# Epoch: Early Middle Ages

## Description

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## Chronology

### 551

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

### 623

• Xiaotong: Chinese calendar reform and the solution of cubic equations.

### 627

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

### 665

• Brahmagupta
• 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 Works on the Linde calendar, which was introduced in 665 and used until 728.

### 781

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

• 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 writes the "Bhasya", a commentary on the "Mahabhaskariya" Ⓣ(The big book of Bhaskara).
• Approximation to the trigonometric sine function by means of a rational fraction.

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

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

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

• 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
• 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 opens an astronomical observatory with a number of famous scientists present such as al-Quhi and Abu'l-Wafa.

### 994

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

### 997

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

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

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### References

#### Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive