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The Great Pyramid: It's Divine Message CHAPTER II. THE EVIDENCES OF SCIENTIFIC ORIGINS IN ANCIENT EGYPT. Section I.—Geometrical Metrology1 and Dynastology.
The evidence of archaeology, folklore, and tradition—together with the astronomical alignments and datings—has established the Eastern origin of the builders of Stonehenge. This evidence has shown that the astronomical ideas of the British megalithic builders had been formulated in ancient Egypt. This formulation reached its highest phase of constructional expression in the work of the Great Pyramid builders. The data confirming this have been supplied by the painstaking researches and comprehensive metrological classifications of Professor Petrie.
From Petrie’s data we find that the Stonehenge Circle is a constructional expression of the geometrical relations holding between the ancient Egyptian square and linear systems of measures. Its constructional diameter shown on Plate I is an important Egyptian unit of linear measures. The area defined by this diameter—i.e., the circular area precisely internal to the outer ring of stones, is the exact area of an important Egyptian unit of square measure.
Thus at Stonehenge we find the Egyptian quarter aroura set out in circular structural form to define, by its alignments, the points and circuit of the solar The Solar year year. A similar association held between the quarter aroura and the year in ancient Egypt. For as Horapollo states:2 “ To represent the current year, they (the Egyptians) depict the fourth part of an aroura : now the aroura is a measure of land of an hundred cubits. And when they would express a year they say a quarter.” Hence in the Egyptian inscriptions there are two hieroglyphic representations of the year—one indicated by a square, and the other by a circle. Herodotus,3 again, states that, the cubit of Samos, as determined by Petrie, is 20.62 British inches, whereas the best average (Petrie’s) for Egypt is 20.63 British inches.
The statement of Horapollo — confirmed by the relations of the Stonehenge — indicates that the aroura was derived from a representation of the year in measures. The original representation was in the form of a circle. The circumference of this circle measured 3652.42 selected units of length. This represented the circle of the solar year to a scale of 10 selected units of length to a day. The diameter then measured 1162.6 selected units of length. To reduce the circular area thus defined to a form suitable for land measurement, a rectangle was formed of length 3652.42 equal to the circumference of the circle, and of breadth 1162.6 equal to the diameter of the circle. The area of this rectangle was therefore equal to four times the area of the circle.1 The rectangle thus produced was the intermediate stage of the aroura. Transformed into the form of a square of equal area, the aroura became a square of length of side 2060.66 selected units. The sequence of derivation is shown on Plate XIII (refer Sect. 3, Description of Plates, ¶135).
The division of the aroura square side into 100 parts—as observed by Herodotus and Horapollo—supplied the common Egyptian cubit of 20.6066 units = 20.63 British inches. The most general value of the common Egyptian cubit observed by Petrie in the best work of the Pyramid builders is 20.629 British inches, from which the original selected unit = 1.0011 British inches, as stated to 4th decimal place, or 11/10,000th of an inch longer than the British inch. The latter values agree closely with the mean Gregorian year value of 365.2425 days as basis, giving a basal circumference of 3652.425 selected units of length. These units we may now define as “Primitive inches,” and hereafter refer to simply as P inches, or P”, avoiding confusion with British inches by stating the latter as B inches, or B”.
With the preceding data as basis, it is found that the ancient Egyptians formulated a system of measures that, in the case of circular areas, and sectors of circles, avoided the repeatedly recurring trouble of the relationship. By employing in their everyday work separate units and scales for circumferences, diameters, and areas, they avoided calculations that embodied the troublesome ratio of diameter to circumference. Simple formulas were drawn up from which the circumferences and areas of circles, or sectors of circles, were immediately obtained from the diameter, or vice versa. Sectors were correctly treated by analogy as triangles, by the following true relationship :—
The geometrical analogy leading to this relationship is explained for the particular case of quadrants in Plate XIV. The same treatment holds for similar sectors, i.e., sectors whose arcs are subtended by the same angle. The principal units of measure formulated to effect the various translations were the following :— The Linear Digit, Foot and Cubit of Diameter. ¶83. THE SYSTEM OF LINEAR UNITS. (The algebraic relationship of units is as stated in Section III, Description of Plates, ¶137a).
