Hi all, I hope everyone is well - keep your distance!
Budge gives a NS distance of 618 itr and an EW distance of 120 itr for the 12 hour circuit of the underworld from the Book of Amduat. Besides 618 being the reciprocal of phi x 1000, I noticed some time ago that 618/120 is a close approximation for the measures from the cubit rods and from the White Chapel of 106 itr for the total length of Egypt, and 20 itr for the length of the Delta. Then I saw that Gayle Gibson, citing Lauer and Firth, gives a distance for Djoser's Heb Sed Court of 95m NS by 18m EW, and 95/18 = 106/20. Anyway, I added a few pages to my article about the remen and the cubit rods and also added a few diagrams that I think look good. In my article the new pages are 27-30. The article link and the text are below. Let me know what you think!
[home.hiwaay.net]
Following the discovery of Kepler’s third law, that the squares of the period of revolution of any two planets are proportional to the cubes of their mean distances from the sun, Kepler stated: “Since the first light eight months ago, since broad day three months ago, and since the sun of my wonderful speculation has shone fully a very few days ago: nothing holds me back. I am free to give my self up to the sacred madness, I am free to taunt mortals with the frank confession that I am stealing the golden vessels of the Egyptians, in order to build of them a temple for my God, far from the territory of Egypt.” (87) Based on Kepler’s second and third laws of planetary motion, for any given period of time, the areas swept by any two planets are proportional to the square root of their mean distances from the sun.
The Kepler triangle and the right triangle of the great pyramid have the same n proportion. The ancient Egyptian funerary text known as the AmDuat is divided into 12 sections, regarded as the 12 hours of the night. The second and third sections are the first two sections of the underworld and the length of each is 309 itr. The combined length of these two sections is 1000/n = 618 itr. The lengths of the remaining sections are unspecified. Chapter 110 of the Book of the Dead gives the length of 1000 itr. The proportion between these lengths is1000/618 = 1.618. The combined length is 1000 itr + 618 itr = 1618 itr. The n proportion of the Kepler triangle and the great pyramid is the same as the proportion between 1000 itr and 618 itr.
According to Budge: The first hour in the Amduat was a western distance of 120 itr before ‘entering into the earth through the hall of the horizon.’ The second and third hours are spent sailing north, 309 itr + 309 itr = 618 itr. Hours four through nine were spent crossing the sandy island realm of Sekar-Osiris. “It is pretty certain that the tenth and eleventh hours comprised a part of the eastern Delta, and that it extended some considerable distance south of Memphis. It follows that when the boat entered this division the god would have to alter his course from east to south. As the kingdom of Osiris marked the limit of his journey northwards, and the boat then turned eastwards, so the northern end of the kingdom of Heliopolis marked the limit of his journey eastwards, and the boat then turned southwards.” (88)
The southern boundary of ancient Egypt was the northern boundary of direct vertical sunlight on the summer solstice. During the early period of ancient Egypt, the solstice also marked the reappearance of Sirius in the eastern sky just before dawn. These events also marked the beginning of the new year in ancient Egypt. If the east-west distance of 120 itr during the first hour also applied to the width of the island of Sekar-Osiris, and the north-south distance of 618 itr also applied to the distance traveled in the tenth and eleventh hours, the journey may have begun on the southern border of Egypt, under the path of the setting sun -- and ended in the twelfth hour, on the southern border of Egypt, under the path of the rising sun.
