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layout: epoch categories: history, early-middle-ages nodeid: bookofproofs$608 orderid: 300 parentid: bookofproofs$2 title: Early Middle Ages description: EARLY MIDDLE AGES (FROM 500 TO 999) ★ history of mathematics ✚ science ➜ visit BookOfProofs now! references: bookofproofs$6909 keywords: ages,early,middle contributors: bookofproofs

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Chronology

532

  • [Simplicius][bookofproofs$Simplicius] writes a commentary on [Aristotle][bookofproofs$Aristotle] and describes the spheres of [Eudoxus][bookofproofs$Eudoxus].

551

  • [Yativrsabha][bookofproofs$Yativrsabha] writes "Tiloyapannatti"
    • Various units for measuring distances and time
    • System of infinite time measures
    • Gives a description of the universe which is of historical importance in understanding Jaina cosmology and mathematics.

575

  • [Varahamihira][bookofproofs$Varahamihira] discovers a version of Pascal's triangle and works on magic squares.
    • Writes "Pancasiddhantika" (The Five Astronomical Canons) treatise on mathematical astronomy which summarizes five lost earlier astronomical treatises, namely the Surya, Romaka, Paulisa, Vasistha and Paitamaha siddhantas.

609

  • [Yativrsabha][bookofproofs$Yativrsabha]'s work "Tiloyapannatti" gives various units for measuring distances and time and also describes the system of infinite time measures.

623

  • [Xiaotong][bookofproofs$Wang_Xiaotong]: Chinese calendar reform and the solution of cubic equations.

627

  • [Chunfeng][bookofproofs$Li_Chunfeng]: Chinese calendar reform, high-ranking court astronomer and historian, being first appointed to the Imperial Astronomical Bureau

665

  • [Brahmagupta][bookofproofs$Brahmagupta]
    • Writes "Brahmasphutasiddhanta" and "Khandakhadyaka"
    • Understanding of arithmetics beyond that of others of the period, e.g. "The product or quotient of two debts is one fortune.", "When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero."
    • Trials to extend arithmetics: "Zero divided by zero is zero."
  • [Chunfeng][bookofproofs$Li_Chunfeng] Works on the Linde calendar, which was introduced in 665 and used until 728.

781

  • [Alcuin][bookofproofs$Alcuin] visits Aachen to meet the leading scholars of the time.
    • Writes elementary texts on arithmetic, geometry and astronomy.

about 830

  • [Al-Jawhari][bookofproofs$Al-Jawhari] best known as a geometer, made observations in Baghdad from 829 to 830 while working for al-Ma'mun.
    • Writes "Commentary on Euclid's Elements"
    • Examples of early attempts by Muslim mathematicians to adopt Euclid's methods (tries to "prove" Euclid's definition 5 (equal ratio) and definition 7 (greater ratio)).
  • [Govindasvami][bookofproofs$Govindasvami] writes the "Bhasya", a commentary on the "Mahabhaskariya" Ⓣ(The big book of [Bhaskara][bookofproofs$Bhaskara_I]).
    • Approximation to the trigonometric sine function by means of a rational fraction.

about 850

  • [Hunayn][bookofproofs$Hunayn] translates Greek of Plato and Aristotle into Arabic.
  • [Al-Mahani][bookofproofs$Al-Mahani] Astronomical observations between the years 853 and 866.
    • Reducing problems such as duplicating the cube to problems in algebra.

about 870

  • [Ibn Yusuf][bookofproofs$Ahmed] works on ratio and proportion and writes a commentary on Euclid's Elements.
  • [Narayana][bookofproofs$Sankara] writes "Laghubhaskariya vivarana", using the katapayadi numeration for the first time.

about 880

  • [Al-Battani][bookofproofs$Al-Battani] catalogues 489 stars (868,929) and makes accurate measurements of the stars, moon and planets.

about 950

  • [Al-Khazin][bookofproofs$Al-Khazin]
    • Writes and proves 19 propositions, e.g. t an equilateral triangle has a greater area than any isosceles or scalene triangle with the same perimeter.
    • Claims to have proven that $x^3+y^3=z^3$ is impossible for whole numbers $x,y,z$, later becoming known as a special case of Fermat's Last Theorem.

969

  • [Al-Sijzi][bookofproofs$Al-Sijzi]
    • makes astronomical observations during 969-970
    • Writes "Book of the measurement of spheres by spheres", in which he gives twelve theorems about volumes of a large sphere containing between one and three smaller spheres.

988

  • [Mohammad][bookofproofs$Abul-Wafa] opens an astronomical observatory with a number of famous scientists present such as al-Quhi and Abu'l-Wafa.

994

  • [Al-Khujandi][bookofproofs$Al-Khujandi] Uses an instrument to observe a series of meridian transits of the sun near the solstices.

997

  • [Al-Biruni][bookofproofs$Al-Biruni] describes an eclipse of the moon on 24 May 997 which he observed at Kath

about 1000

  • [Kushyar][bookofproofs$Kushyar] writes "Principles of Hindu reckoning"
  • [Al-Jayyani][bookofproofs$Al-Jayyani] writes commentaries on Euclid's Elements and a first treatise on spherical trigonometry.
  • [Mansur][bookofproofs$Mansur] discovers the sine rule for triangles.
  • [Gerbert][bookofproofs$Gerbert] (also known as Pope Sylvester II) popularises Indo-Arabic numerals.