The Linear Units of Square measure were derived by dividing the side of the square of area equal to the area of the standard circle into :—
An illustration of the various units in operation is figured on Plate XIII. Here the 1/100th strip of aroura, i.e., a strip of 100 common cubits long by 1 common cubit wide, = area of sector, of arc length 12 circumferential feet, and diameter 50 diametric feet. Worked examples are given in Section III, ¶¶ 137, b and c. ¶ 84. THE SACRED HEBREW CUBIT. Comparative scales of the various units are figured on Plate XV. Reference to this shows that there are 25 Diametric Digits in the Diametric Cubit, and 25 Circumferential Digits in the Circumferential Cubit. These suggest that the Basal Cubit of the original Primitive inch system consisted of 25 P. inches. This gives the value of the Sacred Hebrew Cubit as derived by Sir Isaac Newton, and since confirmed by the metrological researches of Oppert, Petrie, and others. This again confirms the sequence as to Euphratean origins obtained in Chapter I. Completing this connection, Petrie finds the 25 inches’ cubit in use in Egypt during the period of Dynasty XVIII. At this time the Egyptian language and the political and religious institutions of Egypt were strongly influenced by a powerful Semitic faction in Egypt.1 Around the same time Stonehenge and similar monuments were being built in Britain by a race whose astronomical and metrological cults evidence Egyptian influence, yet whose folklore and traditions indicate Semitic origins. The Sacred Cubit of 25 P. inches (Plate XV) never occurs in Egypt unless during periods of Semitic dominance. The other systems of Plate XV belong to the whole period of Egyptian history. The fact that these systems were derived from the scale of the Sacred Cubit of 25 P. inches again confirms that the Egyptian units of measure were not formulated in Egypt. The sacred system and its derived Egyptian Units all clearly belong to the period of the former civilization pictured in ¶ ¶41-47.
According to Petrie, the half-cubit (12½ inches) appears in Babylonia as the foot of the Babylonian system of measures. It appears also in ancient Greece (12.44 to 12.62 B”), in Etruria (12.45 B” average), in what Petrie deems to be Roman Britain, and in medieval England (12.47 B” average). The migratory sequence indicated clearly confirms the Euphratean connections established in Chapter I. A statute of Richard I, belonging to the year 1199, defines an acre in Cornwall as “40 perches in length and 4 in breadth and every perch of 16 feet in length.”2 Cornwall was the principal British centre of the Oriental colonists from 2000 B.C. onwards. Their influence still predominates in the folklore, traditions, and customs of Cornwall. It is obviously from this race, with its Mediterranean and Atlantic ports of call, that ancient Greece, Etruria and Britain derived the Sacred half-cubit of 12½ P. inches. Now 16 feet of 12½ P. inches give the ancient perch in Cornwall as consisting of 200 P. inches. The modern perch or rod consists of 16½ feet of 12 inches, or 198 inches. The numerical interchange and the reason for it are obvious. The inch remained the basal unit, unchanged, except for small local variations. The perch also remained practically unchanged — losing but 1% of its original value.
Table XV
¶86. THE RELATION BETWEEN ANCIENT AND MODERN BRITISH MEASURES. The manner of effecting the change from the ancient to the modern value of the perch or rod suggests that the numerical relations between the perch and the higher units were maintained. Now there are 40 perches or rods in the furlong, and 8 furlongs in the mile. With the ancient perch as 200 inches, this gives the primitive basal furlong as consisting of 8,000 inches, and the primitive basal mile of 64,000 inches. An acre in Cornwall (in 1199 A.D. and earlier) was measured as 40 perches by 4 perches. This is the 1/100th strip of a square of 10 acres area. The side of the square of 10 acres therefore measured 1 furlong, or 8,000 inches, and the circuit 10 acres square, 4 furlongs or the half-mile, —32,000 inches. Following from these relations we find that: This relation between the acre and the square mile still holds. The decimal subdivision of areas into 1/10th and 1/100th strips of squares— indicated by the definition of the ancient acre in Cornwall—is both Egyptian and Semitic. It occurs in the case of the Egyptian aroura. The 10 acre square was a large unit of square measure of the Hebrews. (Isaiah v. 10.)
A decimal subdivision of the ancient Perch of 200 inches gave the ancient Ancient Ell or yard of 40 inches. Petrie gives the latter as averaging 39.66 B”. The foot of this system — the Belgic Foot — is 1/3 of the ell or yard = 13½” (13.22 B” Petrie). With this system Petrie finds a longer mile of 10 furlongs in use as far back as the 13th century. This system is as follows :—
It will be observed that the furlong (8,000”) is of the same value as was obtained in ¶86. The reason for the difference evidenced by Petrie’s examples is that these are all from buildings belonging to the 10th to 15th centuries, when the Belgic foot and the foot of 12½ inches still competed with the legal foot of 12 inches instituted in the 10th century. The legal foot altered the perch or rod to 198” in place of the former 200”, which contained 15 Belgic feet of 13.½ P inches. To effect a compromise between the two competing systems, the perch or rod of 198” was reckoned as containing 15 Belgic feet. This gave an adjusted foot of 13.2 P” (13.22 B”, as Petrie above). Petrie, however, observes that the latter foot originated around Asia Minor, averaging there 13.35 B”, and passed to Greece as 13.36 B”. Now 13½ Primitive inches of value 1.0011 British inches (¶ 81) equal 13.348 B. inches, or to 2nd place, 13.35 B. inches, as in Asia Minor.