The ancient Egyptian Heb-Sed festival was also celebrated at the beginning of the New Year. Eric Uphill stated: “One of the first rites to be performed was the raising of the Djed-pillar at dawn, which is not shown at Bubastis but appears elsewhere, to symbolize the king’s triumph over death, the victory of the new Horus over Set. Also at this time the king would need to perform the four running ceremonies in order to demonstrate his returned vigor and thus ensure continued prosperity for the country. These rites seem to have been performed in an enclosed area not far from the Sed festival palace.” (89)
Gardiner stated. “Some attention must be paid to the word itrt. My rendering as ‘conclave’ confessedly sacrifices accuracy to intelligibility. The accepted translation is ‘sanctuary’ but this I hold to be altogether wide of the mark. In its religious application the term seems so much bound up with the great royal Sed festival or Jubilee that no single English word could possibly convey an adequate notion of its signification. I believe itrt to be related to ‘river’, ‘river channel’ and to mean fundamentally something like ‘line’ or ‘row’. Occurring frequently in the dual, it there means ‘the two sides’ or ‘rows’. Now in the Sed festival, which was normally celebrated in Memphis, all the deities of the two halves of the country were summoned thither, their statues or emblems housed in two rows of shrines on opposite sides of a jubilee court, the lower Egyptian shrines with the appearance of the primitive sanctuaries of the cobra-goddess of Buto, while the upper Egyptian shrines resembled that of the vulture-goddess of El-Kab. In effect, the expression itrt smrt would thus mean ‘the company or conclave of Egyptian deities’, though simultaneously it would conjure up the image of rows of Egyptian shrines such as could be seen at Memphis on the occasion of the great national festival. Excavation has actually unearthed imitations of them in the marvelous temple attached to King Djoser’s step pyramid.” (90) In ancient Egypt, ‘river’ was associated with the country itself and was also associated with the journey through the underworld. Given that itr was a unit of measure, itrt could be rendered as ‘area’, or ‘the area of Egyptian deities’, or the area of the underworld, or the area of Egypt.
Christine Schnusenberg stated: “The new year was often set apart for great reenactments of the acts of Re at the times of creation...Sometimes the Sed festival was celebrated at the beginning of the new year and the two became interwoven with each other...The Sed festival intertwined the visible and the invisible, of life here and now and of life after death.” (91)
The shrines that surrounded and defined the area of the Heb-Sed court were typically installed for the festival and removed afterwards, but the step pyramid complex of King Djoser included a permanent Heb-Sed court, with dummy shrines constructed of solid masonry. The size of Djoser’s court is 95 meters NS × 18 meters EW.92 The proportion of Djoser’s court is approximately the same as the proportions of the NS and EW distances in the Amduat: 618/120 = 95/18.4.
Dieter Kurth translated the Edfu geographical inscription referred to by Griffith and shown above from the hand copy by Brugsch.93 “The cultivable lands of all Egypt, from Elephantine to the marshes, 27,000,000 setat of land. All the fields with barley and wheat, 9,000,000. The waters of the Delta with papyrus, lotus, and all the vegetation grown by the inundation: 18,000,000(a) setat. In specification: All the rivers of upper and lower Egypt, 2,400,000 setat, the marshland of lower Egypt, that is Lake Moeris and its canal, 6,600,000 setat. Length from Elephantine in its entirety is 106 itr, its width on the land from the western river branch of Egypt to the eastern branch is 14 itr. (a) The number here is written 1800 or 1000 × 800 = 800,000, but the number 10,000 was omitted through oversight and the intended number was 1800 × 10,000 = 18,000,000.” (94)
The bottom of the tenth column shows two coils of 100 each and seven hobbles of 10 each, for a total of 270. The frog is 100,000, and 270 × 100,000 = 27,000,000 setat. The setat, or Greek aroura, is a square measure with sides of 100 royal cubits and an area of 10,000 square cubits. Griffith stated: “27,000,000 arouras mean about 73,918 square kilometers or 28,420 square miles, while Schweinfurth, who gives the length of Egypt proper as 550 miles, makes the cultivable area only 11,342 square miles.” (95) Although parts of the Delta are much wider than the 14 itr distance given between branches of the Nile; and the cultivable area of the Nile valley is much narrower; and the Nile valley drifts east of the Delta, Griffith calculated a rectangular area of 106 itr × 14 itr = 1484 square itr. Assuming 27,000,000 aroura equals 1484 square itr, the square itr would contain 18,194 aroura, or 181,940,000 square cubits, and /181,940,000 = 13,487 royal cubits for the length of the itr. Given the length of 15,000 cubits for the itr, 150002 = 225,000,000 royal cubits. 225,000,000/10,000 = 22,500 setat per square itr. 27,000,000 setat/22,500 = 1200 square itr.
