
Barrow
resigns the Lucasian Chair of Mathematics at Cambridge University to allow
his pupil Newton
to be appointed.
1669
Wallis
publishes his Mechanica (Mechanics) which is a detailed
mathematical study of mechanics.
1670
Barrow
publishes Lectiones Geometricae which contains his important work
on tangents which forms the starting point of Newton's
work on the calculus.
1671
De
Witt publishes A Treatise on Life Annuities. It contains the
idea of mathematical expectation.
1671
James
Gregory discovers Taylor's
Theorem and writes to Collins
telling him of his discovery. His series expansion for arctan(x)
gives a series for /4.
1672
Mengoli
publishes The Problem of Squaring the Circle which studies infinite
series and gives an infinite product expansion for /2.
1672
Mohr
publishes Euclides danicus in which he shows that all Euclidean
constructions can be carried out with compasses alone.
1673
Leibniz
demonstrates his incomplete calculating machine to the Royal Society.
It can multiply, divide and extract roots.
1673
Huygens
publishes Horologium Oscillatorium sive de motu pendulorum. As
well as work on the pendulum he investigates evolutes and involutes of curves and finds the evolutes of the cycloid
and of the parabola.
1675
La
Hire publishes Sectiones conicae which is a major work on conic sections.
1675
Leibniz
uses the modern notation for an integral for the first time.
1676
Leibniz
discovers the differentials of basic functions independently of Newton.
1677
Leibniz
discovers the rules for differentiating products, quotients, and the function
of a function.
1678
Giovanni
Ceva publishes De lineis rectis containing "Ceva's theorem".
1678
Cocker's
Arithmetic is published two years after Cocker's death. It would
run to more than 100 editions over a period of about 100 years.
1679
Leibniz
introduces binary arithmetic. It was not published until 1701.
1680
Cassini
studies the "Cassinian curve" which is the locus of a point the product
of whose distances from two fixed foci is constant. (See this Famous
curve.)
1682
Tschirnhaus
studies catacaustic curves, being the envelope of light rays emitted from
a point source after reflection from a given curve.
1683
Seki
Kowa publishes a treatise that first introduces determinants. He considers integer solutions of ax
- by = 1 where a, b are integers.
1684
Leibniz
publishes details of his differential calculus in Nova Methodus pro
Maximis et Minimis, itemque Tangentibus. In contains the familiar
d notation, and the rules for computing the derivatives of powers,
products and quotients.
1685
Wallis
publishes De Algebra Tractatus (Treatise of Algebra) which
contains the first published account of Newton's
binomial theorem. It made
Harriot's
remarkable contributions known.
1685
Kochanski gives an approximate method to find the length of the circumference
of a circle.
1687
Newton
publishes The Principia or Philosophiae naturalis principia
mathematica (The Mathematical Principles of Natural Philosophy).
In this work, recognised as the greatest scientific book ever written,
Newton presents his theories of motion, gravity, and mechanics. His theories
explain the eccentric orbits of comets, the tides and their variations,
the precession of the Earth's axis, and motion of the Moon.
1690
Jacob
Bernoulli uses the word "integral" for the first time to refer to
the area under a curve.
1690
Rolle
publishes Traité d'algèbre on the theory of equations.
1691
Jacob
Bernoulli invents polar coordinates, a method of describing the location
of points in space using angles and distances.
1691
Rolle
publishes Méthods pour résoudre les égalités which contains Rolle's
theorem. His proof uses a method due to Hudde.
1692
Leibniz
introduces the term "coordinate".
1693
Halley
publishes his mortality tables for the city of Breslau (now Wroclaw) in
Poland. His attempts to relate mortality and age in a population and proves
highly influential in the future production of actuarial tables in life
insurance.
1694
Johann
Bernoulli discovers "L'Hôpital's rule".
1696
Johann
Bernoulli poses the problem of the brachristochrone and challenges
others to solve it. Johann
Bernoulli, Jacob
Bernoulli and Leibniz
all solve it.
1702
David
Gregory publishes Astronomiae physicae et geometricae elementa
which is a popular account of Newton's
theories.
1706
Jones
introduces the Greek letter to represent the ratio of the circumference
of a circle to its diameter in his Synopsis palmariorum matheseos
(A New Introduction to Mathematics).
1707
Newton
publishes Arithmetica universalis (General Arithmetic) which
contains a collection of his results in algebra.
