Luo Shu Time Line

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
Timaeus.
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       
Moschopoulos.

ITALIAN RENAISSANCE

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
squares.  

                                           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.

The Enneagram 

THIS IS A SAMPLE FROM A CHAPTER IN NUMBER, TIME, AND ARCHETYPE.

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