Kurth’s translation gives a measure of 18,000,000 setat for the Delta. 18,000,000 setat is twice the entire area of the Delta. The figure of 9,000,000 setat is an accurate measure of the area of the Delta, and depending on the copying and punctuation of the inscription and the translation, 9,000,000 setat may have been the intended expression of the area of the Delta.
The 95/18 meter proportion of the Heb-Sed court is equal to the proportion of 106/20 itr. The inscriptions on the cubit rods and in the White Chapel divide the length of Egypt into 86 itr for upper Egypt and 20 itr for lower Egypt. 202
= 400 square itr. Given 15,000 cubits for the length of the itr, 400 square itr = 9,000,000 setat. A circle with a radius of 20 itr has an area of 1256 square itr. The area marked by the arc in the diagram is just under two-thirds of the upper half of the area of the circle, or 400 square itr, or 9,000,000 setat. 106 × 20 = 2120 square itr, or 47,700,000 setat. If the 18,000,000 setat of land from the Edfu inscription was intended to be added to rather than included in the 27,000,000 setat of land, then the total would be 45,000,000 setat of land, or 2,700,000 setat less than the area shown above. 2,400,000 setat is the area given for Egypt’s rivers.
The itr measures from the Amduat are a 6x multiple of the itr measures from the cubit rods. The arc of the Delta intersects the EW boundaries 3 itr, or 18 underworld itr, south of the northern boundary. 106/20 = 636/120 and 103/20 = 618/120. The proportions of the Heb-Sed Court express the given proportions of Egypt and the underworld as shown above.
Budge gives a NS distance of 618 itr and an EW distance of 120 itr for the 12 hour circuit of the underworld from the Book of Amduat. Besides 618 being the reciprocal of phi x 1000, I noticed some time ago that 618/120 is a close approximation for the measures from the cubit rods and from the White Chapel of 106 itr for the total length of Egypt, and 20 itr for the length of the Delta. Then I saw that Gayle Gibson, citing Lauer and Firth, gives a distance for Djoser's Heb Sed Court of 95m NS by 18m EW, and 95/18 = 106/20. Anyway, I added a few pages to my article about the remen and the cubit rods and also added a few diagrams that I think look good. In my article the new pages are 27-30. The article link and the text are below. Let me know what you think!
[home.hiwaay.net]
Following the discovery of Kepler’s third law, that the squares of the period of revolution of any two planets are proportional to the cubes of their mean distances from the sun, Kepler stated: “Since the first light eight months ago, since broad day three months ago, and since the sun of my wonderful speculation has shone fully a very few days ago: nothing holds me back. I am free to give my self up to the sacred madness, I am free to taunt mortals with the frank confession that I am stealing the golden vessels of the Egyptians, in order to build of them a temple for my God, far from the territory of Egypt.” (87) Based on Kepler’s second and third laws of planetary motion, for any given period of time, the areas swept by any two planets are proportional to the square root of their mean distances from the sun.
The Kepler triangle and the right triangle of the great pyramid have the same n proportion. The ancient Egyptian funerary text known as the AmDuat is divided into 12 sections, regarded as the 12 hours of the night. The second and third sections are the first two sections of the underworld and the length of each is 309 itr. The combined length of these two sections is 1000/n = 618 itr. The lengths of the remaining sections are unspecified. Chapter 110 of the Book of the Dead gives the length of 1000 itr. The proportion between these lengths is1000/618 = 1.618. The combined length is 1000 itr + 618 itr = 1618 itr. The n proportion of the Kepler triangle and the great pyramid is the same as the proportion between 1000 itr and 618 itr.
