Tips on Sirius’s Heliacal Rising in August

Sopdet in the tomb of Seti by Jean- Pierre Dalberra. CC By 2.0. The image was altered from its original.

Tips on Sirius’s Heliacal Rising in August

How to celebrate and worship the annual flooding of the Nile, the yearly birth of a high- magnitude star, and the symbolic start of the ancient Egyptian new year

 

Each August, the fixed star Sirius’s heliacal rising occurs in various latitudes. A heliacal rising is when a star or celestial body becomes briefly visible prior to sunrise after a period of invisibility. In Hellenistic astrology, the heliacal rising was associated with prominence and activity.1 Manetho associates the heliacal rising with age: “All the stars rejoice when they are at their rising, just as each is exalted in its own rulerships. Being on the rise, as it were unto their youth, being quite powerful, they accomplish all things for men.”2 The heliacal rising and its association with youth and reappearance can be seen as a sort of rebirth or annual birth. Historically, heliacal risings had significance in some cultures. Sirius’s heliacal rising, in particular, was important to cultural and religious developments in ancient Egypt. I will discuss the origins of Sirius’s value in Egyptian culture, the value it still has for followers of Western spiritual traditions, and explain how to worship Sirius in a traditional Egyptian way this August.  

Sirius’s heliacal rising was very important in ancient Egyptian culture, time- keeping, and religion. Ancient Egyptians had three seasons: Akhet, meaning season of the flood, Peret, which meant the season after the land emerged, and Shomu, which meant low water.3 At the beginning of Egyptian history, Sirius’s heliacal rising occurred at the beginning of the flooding season, which corresponded with the months of May through August. Central and southern Egypt hasn’t had much rainfall for the last ten thousand years. However, monsoon rains would hit the Ethiopian highlands south of Egypt and then be carried by the Nile to the Mediterranean. At this time, the Nile would flood, and the flooding was irregular.4 The Egyptians noticed that Sirius made it’s heliacal rising in tropical Cancer, and used the yearly event to both mark the flooding of the Nile and to begin their yearly lunar and civil calendars, both of which dated to the Old Kingdom. The calendars began on the new moon after Sirius’s heliacal rising.5 Numerous academics have noted that Akhet was the season of fertility and nourishment. It was an important season, one that ancient Egyptians and wildlife depended on for survival. thus fittingly the start of the Egyptian new year and calendar. The flood season had an abundance of festivals, such as the Opening of the Year, the Wag festival, the Thoth festival, and the Opet festival amongst others.6 The festival associated with Sirius was called the Coming of Sopdet.7 Sirius was called Sothis in ancient Greek and Sopdet in ancient Egyptian.8 There is one additional aspect that indicates Sirius’s substantial religious value. In the Pyramid Texts, Osiris is identified with the constellation Orion, and Isis is identified with Sirius.9 Orion went by the name of Sah, as Sirius was called Sopdet. Sah and Sopdet had a child named Soped that was identified with Horus. The linking of the star deities with Osiris and Isis should not be understated. Osiris and Isis were the first children of Nut and Geb, the sky and earth. They were members of the Great Ennead of Heliopolis. They held a prominent place in Egyptian religious life throughout the millennia of its existence, despite the many changes that occurred. The connection to the new year, the flooding of the Nile, the worship as star deities, and association with Osiris and Isis all illustrate the religious importance of Sirius. The Egyptian calendar, religion, and culture were all influenced by the lore surrounding Sirius and its heliacal rising. 

