4000 BC Ur - pottery plates with 6x6 magic square, tetractys, swastika, and divine proportion
using the Chinese model of the Pythagorean theorem.
2000 BC Fu Hsi is presented the Luo Shu from Heaven in the form of turtle.
1700 – 1100 BC The Shang Dynasty utilizes the Luo Shu in city planning, royal tombs.
1100 – 600 BC Zhou pei suan jing – first known math book - discusses the gnomon, right angle.
550 BC Plato’s Republic mentions the 27x27 magic square.
400 BC -18 AD TLV bronze mirror incorporates the cosmology of the Luo Shu and gnomon.
165 BC Tomb of Fuyang Yijing features numerical Luo Shu on a divination board.
100 BC The Da Dai Li Ji is the oldest known text to publish the Lo Shu.
100 AD Plutarch refers to the number of the sun as 729 in his Generation of the Soul in the
140 AD Reliefs in royal tombs (China) show the carpenter’s square and compass.
200 - 300 AD Runic Magic square of three found in runic script, used by Celtic priests for rituals.
500 – 1300 AD Several quincunx churches built throughout the Byzantine Empire.
550 – 650 AD Luo Shu/quincunx pattern and other Chinese symbols used in early Christian art.
550 AD India, first mention of magic squares used in the making of perfume.
600 – 1100 AD Several illuminated manuscripts with the Luo Shu/quincunx pattern on the cover.
700 – 1200 AD Magic squares gain popularity in the Islamic world and are published for the first
time in 900 AD.
1300 – AD Tibetan Llama mandalas use the Luo Shu pattern as the basis of mandala design.
1300 AD First book on Magic Squares published by a Westerner, Greek byzantine Manual
1470 - 1490 AD Lucas Pacioli (friend, collaborator, and roomate of Leonardo) amasses large
collection of Magic Squares, writes three math books and teaches math at universities.
1485 AD Leonardo da Vinci incorporates the Luo Shu/quincunx pattern into architectural
and church plan drawings.
Leonardo da Vinci's church drawings uses the cross in square design, the quincunx design, the 3x3 square, and the concept of squaring the circle.
1491 AD Pacioli is banned from teaching in his home town.
1500 AD Pacioli and da Vinci share a house in Florence, Italy.
1505 - 1507 AD Albrecht Durer travels to Italy to meet with Pacioli, whom Durer feels posseses
thesecret of mathematics and art.
1506 Donato Bramante provides ground plan for St. Peter's Basilica, a classic quincunx and
Lo Shu design.
1509 AD Pacioli (da Vinci the illustrator) publishes The Divine Proportion.
1514 AD Durer uses the 4x4 magic square in his masterpiece Melancholia II.
1533 AD Cornelius Agrippa publishes de Occulta Philosophia, which included all the magic
squares used in Renaissance magic.
1566 AD The Villa Capra "La Rotonda" incorporates the Lo Shu in the ground plan design, by
talian architect Andrea Palladio.
The ground plan of the Villa Rotonda with the 3x3 Magic Square used as the template for temple design.
1655 AD Athanasius Kircher writes Arithmologia and publishes the first nine magic
Athanasius Kircher - Arithmology
FRONTPIECE FOR ARITHMOLOGIA
The above art work by Athanasuis Kircher for his book Arithmologia (1655) demonstrates the symbolism of the tetractys, the Lo Shu, and the Pythagorean Theorem. This suggests that Kircher may have realized the connection of the Pythagorean Theorem and the Lo Shu, the Chinese cosmological model for Time and Space.
Kircher was an avid Sinologist and wrote over 40 books including China Illustrated in Monuments (1667); therefore, Kircher may have been aware of the Chinese reverence for the Lo Shu.
Kircher assigns the Lo Shu Magic Square a higher hierarchy than the Pythagorean Theorem and the Tetractys. The 3x3 Magic Square is being held by an angel in Heaven, a parallel reference to the Chinese belief that the Lo Shu was presented to humankind from Heaven. The model of the Pythagorean Theorem, in contrast, sits on the terrestrial Earth.
A clue to Kircher's research into China's ancient history through his own study of the Chinese language can be found in Kircher's book Oedipus Aegyptiacus (Vol. 1., p. 70):
I confess, for a long time I had regarded all this (dynastes and the Atlantis) as pure fables to the day when, better instructed in Oriental languages, I judged that all those legends must be, after all, only the development of a great truth.....
Kircher must have used his better understanding of the Chinese language to read and comprehend ancient Chinese books that were in the possession of the Vatican. The burning of libraries and books took place in China, c. 213 BC and many times since. The priceless Chinese texts were the oldest books in the world, some found safety via the Silk Road and fell into the hands of the Church. This would explain how Kircher was aware of the Luo Shu as a gift from Heaven and its relationship to the Pythagorean Theorem. Perhaps there even is a connection of the Luo Shu with Atlantis!
Kircher also uses the Enneagram at the top of the frontpiece, possibly suggesting that the Enneagram and the Luo Shu are Heavenly gifts to Humankind and are connected to the language of numbers.
THIS IS A SAMPLE FROM A CHAPTER IN NUMBER, TIME, AND ARCHETYPE.
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