Returning to consideration of the Egyptian system of diametric and circumferential measures and their linear standards for areas, we find that all the values of ¶ 83 are found indicated in the structural measurements of the ancient Egyptians. A half diametric foot and the circumferential cubit were actually, in one case noted by Petrie, found on the same cubit rod. This is a graphical representation of the relationship, as the half diametric foot (5.813 P”) was the radius of a circle of 36.525 P” circumference, of which the circumferential cubit (18.2625 P”) was the half circumference. (Refer Plate XV, lower portion.) Metrologists, having failed to observe the origin of the system of measures, have universally supposed the diametric digit (0.7274 B”), and the circumferential digit (0.7313 B”), and also the diametric cubit (18.1856 B”), and the circumferential cubit (18.2822 B”), to be variable values of the same digit and the same cubit respectively. They therefore average the two values, in each case, obtaining the mean values as follows :—
This is stated by Petrie as averaging 0.729 B”. From Greek remains Petrie obtained 0.7296 B”. It is quite possible, however, that for ordinary everyday commercial use, the two separate systems were merged into a single “ rule-of-thumb “ system at a comparatively early date in the dynastic history of Egypt. After all, as we have seen, Egypt is only a stage in the tracing of origins to their source in a former civilisation. The Egyptians, at an early date, lost the meaning and application of much that they have handed on to later days for elucidation.
With the average values of ¶88 as basis, Petrie has grouped the known data from buildings in Greece as follows : —
But with the stadion = 7,296 B”, as stated by Petrie above, the values are accurately :—
Thus indicating that the system tabulated is the mean of the two early Egyptian systems—diametric and circumferential. Petrie further shows that the cubit of 18.24 B”, was also divided by the Greeks into 24 digits, obtaining the new Greek digit as 0.76 B”. He shows again that the Greek foot was taken as 2/3 of the mean cubit of 18.24 B”, and therefore as 12.16 B”. This is closely approximate to the Measures Egyptian diametric foot of 12.1748 P” = 12.188 B”. ¶ 83.)
The early Greeks also used the diametric foot of 11.626 inches. (¶ 83.) ¶ 90. THE ROMAN SYSTEM OF MEASURES. The Roman system of measures was derived—through the Greeks— from the Egyptian diametric system. Its basis was the diametric digit of 0.7266 inches, and the diametric foot of 11.626 inches (¶ 83). As an average from existing Roman remains, Petrie gives the system as follows :—
The above system was used by the Romans in Britain and Africa. The Roman foot appears in Medieval England as 11.6 B”.
The data from ancient Egyptian documentary sources show that the various metrological dimensions and standards of linear and square measure were preserved in the form of an existing Pyramid. The primary unit of measurement, the various outstanding dimensions and structural peculiarities, and the angles of the face slope and the Apex angle of this existing Pyramid are all precisely defined by the Egyptian literary data. The data define as follows :— (i) GENERAL BASIS OF PYRAMID’S DESIGN.
The Pyramid measures thus standardised were all associated with the geometry of the year. For this reason, and for other reasons to be explained later, the Egyptians of various periods, subsequent to the erection of the monument, deemed that all its measurements denoted the duration in years of astronomical periods. In accordance with this conception, they formulated various systems of fictitious or mythological chronology. Each cult had its particular system, always, however, based numerically on the Pyramid year cycle geometry. Each system claimed to be a presentation of the chronology of the Egyptian Dynasties—Divine and human. The systems all differed considerably, so that it is impossible to synchronize the various intervals given for the same Dynastic periods. All the systems in existence in the third century B.C., were edited by the Egyptian priest, Manetho, and entered in his work on Egyptian History, “Ǽgyptiaci,” written in Greek. Several versions of the systems of fictitious chronology, known as the Egyptian “ King Lists,” were extracted from Manetho’s work by Julius Africanus in the third century A.D. The composite nature of the King Lists as given by Africanus is seen by analysis of the various alternative details of summations of years. Another version was preserved by Eusebius—also in the third century A.D.—together with the version known as the Armenian Version of Eusebius. The versions of Africanus and Eusebius were, in turn, preserved by George Syncellus about 800 A.D. With the exception of certain important extracts from Manetho’s history, preserved by Josephus in his Contra Apion., this is all that now remains of Manetho’s notable work. To account for the difference between the chief version of Africanus and the version of Eusebius, Syncellus accused Eusebius of tampering with the figures as given by Manetho. The analysis given in this chapter, however, shows that the version preserved by Eusebius, as stated to the reign of Amasis II, was in existence in the fifth century B.C. — 700 years before Africanus was born, and 200 years before Manetho. A typical tabulation and analysis of the King Lists of Manetho—and the different versions of these and other lists are shown on Plate XVI. Had this matter been dealt with otherwise than by the comprehensive tabulation and analysis given, the subject-matter would have extended to many tedious pages of text, without giving a fraction of the elucidation resulting from the graphical presentation of Plate XVI. For the statement of Manetho’s, and other King Lists, and for the historical evolution of the various dynastic schemes of Plate XVI, the reader is referred to the Appendix.