Observing Sirius’s heliacal rising is useful and significant for traditional astrologers, theurgists, magicians, polytheists, and other followers of traditional Western spiritual paths. One may have never seen the Nile, have no known Egyptian blood ties or ancestors, and may live in a locality far removed from Egypt. However, the connection to ancient Egypt, and by extension, Sirius, is not unthinkable. Much of the divinatory arts, magic, and elements of the Western spiritual tradition came from ancient Egypt and the multi-cultural melting pot of Alexandria. Sirius had a special relationship with ancient Egypt, and so in a way, Sirius was an ancient forebear not only to ancient Egyptian culture but also to the many traditions that borrowed from it. In particular, traditional horoscopic astrologers and theurgists have a special bond to ancient Greek and ancient Egyptian culture and religion, and Graeco- Egyptian Alexandria. Traditional astrology’s seminal texts by the legendary Hermes Trismegistus, Nechepso and Petosiris, and Asclepius date from late Ptolemaic Egypt. Likewise, the original Corpus Hermeticum comes from 1st to 3rd century A.D. Roman Egypt. Next, the Greek magical papyri are seminal texts for magic, ritual, and spells in the ancient world. They date from 2nd century B.C. Ptolemaic Egypt to 5th century A.D. Roman Egypt, and have been a source for occultists and magicians since their publication in recent times. Iamblichus, the founder of theurgic thought and an early Neo- Platonist, lived in the late Roman empire and had been influenced by Egyptian religion as well as the syncretism of the Hellenistic world. Theurgy, traditional astrology, and Hermeticism were traditions that took form and thrived in ancient Egypt. On a spiritual level, there is causality between Sirius and the later traditions that were born or took on new forms in Egypt. In other words, a follower of a Western path that has roots in ancient Egypt has a lot to gain from observing Sirius with a ritual. It should allow a better understanding of your own practice, the causal forces that led to the environment that bred it, and the influences from which it stemmed. The origins of any way or path are important to understanding the path in totality. Knowledge of ancient progenitors is helpful for a complete understanding. There is a relationship between Sirius and some of these traditions, and the relationship can be explored.

Worship takes many forms, and I will tell how to perform a ritual for Sirius’s heliacal rising based on analysis of some ancient Egyptian literary sources. In order to recreate a Sirius ritual that is inspired by ancient Egyptian tradition and religion, there are a few things that should be discussed. These include the deities involved, issues arising from taking on a ritual in a new religious tradition, how to perform a ritual in an ancient Egyptian religious context, and the creation of a sacred space. Further, a ritual script is essential with so much information to synthesize in a ritual context. As a result, the ritual will include a script, with ancient hymns as well as interpretations of ancient Egyptian worship practices. The Sirius script is being published concurrently with this article. In the script, I’ve tried to follow and adopt some of the steps from two papyri from the cult of Mut and one from the cult of Amun.10 Even with a few extant sources, a ritual is not complete. It’s not possible to reconstruct an ancient Egyptian ritual from scratch or with just a few fragments of information. So, the rest of the Sirius ritual found in the accompanying script is based on ritual descriptions that can be found in ancient Greek literature, the Greek Magical Papyri, and the Picatrix. Finally, the ritual should take place on the date of Sirius’s heliacal rising, which differs in each latitude. Practitioners should look at Table 111 to see the heliacal rising dates in their latitudes. There are many aspects to reconstructing an ancient Egyptian ritual.

TABLE 1: Sirius Heliacal Rising Dates in Northern Latitudes

Northern Latitude Approximate Date of Heliacal Rising
32° August 3
33° August 4
34° August 5
35° August 6
36° August 7
37° August 8
38° August 9
39° August 10
40° August 11
41° August 12
42° August 13
43° August 14
44° August 15
45° August 16
46° August 17
47° August 18
48° August 19
49° August 20
50° August 21

Source: King, Bob. A Real Scorcher- Sirius at Heliacal Rising Sky and Telescope. August, 10, 2016. https://skyandtelescope.org/observing/a-real-scorcher-sirius-at-heliacal-rising/ Last accessed August 10, 2020.

Before getting to the ritual, it would be good to share some thoughts on the Sirius heliacal rising ritual and what it means for a modern person. Ideally, a Sirius ritual would be followed by daily observances following the Egyptian calendar, its gods, and its festivals. That is how the religion was followed in the past. The relationship with the gods was daily and routine. However, for a new practitioner, doing so is time-consuming. Initiates would have to familiarize themselves with the numerous gods of ancient Egypt, decide upon a pantheon and associated time period to work with, learn more about ancient Egyptian culture and religion, and follow and incorporate the Egyptian lunar or civil calendar into their daily lives. Even after all of that, they would still have to have the free time in their schedules to take on a new daily religious practice. For most people, especially those with existing spiritual practices, it’s just not feasible or desirable. Instead, the reconstructed Sirius ritual is meant to be a one-off. It is to be done in a syncretistic mindset. Principally, it is an attempt to explore origins and pay homage to spiritual ancestors. It also can act as a gateway to further understanding of the Pyramid Texts and ancient Egyptian religion and culture. 

First, the ritual should be performed in a way that aligns with ancient Egyptian worship and liturgy. University College London’s Egyptology department has extensive online resources that include a daily offering ritual from ancient Egpytian temples. The two primary sources are: 

 

“1. depictions with accompanying hieroglyphic inscriptions, in the temple for the cult of king Sety I at Abydos(1290- 1279-8 BC)

 

  1. 2. Full record of the words in the hieratic script, without illustrations, on papyrus manuscripts referring to the cult of the god Amun and the goddess Mut at Karnak, East Thebes- these manuscripts referring to the cult of the god Amun and the goddess Mut at Karnak, East Thebes – these manuscripts date to the first part of the Twenty-second Dynasty (about 945-800 BC), and are preserved in the Egyptian Museum and Papyrus Collection, Berlin (nos.3014 and 3053 for the cult of Mut, and the better-preserved no.3055 for the cult of Amun)”12

In summary, the ritual starts with the temple attendant burning incense prior to entering the shrine, then the opening of the shrine, as the attendant breaks the seals and unties the cords that were placed around the door knobs. After that, the attendant pays homage to the statue of the deity by bowing and kissing the ground, and by standing and holding hands up while singing religious hymns. Offerings of incense and scented oil occur, and then the process is repeated for possibly a second shrine. Next, an offering is given to Maat. Then incense is offered to the Nine Gods, basically the other deities in the temple. Purification of water with incense then occurs. The image of the deity is then clothed with robes of four types of cloth. Afterwards, the deity’s image is offered scented oil, which is administered on the image. It is also offered eye green and black eye paint. Finally, the attendant sweeps his footprints to leave. The attendant also offers natron, water, and incense. Natron is a naturally occurring mixture of soda ash and baking soda. It was used as a salt mixture and dug up from dry lake beds in ancient Egypt. In the ritual, an offering of smin natron is done twice, once in a circuit of four times. In the Pyramid Texts, there is mention of smin natron as natron pellets are given along with prayers of purification.13 That is the end of the daily ritual, according to the incomplete papyrus. It should also be noted that food and drink were likely also offerings, though not mentioned in the text. The extant ritual from the papyri is good source material for understanding ancient worship, and it lists a process of steps that a temple worshipper followed.

The ritual should be adapted, as it’s set in a temple complex that won’t apply to any modern practitioners. The ancient Egyptians used idols that went through the Opening of the Mouth ceremony, in which it was believed a spirit of the deity was entombed in the idol. As a result, much of the ritual from the papyri wouldn’t apply to a worshipper at home. Table 2 shows each step in the ritual, and has interpretations for each step. Mainly, a few portions are relevant for reconstructing a ritual at home. The use of a censer with fire and incense at the start, the worshipper’s prostration and kissing of the ground, the worshipper’s standing with hands raised and palms facing down at the shoulders, the central role of Maat, and the offering of salt, water, and incense at the end are all components that can be included in the Sirius ritual. Other parts, such as the dressing of the idols, the opening of each sealed shrine, and the sweeping away of the footprints have not been included. The parts of the Amun and Mut ritual that are replicable such as the materials, the order in which they are used, and the worship gestures should be included in the Sirius ritual. 

TABLE 2 Steps in Extant Rituals and Interpretations

Steps in the Ritual from the Papyrus nos. 3014, 3053, and 3055 Interpretations of the Ritual Steps
1. Burning of censer. by lighting fire and placing incense or resin in censer and burning it.

Not sure if flame or coals, or incense itself

Interpretation: Light candle and burn incense right after unless one has a thurible or censer for incense.
2. Open altar seals and untying them.

Opening the sealed shrine.

Interpretation: Not relevant to non- temple priests. Face the east or the assigned direction of deity. Invoke the deity using a hymn.
3. Placing the body prostrate on the ground and kissing it.

Hands are raised and hymns sung.

