FISICA/MENTE

 

 

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.

 

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