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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.

List of mathematicians alive in 1100.

List of mathematicians alive in 1300.

JOC/EFR August 2001
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