Interpretation: It can be done exactly the same way as stated in the papyrus. Place the body prostrate on the ground and kiss it. Then stand, raise the hands to shoulder level, with the palms facing downward. After that, the hymn can be spoken.
4. Offering of incense and scented oils.  Interpretation: Offer incense to each deity included in the ritual.
5. It is done again: attendant lies prostrate, kisses the ground, stands, raises hands, and sings hymns. Interpretation: Repeat the ground prostration, kissing, standing, hands raised, and reading of the hymn.
6. Offering incense to Maat. Interpretation: Offer incense to Maat. 
7. Offering incense to Nine Gods. Interpretation: Offer incense to other deities included in the ritual.
8. Purification of four vessels of two types of water with incense, clothing the image with four types of cloth robe, and painting the eyes green and black. Interpretation: This part is not relevant as the spirits of the deities are summoned rather than embodied in statues in a temple complex.  
9. Footsteps are swept away in the sand as the attendant leaves the shrine.  Interpretation: The ritual will not be performed at a temple complex to statues nor be around any sand. Instead, ask that the spirits of the deities return to their abodes and leave the sacred space.
10. Natron, water, and incense are used for purification and as offerings.  Interpretation: This step won’t be last, but near the end. Offer salt, water, and incense to each of the deities before the final part. 

The Sirius ritual will include other deities before calling on Sopdet. There are a few reasons for this. First, Sirius became important in a religious and cultural context that included other deities like Osiris, Isis, Nut, Maat, and the Nile. Osiris was equated with the Nile flooding and with the constellation Orion, which preceded Sirius’s heliacal rising. Isis was long associated with Sopdet, as already mentioned. Nut was often said to have given birth to the stars, and Sopdet is a star goddess. The hymn to the flooding of the Nile is appropriate to the context of the ritual as a whole. Second, it seems that Egyptians often invoked Maat before communicating with and worshipping the gods. The ritual papyri seem to indicate Maat as being separate from the Ennead. So, the ritual will first invoke Maat, then Nut, as the goddess of sky gave birth to the stars. After Nut, Osiris will be called upon, as he was associated with Sah and Orion, and as Orion rose first before Sirius. Since Osiris was associated with the Nile, the Nile hymn will follow the invocation of Osiris. Finally, Isis will be called upon, and then Sopdet herself. Maat, Nut, Osiris, the Nile, Isis, and Sopdet will be included in the ritual because of their connections to Sirius’s heliacal rising.

The hymns for the ritual are included in the Sirius ritual script. The hymns are for Maat, Nut, Osiris, the flooding of the Nile, Isis, and Sopdet. All of these hymns are from ancient sources, but some are adapted to suit the purposes of the Sirius ritual. First, the Maat hymn is taken from the Hymn to Maat at the Temple of Amun at el- Hibis.14 The Nut hymn is taken from the Pyramid Texts, and the utterance is about protecting the dead pharaoh.15 So, I’ve chosen Utterance 427 and 432, and have omitted reference to the pharaoh. The Osiris hymn is taken from the Introductory Hymn to Osiris Wennifer, CH XV Papyrus of Ani.16 The Nile hymn is from Papyrus Chester Beatty V. 17 It has been edited for the sake of brevity, as the Sirius ritual script is already quite long. Isis’s hymn is from Hor: Invocation to Isis.18 The final hymn to Sopdet is from the temple of Isis at Philae and was translated by Chelsea Bolton.19 All of the hymns have small edits to make them easy to read, even if the edits mean that editor brackets or parentheses were deleted.

The purification and creation of the sacred space is an additional issue that doesn’t have clear answers. To ancient Greeks, for example, cleaning and purification were important steps prior to rituals. Miasma, which translates as pollution, was a big concern in ancient Greek thought. There seem to be references to types of purification in the various Egyptian writings that are extant, but not any common ritual that priests or regular worshippers undertook prior to worshipping the Egyptian gods. Authors Judith Page and Ken Biles speculate that the ancient Egyptian creation myth was used for creating a sacred space in the early days and then in later periods the Four Sons of Horus were used for a similar purpose.20 It is tempting to link either one to later traditions for purifying and creating a sacred space. Enochian tradition and the Golden Dawn as well as later occult traditions have similarities to elements of both suggestions. The Sons of Horus were identified with the cardinal directions in afterlife rituals. They are similar to the watchtowers or guardians of the four directions in the Golden Dawn. In both traditions, divine beings were associated with the east, south, west, and north. The Opening by Watchtower ritual also has purification and the invocation of the guardians of the four quarters as its goal. There is a good argument, using modern occult knowledge, for linking creation and purification of the sacred space to the Sons of Horus. Likewise, the ancient Egyptian creation myth has parallels as well. The Golden Dawn guardians are linked to the four elements, and the creation myth has the creation of the four elements of water, earth, fire, and air as part of its story. Further, the four elements have been symbols of purification in many cultures throughout history. The Opening by Watchtower ritual and its use of elements in each quarter draws upon the traditions of millennia. So, both the creation myth and the Sons of Horus could conceivably be used to reconstruct a sacred space creation and purification ritual. It does seem unlikely that they were actually used that way in ancient Egypt without further evidence though. 

