# Epoch: Late Ancient World (from 1 AD to 499 AD)

## Description

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## Chronology

• Cleomedes writes his book "On the Circular Motions of the Celestial Bodies".
• Heron writes "Pneumatica", a book with descriptions of over 100 machines such as a fire engine, a wind organ, a coin-operated machine, and a steam-powered turbine called an aeolipile.

### about 120 - 140

• Yavanesvara invents methods for computing horoscopes.

• Nicomachus writes "Introduction to Arithmetic", becoming later a standard arithmetic text for more than 1000 years.

### 127

• Ptolemy: first astronomical observation (26 March 127, last was made on 2 February 141).
• He compares his own observations of equinoxes with those of Hipparchus and Meton.
• He propounded the geocentric theory of the solar system that prevailed for 1400 years.
• Theon making astronomical observations of Mercury and Venus between 127 and 132

### 132

• Heng invents the first seismograph for measuring earthquakes.

• Hipparchus
• Compiles trigonometric tables and gave methods for solving spherical triangles
• His image "sitting and looking at a globe" appears on coins minted under five different Roman emperors between 138 AD and 253 AD.
• Heng's seismograph detects an earthquake, no other evidence of the earthquake being felt in the capital Lo-yang.

• Nicomachus finds perfect numbers, namely 6, 28, 496 and 8128.
• Wrongly "deducts" from this that $n$th perfect number has $n$ digits, and that all perfect numbers end in 6 and 8 alternately.

• Apollonius writes "Conics", containing 387 separate propositions.
• Obtains an approximation of $\pi$ between $\frac{223}{71}<\pi<\frac{22}{7}$.

• Diophantus writes "Arithmetica" which had an enormous influence on the development of number theory

• Callippus forms what has been called the Callippic period, essentially a cycle of four Metonic periods.
• It was more accurate than the original Metonic cycle and made use of the fact that 365.25 days is a more precise value for the tropical year than 365 days.

### 320 to 340

• Pappus to write his commenatary on Ptolemy's Almagest
• Major work "Synagoge" or the "Mathematical Collection" which is a collection of mathematical writings in eight books.
• One of his theorems is still cited as the basis of modern projective geometry.

### 364

• Theon observes a solar eclipse on 16 June 364 at Alexandria and a lunar eclipse, again in Alexandria, on 25 November 364.

### 400

• Hypatia becomes head of the Platonist school at Alexandria.
• Wrote commentaries on Diophantus's Arithmetica, on Apollonius's Conics and on Ptolemy's astronomical works.
• Killed by a fanatical Christian sect.

### about 468 to 486

• Qiujian writes his mathematical text "Zhang Qiujian Suanjing" (Mathematical Manual of Quijian)

### 474

• Zi A new scale between chih and tuan established.
• Writes his mathematical text "Sunzi suanjing" (Mathematical Manual of Sunzi)

### 510

• Boethius's "Arithmetic" texts the best available for many centuries during a time when mathematical achievement in Europe was at a remarkably low point.

### 529

• Plato's Academy closed down by the Christian Emperor Justinian who claimed it was a pagan establishment.

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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