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1303

Zhu Shijie writes

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 π 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 π 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.

List of mathematicians alive in 1300.

List of mathematicians alive in 1500.

JOC/EFR August 2001
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