1300 - 1500

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(1100 - 1300)
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(1500 - 1600)


  • 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.



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


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


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


  • 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.


  • Jean de Meurs writes Quadripartitum numerorum (Four-fold Division of Numbers), a treatise on mathematics, mechanics, and music.
  • Levi ben Gerson (Gersonides) writes De harmonicis numeris (Concerning the Harmony of Numbers), which is a commentary on the first five books of Euclid.


  • 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.


  • 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.


  • 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.


  • Al-Kashi writes Compendium of the Science of Astronomy.


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


  • 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.


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


  • 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.


  • 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.


  • Chuquet writes Triparty en la science des nombres, the earliest French algebra book.


  • 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.


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


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



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


  • 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.