According to Budge: The first hour in the Amduat was a western distance of 120 itr before ‘entering into the earth through the hall of the horizon.’ The second and third hours are spent sailing north, 309 itr + 309 itr = 618 itr. Hours four through nine were spent crossing the sandy island realm of Sekar-Osiris. “It is pretty certain that the tenth and eleventh hours comprised a part of the eastern Delta, and that it extended some considerable distance south of Memphis. It follows that when the boat entered this division the god would have to alter his course from east to south. As the kingdom of Osiris marked the limit of his journey northwards, and the boat then turned eastwards, so the northern end of the kingdom of Heliopolis marked the limit of his journey eastwards, and the boat then turned southwards.” (88)
The southern boundary of ancient Egypt was the northern boundary of direct vertical sunlight on the summer solstice. During the early period of ancient Egypt, the solstice also marked the reappearance of Sirius in the eastern sky just before dawn. These events also marked the beginning of the new year in ancient Egypt. If the east-west distance of 120 itr during the first hour also applied to the width of the island of Sekar-Osiris, and the north-south distance of 618 itr also applied to the distance traveled in the tenth and eleventh hours, the journey may have begun on the southern border of Egypt, under the path of the setting sun -- and ended in the twelfth hour, on the southern border of Egypt, under the path of the rising sun.
The ancient Egyptian Heb-Sed festival was also celebrated at the beginning of the New Year. Eric Uphill stated: “One of the first rites to be performed was the raising of the Djed-pillar at dawn, which is not shown at Bubastis but appears elsewhere, to symbolize the king’s triumph over death, the victory of the new Horus over Set. Also at this time the king would need to perform the four running ceremonies in order to demonstrate his returned vigor and thus ensure continued prosperity for the country. These rites seem to have been performed in an enclosed area not far from the Sed festival palace.” (89)
Gardiner stated. “Some attention must be paid to the word itrt. My rendering as ‘conclave’ confessedly sacrifices accuracy to intelligibility. The accepted translation is ‘sanctuary’ but this I hold to be altogether wide of the mark. In its religious application the term seems so much bound up with the great royal Sed festival or Jubilee that no single English word could possibly convey an adequate notion of its signification. I believe itrt to be related to ‘river’, ‘river channel’ and to mean fundamentally something like ‘line’ or ‘row’. Occurring frequently in the dual, it there means ‘the two sides’ or ‘rows’. Now in the Sed festival, which was normally celebrated in Memphis, all the deities of the two halves of the country were summoned thither, their statues or emblems housed in two rows of shrines on opposite sides of a jubilee court, the lower Egyptian shrines with the appearance of the primitive sanctuaries of the cobra-goddess of Buto, while the upper Egyptian shrines resembled that of the vulture-goddess of El-Kab. In effect, the expression itrt smrt would thus mean ‘the company or conclave of Egyptian deities’, though simultaneously it would conjure up the image of rows of Egyptian shrines such as could be seen at Memphis on the occasion of the great national festival. Excavation has actually unearthed imitations of them in the marvelous temple attached to King Djoser’s step pyramid.” (90) In ancient Egypt, ‘river’ was associated with the country itself and was also associated with the journey through the underworld. Given that itr was a unit of measure, itrt could be rendered as ‘area’, or ‘the area of Egyptian deities’, or the area of the underworld, or the area of Egypt.
Christine Schnusenberg stated: “The new year was often set apart for great reenactments of the acts of Re at the times of creation...Sometimes the Sed festival was celebrated at the beginning of the new year and the two became interwoven with each other...The Sed festival intertwined the visible and the invisible, of life here and now and of life after death.” (91)
The shrines that surrounded and defined the area of the Heb-Sed court were typically installed for the festival and removed afterwards, but the step pyramid complex of King Djoser included a permanent Heb-Sed court, with dummy shrines constructed of solid masonry. The size of Djoser’s court is 95 meters NS × 18 meters EW.92 The proportion of Djoser’s court is approximately the same as the proportions of the NS and EW distances in the Amduat: 618/120 = 95/18.4.