For the purpose of the Sirius ritual, a sacred space creation and purification ritual based on the creation myth is included. The ritual has three components: it retells the story of both the Hermopolis creation and Heliopolis creation, the ritual script has many breaks in the retelling for visualization, and it includes water, salt, and incense offerings in each of the four cardinal directions at the end. First, much of the telling of the tale was influenced by the University College of London’s online Egyptology resources and John Foster’s Hymn, Prayers, and Songs: An Anthology of Ancient Egyptian Lyric Poetry. In particular, Leiden Hymns such as The Hymn at Sunrise, The Primacy of Thebes and Pyramid Texts Utterance  were influential in writing the creation retelling. As noted by many, there were many competing versions of the creation myth and there doesn’t seem to be a version that was ever treated as the one definitive source. Second, the visualizations take more time but are useful in recreating the archetypal forces that the ancient Egyptians likely identified with the creation of the cosmos. Third, the use of water, salt, and incense to purify the cardinal directions has its reasons. The elements are chosen in the order they appear in the creation myth, as Nun and Nunet, the Primordial Water deities existed and then the Benben, or earthen mound, rose out of it. After Ra was born, he gave birth to Shu and Tefnut, the air deities. In the same way, the ritual starts with water, moves on to salt or earth, and finishes with air. The offering of salt was also influenced by the Pyramid Texts, where natron is offered to various deities. This part was insightful, as with each pellet of salt that is offered, the hymn mentions to purify oneself and to purify the deity. The text of the hymn is imitated in the ritual, especially the dual type format of purifying oneself and purifying the deity. It is also tempting to link the number two to the ritual, as two represents the dyad in traditional ancient Greek thought, and the ritual centers on the creation myth. The dyad was linked to matter by the Pythagoreans.21 The dyad was also seen as the midpoint between the monad and the triad. Therefore, the purification ritual at the beginning of the Sirius ritual script has been reconstructed from translated texts and the guidance of the University College of London’s online Egyptology resources, and includes three main aspects. 

Now that the parameters and the logic behind the construction of the ritual have been explained, there are steps for preparing the ritual. First, worshippers should look at Table 1 and find the Sirius heliacal rising for their latitude. Next, they should plan to start the ritual at the closest time to the heliacal rising. After that, it would be good to read over the hymns and get some background on Maat, Nut, Osiris, the Nile, Isis, and Sopdet. Print out the script after making personal changes or adjustments. Another option is to just read them out from an electronic device. Another step is to get some paper and write out the hieroglyphs for Sopdet. Worshippers can also write Sothis in the Greek alphabet, and Sirius in the Latin alphabet. Then, they should get incense and candles. Seven pieces of incense would be ideal. Six candles, one for each deity, would also fit the script. However, one piece of incense and one candle would be sufficient as well. The materials are listed at the beginning of the Sirius ritual script. Also, one should obtain natural spring water and salt. Finally, obtain some food and beer that match ancient Egyptian diets. After making such preparations, the worshipper should be ready for the ritual. Refer to Table 3 for a summary of the preparatory steps.

TABLE 3: Sirius Ritual Preparation Steps

Sirius Ritual Preparation Steps 
  1.  Look at Table 1 and find the Sirius heliacal rising for your latitude. 
  • 2. Plan to start the ritual at the closest time to the heliacal rising, or if there isn’t any other option, find a time slot for that day or night.
  • 3. It would also be good to read over the hymns and get some background on Maat, Nut, Osiris, the Nile, Isis, and Sopdet itself. Print out the script or read over the hymns from an electronic device. Practice reading them if possible. 
  • 4. Get some paper, and draw the hieroglyphs for Sirius.
  • Get candles and incense. The incense can be frankincense or another traditional incense. One candle is enough, but if possible six candles, one for each deity, would also suffice. 
  • Obtain natural spring water and salt.
  • Get some traditional Egyptian food that can be included in the offerings. This can be garlic, cabbage, radishes, turnips, legumes, cucumbers, bread, beer, lentils, onions, fish, eggs, dates, and figs.   