1707
De
Moivre uses trigonometric functions to represent complex numbers in
the form r(cos z + i sin x).
1708
La
Hire calculates the length of the cardioid. (See this Famous
curve.)
1710
Arbuthnot
publishes an important statistics paper in the Royal Society which discusses
the slight excess of male births over female births. This paper is the
first application of probability to social statistics.
1711
Giovanni
Ceva publishes De Re Nummeraria (Concerning Money Matters)
which is one of the first works in mathematical economics.
1713
Jacob
Bernoulli's book Ars conjectandi (The Art of Conjecture)
is an important work on probability. It contains
the Bernoulli numbers which appear
in a discussion of the exponential series.
1715
Brook
Taylor publishes Methodus incrementorum directa et inversa
(Direct and Indirect Methods of Incrementation), an important contribution
to the calculus. The book discusses singular solutions to differential
equations, a change of variables formula, and a way of relating the derivative
of a function to the derivative of the inverse function. There is also
a discussion on vibrating strings.
1717
Johann
Bernoulli declares that the principle of virtual displacement is applicable
to all cases of equilibrium.
1718
Jacob
Bernoulli's work on the calculus of variations is
published after his death.
1718
De
Moivre publishes The Doctrine of Chances. The definition of
statistical independence appears in this book together with many problems
with dice and other games. He also investigated mortality statistics and
the foundation of the theory of annuities.
1719
Brook
Taylor publishes New principles of linear perspective. The
first edition appeared four years earlier under the title Linear perspective.
The work gives the first general treatment of vanishing points.
1722
The work unfinished by Cotes
on his death is published as Harmonia mensurarum. It deals with
integration of rational functions. It contains a thorough treatment of
the calculus applied to logarithmic and circular functions.
1724
Jacapo
Riccati studies the Riccati differential equation in a paper.
He gives solutions for certain special cases to the equation which was
first studied by Jacob
Bernoulli.
1724
Academy of Sciences is founded in St Petersburg.
1727
Euler
is appointed to St Petersburg. He introduces the symbol e for the
base of natural logarithms in a manuscript entitled Meditation upon
Experiments made recently on firing of Cannon. The manuscript was
not published until 1862.
1728
Grandi
publishes Flora geometrica (Geometrical Flowers). He gives
a geometrical definition of curves which resemble petals and leaves of
flowers. For example the rhodonea curves are so called since they
look like roses while the clelie curve is named after the Countess
Clelia Borromeo to whom he dedicated his book.
1730
De
Moivre gives further theorems concerning his trigonometric representation
of complex numbers. He gives Stirling's
formula.
1731
Clairaut
publishes Recherches sur les courbes à double coubure on skew curves.
1733
De
Moivre first describes the normal distribution curve, or law of errors,
in Approximatio ad summam terminorum binomii (a+b)n
in seriem expansi. Gauss,
in 1820, also investigated the normal distribution.
1733
In Euclides ab Omni Naevo Vindicatus Saccheri
does important early work on non-euclidean geometry, although he considers it an attempt
to prove the parallel postulate of Euclid.
1734
Berkeley
publishes The analyst: or a discourse addressed to an infidel mathematician.
He argues that although the calculus led to true results its foundations
were no more secure than those of religion.
1735
Euler
introduces the notation f(x).
1736
Euler
solves the topographical problem known as the "Königsberg bridges problem".
He proves mathematically that it is impossible to design a walk which
crosses each of the seven bridges exactly once.
1736
Euler
publishes Mechanica which is the first mechanics textbook which
is based on differential equations.
1737
Simpson
publishes his Treatise on Fluxions written as a textbook for his
private students. In the book he uses infinite series to find the definite
integrals of functions.
1738
Daniel
Bernoulli publishes Hydrodynamica (Hydrodynamics). It
gives for the first time the correct analysis of water flowing from a
hole in a container and discusses pumps and other machines to raise water.
He also gives, in Chapter 10, the basis of the kinetic theory of gases.
1739
D'Alembert
publishes Mémoire sur le calcul intégral (Memoir on Integral
Calculus).
1740
Simpson
publishes Treatise on the Nature and Laws of Chance. Much of this
probability treatise is based
on the work of de
Moivre.
1740
Maclaurin
is awarded the Grand Prix of the Académie des Sciences for his work on
gravitational theory to explain the tides.
1742
Maclaurin
publishes Treati