Ancient Egyptian Geometry

 

Alice C. Linsley

The American mathematician Abraham Seidenberg (1916-1988) believed that there were two traditions in ancient mathematics. One was a geometric-constructive tradition and the other an algebraic-computational tradition. He claimed that both originated from a common source prior to Greek, Babylonian, Chinese, and Vedic mathematics. If he is correct, that leaves the ancient Nile.

In 1962, Seidenberg expressed the opinion that “the elements of ancient geometry found in Egypt and Babylonia stem from a ritual system of the kind found in Shulba Sūtrās.” However, the geometry used by those pyramid builders predates the Shulba Sūtrās by about 1800 years. The oldest of the Pyramids of Giza is that of King Khufu and dates to 2609 B.C. South of Khufu’s pyramid is the step pyramid of King Djoser, a ruler of the Third Dynasty (2670-2613 B.C.). Djoser inaugurated an era of monumental building in stone which inspired the Great Pyramids.

The geometry used in the construction of the Great Pyramids is evident in their alignment. As Giulio Magli (Faculty of Civil Architecture - Politecnico di Milano) noted, “Indeed, the south-east corners of these monuments align towards the site of the temple of Heliopolis, which was plainly visible in ancient times. It was later discovered that a similar situation occurs in the main pyramid field of the subsequent dynasty at Abu Sir. Here, the north-west corners of three chronologically successive pyramids again voluntarily align towards Heliopolis.” (“Topography, astronomy and dynastic history in the alignments of the pyramid fields of the Old Kingdom” by Giulio Magli)

It has been shown that the pyramids at Giza, Abusir, and Saqqara all align to the sacred shrine city of Heliopolis, that is, biblical On. The Pyramid Texts speak of On as the place on earth where Ra ruled (Utterance 307). In Genesis 41:45 we are told that Jacob's son Joseph married Asenath, a high-status bride whose father was a priest of On. 

Related reading: Horite and Sethite Mounds, Early Resurrection Texts; Sun Cities of the Ancient World

Sun Cities of the Ancient World

Great Hypostyle Hall within the Karnak temple complex

Alice C. Linsley

The Sun Cities of the ancient world extended from the Nile Valley to Mesopotamia and the Indus Valley. These were royal complexes with a temple dedicated to the High God whose symbol was the Sun. 

Head of Userkaf, recovered from his sun temple.

The sun cities were built near rivers and lakes and on elevated sites to avoid flooding. At the center of these royal cities were the temple, the palace, housing for priests, and quarters for the royal guard. The temple typically was aligned to the solar arc and was called O'piru, which means "house of the Sun."

Six Nilotic kings are known for having built sun temples in Egypt. The temple of Nyuserre has a central sacrificial altar in an open-air courtyard. The altar is composed of a number of alabaster parts.

Some of the priests who served at the ancient sun cities were called 'apiru, ha'piru or ha'biru. The English word Hebrew is a variant of Ha'biru and likely is derived from the Akkadian word abru which means priest. (Akkadian is the oldest known Semitic language.) 

Abraham is called "Hebrew" in Genesis 14:13. The Harris papyrus speaks of 'apriu of Re at Heliopolis, a very prestigious sun city. Plato, who studied under a Horite priest at Memphis for thirteen years, wrote "Tell me of the God of On, which was, is and shall be. 

Heliopolis (biblical On) is mentioned in Isaiah 19:18 as one of five Egyptian cities that swore allegiance to the Lord of Hosts. 

The people who lived at On called it Iunu, which means "place of pillars." There were many pillars bearing inscriptions to the high king, prayers to the High God and to his son Horus. Some pillars depicted great victories in war, the details of treaties, and dedications. Isaiah 19:19 refers to a pillar erected in Egypt as a sign that the Lord will send the Egyptians a savior.

It was common for pillars to be inscribed in memory of holy ancestors, as stained-glass windows in churches are dedicated to "pillars" of the congregation. The entrance pillars of Solomon's temple were called Boaz and Joktan. Boaz was Solomon's holy ancestor on his father's side and Joktan was a holy ancestor on his mother's side.

John Ogutu notes that in his Nilotic Luo language, "O'mbiru, obiru refers to a small house built like a shrine or as a symbol among the Luo. A man who died before he could build his house would have the mourners erect one before his burial." The O'piru was a place where loved ones were memorialized.

According to Genesis 41:45, Joseph married into the royal priest family of Heliopolis. Study of the Heliopolitan cosmogony makes it apparent that Heliopolis was conceived as the sacred center of the primeval ocean, called Nun. The many pillars of the temple symbolized the connection between the waters below and the waters above (Gen. 1:7). Seeing as "he was a son of Nun" (Num. 11:28), Joshua likely belonged to a Horite Hebrew clan associated with On. 

The Prestige of Biblical On

Biblical On was perhaps the most prestigious shrine city of the ancient world. It was the geodetic center of Egypt. On was known for the purity of life of its priests. Plutarch wrote that the “priests of the Sun at Heliopolis never carry wine into their temples, for they regard it as indecent for those who are devoted to the service of any god to indulge in the drinking of wine whilst they are under the immediate inspection of their Lord and King. The priests of the other deities are not so scrupulous in this respect, for they use it, though sparingly.” 

The Horite and Sethite priests purified themselves before entering their temples. The purification involved fasting, abstinence from sexual relations and alcohol, ritual bathing, and an intense period of prayer. Korah, Moses' half-brother, was a priest according to Numbers 16:17,18. His name means "shaved one." Shaving was part of the purification ritual.

Note that Jerusalem is near the center of the triangle of shrine cities.

Heliopolis means "city of the Sun" and there were other such cities dedicated to the Creator whose emblem was the sun. The shrine city of Baalbek in Lebanon, with its massive stones, aligned to On (see map above). The pyramids at Giza, Abusir and Saqqara were aligned to the obelisk at On. 

King Tut established another Heliopolis at Thebes. The temple of Thebes was called "Heliopolis of the South." Thebes was the spiritual center of Upper Egypt and rivaled the importance of Heliopolis in the North.

Tutankhamun's cartouche bears the words heqa-iunu-shema, which is usually rendered "Ruler of On of the South." Heqa refers to the sceptre or shepherd's crook of the Egyptian rulers. Shema or ta-shema refers to Upper Egypt, the narrow valley extending south of Memphis to Abu on the First Cataract in Nubia. King Tut's sacred center was Thebes, between Memphis and Abu.

Herodotus reported that it took nine days to sail from Heliopolis to Thebes, Tutankhamun's shrine city. By relocating his court to Thebes, Tutankhamun was attempting to regain the glory of his forefathers at a time of Egypt's decline.

Related reading: Horite and Sethite Mounds, Ancient Sun Temple Discovered in Cairo Suburb; The Unveiling of Joseph; The Shrine City of Nekhen; Solar Symbolism of the Proto-Gospel