Dieter Kurth translated the Edfu geographical inscription referred to by Griffith and shown above from the hand copy by Brugsch.93 “The cultivable lands of all Egypt, from Elephantine to the marshes, 27,000,000 setat of land. All the fields with barley and wheat, 9,000,000. The waters of the Delta with papyrus, lotus, and all the vegetation grown by the inundation: 18,000,000(a) setat. In specification: All the rivers of upper and lower Egypt, 2,400,000 setat, the marshland of lower Egypt, that is Lake Moeris and its canal, 6,600,000 setat. Length from Elephantine in its entirety is 106 itr, its width on the land from the western river branch of Egypt to the eastern branch is 14 itr. (a) The number here is written 1800 or 1000 × 800 = 800,000, but the number 10,000 was omitted through oversight and the intended number was 1800 × 10,000 = 18,000,000.” (94)
The bottom of the tenth column shows two coils of 100 each and seven hobbles of 10 each, for a total of 270. The frog is 100,000, and 270 × 100,000 = 27,000,000 setat. The setat, or Greek aroura, is a square measure with sides of 100 royal cubits and an area of 10,000 square cubits. Griffith stated: “27,000,000 arouras mean about 73,918 square kilometers or 28,420 square miles, while Schweinfurth, who gives the length of Egypt proper as 550 miles, makes the cultivable area only 11,342 square miles.” (95) Although parts of the Delta are much wider than the 14 itr distance given between branches of the Nile; and the cultivable area of the Nile valley is much narrower; and the Nile valley drifts east of the Delta, Griffith calculated a rectangular area of 106 itr × 14 itr = 1484 square itr. Assuming 27,000,000 aroura equals 1484 square itr, the square itr would contain 18,194 aroura, or 181,940,000 square cubits, and /181,940,000 = 13,487 royal cubits for the length of the itr. Given the length of 15,000 cubits for the itr, 150002 = 225,000,000 royal cubits. 225,000,000/10,000 = 22,500 setat per square itr. 27,000,000 setat/22,500 = 1200 square itr.
Kurth’s translation gives a measure of 18,000,000 setat for the Delta. 18,000,000 setat is twice the entire area of the Delta. The figure of 9,000,000 setat is an accurate measure of the area of the Delta, and depending on the copying and punctuation of the inscription and the translation, 9,000,000 setat may have been the intended expression of the area of the Delta.
The 95/18 meter proportion of the Heb-Sed court is equal to the proportion of 106/20 itr. The inscriptions on the cubit rods and in the White Chapel divide the length of Egypt into 86 itr for upper Egypt and 20 itr for lower Egypt. 202
= 400 square itr. Given 15,000 cubits for the length of the itr, 400 square itr = 9,000,000 setat. A circle with a radius of 20 itr has an area of 1256 square itr. The area marked by the arc in the diagram is just under two-thirds of the upper half of the area of the circle, or 400 square itr, or 9,000,000 setat. 106 × 20 = 2120 square itr, or 47,700,000 setat. If the 18,000,000 setat of land from the Edfu inscription was intended to be added to rather than included in the 27,000,000 setat of land, then the total would be 45,000,000 setat of land, or 2,700,000 setat less than the area shown above. 2,400,000 setat is the area given for Egypt’s rivers.
The itr measures from the Amduat are a 6x multiple of the itr measures from the cubit rods. The arc of the Delta intersects the EW boundaries 3 itr, or 18 underworld itr, south of the northern boundary. 106/20 = 636/120 and 103/20 = 618/120. The proportions of the Heb-Sed Court express the given proportions of Egypt and the underworld as shown above.