The discussion and analysis of extant sources helps to better understand the elements of ancient Egyptian ritual. With the Sirius ritual script, and the information in the previous paragraphs, any worshipper should be able to understand and recreate an ancient Egyptian ritual on the occasion of Sirius’s heliacal rising. The ritual can be performed each August in the years ahead, if desired. Likewise, readers should have a better understanding of the origins of Sirius’s value in Egyptian culture. Finally, the value of Sirius’s heliacal rising still has for followers of Western spiritual traditions should be apparent.

 

The accompanying Sirius ritual script can be found here.

 

Bibliography

1.Brennan, Chris. Hellenistic Astrology: The Study of Fate and Fortune. Amor Fati Publications, Denver, Colorado. 2017. 202-203.

2.Manetho. The Apotelesmatika of Manetho, ed. And trans. By Robert Lopilato, PhD diss. Brown University. Providence, Rhode Island. 1998. 216-217.

3. University College London. Digital Egypt. “Festivals in the ancient Egyptian calendar.” Last accessed August 14 2020.  https://www.ucl.ac.uk/museums-static/digitalegypt/ideology/festivaldates.html

4. Budge, Wallis E A. The Nile Notes for Travellers in Egypt. Thos. Cook and Son, Ltd. Ludgate Circus, London. 1895. 45-49.

5. University College London. Digital Egypt. “Festivals in the ancient Egyptian calendar.” Last accessed August 14 2020.  https://www.ucl.ac.uk/museums-static/digitalegypt/ideology/festivaldates.html

6. University College London. Digital Egypt. “Festivals in the ancient Egyptian calendar.” Last accessed August 14 2020.  https://www.ucl.ac.uk/museums-static/digitalegypt/ideology/festivaldates.html

7. Seawright, Caroline. “Sopdet, Goddess of Sirius, the new Year, and the Inundation.” Tour Egypt. http://www.touregypt.net/featurestories/sopdet.htm

8.Seawright, Caroline. “Sopdet, Goddess of Sirius, the new Year, and the Inundation.” Tour Egypt. http://www.touregypt.net/featurestories/sopdet.htm

9.Seawright, Caroline. “Sopdet, Goddess of Sirius, the new Year, and the Inundation.” Tour Egypt. 

http://www.touregypt.net/featurestories/sopdet.htm

10.University College London. Digital Egypt. “Daily Offering Ritual in ancient Egyptian temples.” Last accessed August 14 2020.  

https://www.ucl.ac.uk/museums-static/digitalegypt/religion/dailycult.html

11. King, Bob. “A Real Scorcher- Sirius at Heliacal Rising.” Sky and Telescope. August, 10, 2016. last accessed August 10, 2020

https://skyandtelescope.org/observing/a-real-scorcher-sirius-at-heliacal-rising/

12.University College London. Digital Egypt. “Daily Offering Ritual in ancient Egyptian temples.” Last accessed August 14 2020. https://www.ucl.ac.uk/museums-static/digitalegypt/religion/dailycult.html

13. Internet Sacred Text Archive. “The Pyramid Texts, Utterance 35.” Translated by Samuel A. B. Mercer, 1952. Accessed August 15, 2020.

https://www.sacred-texts.com/egy/pyt/pyt05.htm

14. Foster, John L. Hymns, Prayers, and Songs: An Anthology of Ancient Egyptian Literature and Lyric Poetry Atlanta, Georgia. Scholars Press. 1995. 143.

15. Foster, John L. 21.

16. Foster, John L. 98.

17. Helck, Wolfgang. Der Text des “Nilhymnus”. Kleine Aegyptische Texte Publisher. Wiesbaden. 1972. 

18. Kockelmann, H. Praising the Goddess. De Gruyter. 2008.

19. Luellon Bolton, Chelsea. Flaming Lioness: Ancient Hymns for Egyptian Goddesses. Lulu Publishing, USA, 2019. 49.

20. Page, Judith and Biles, Ken. “Invoking the Egyptian Gods.” Llewellyn. December 12, 2011 accessed 08.09.2020

https://www.llewellyn.com/journal/article/2256

21. Attributed to Iamblichus. Theology of Arithmetic: On the Mystical, Mathematical, and Cosmological Symbolism of the First Ten Numbers. Translated by Waterfield, Robin.Phanes Press. Grand Rapids, Michigan. 1988. 40.

 

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