¶ 93- EGYPTIAN KING LISTS DEFINE THE STANDARD PYRAMID. Reference to Plate XVI shows that the numerical details of the King Lists define the standard Pyramid as follows :—
The Old Chronicle of Egypt (Plate XVI, Table E) gives, for the first 15 generations of the Cynic (Sothic) Cycle, the duration of 443 years. This is the initial item of the human dynasties in this List. Now the base side AB (Plate XVI, Figs. A and B) of the Standard Pyramid consists of 9,131¼ units, and a measure of 9,131¼ Primitive inches (each 1.0011 B. inches) consists of 443.1 Common Egyptian Cubits of 20.6066 P. inches (20.63 British inches). The occurrence of the number 443 in the Old Chronicle therefore proves that the base side of the Standard Pyramid consisted of 443 common cubits, and that this measure equalled standard units. As the common cubit is known (20.63 B”), the identity gives the standard unit as the Primitive inch of the .value of 1.0011 British inch. That the number 443 was known to be connected with the Standard Pyramid, and that the latter was identified with the Great Pyramid is proved by the following :— (a) That the King List of Eratosthenes gives the duration of the first 15 Dynastic kings of Egypt as 443 years—this proving that the 15 generations of the Old Chronicle for 443 years are the first 15 Dynastic Kings.
The occurrence of 443 as the number of years for the first 15 dynastic kings of Egypt, and the fact that 443 is the number of common cubits in the Standard Pyramid’s base side suggest a further identification. This is that the Divine Dynasties and the first 15 human kings were given the duration of 4 × 443 years, this being derived from the Standard Pyramid’s base circuit of 1,772 common cubits = 36,524 or 5 primitive inches. The latter identity thus obviously suggested the later extension to the duration of Gods and Kings for 36,525 years, as given in the Old Chronicle.
.. Now the height of the aroura rectangle is 1162.6 and the Standard Pyramid section as represented in Plate XVI, Fig. C, contains two aroura rectangles. Confirming the relationship inferred,
¶ 96. THE MYSTERY OF MANETHO’S 113 GENERATIONS. Now the generations of Gods and kings in the Old Chronicle are totalled as follows :—
Syncellus, in introducing the List, however, states that the 30 dynasties contained 113 descents. ”The period of the 113 generations described by Manetho in his three volumes, comprises a sum total of 3,555 years.” The latter total is one cycle of 97 years (¶ 33, ii (c),) short of 3,652 years, the basal total of the original Old Chronicle. It is also derived as follows:— Circuit of square equal in area to circle of 29,220 circumference
These details and identities all assist in confirming that the later systems of the Lists were expanded from an original form—similar to that inferred for the original Old Chronicle—in which the basal total was 3,652 or 3 years.
In one version of Castor we have the following :—
The statement confirms the general arrangement of the inferred original Old Chronicle. In detail it is confirmed by the 217 years of Castor appearing as the duration of the eight demi-gods in the Old Chronicle, and by the initial period of Castor—1,333 years—agreeing within four years with the inferred initial 1,329 years of the original Old Chronicle. The original Old Chronicle, therefore, defined the-inscribed aroura rectangle, 3652.5 × 1162.6 (Plate XVI, Fig. C), and the square base circuit (1,772 common cubits) of the Standard Pyramid. ¶ 98. THE SQUARE CIRCUIT OF 29,220. At the upper level of the aroura rectangles in the Standard Pyramid section (Plate XVI, Fig. C)—i.e., at level 1162.6 — the square circuit is 29,220. This is the total number of years for gods and kings to the first year of Amasis II (Plate XVI, Table A). Comparison of the data narrated to Herodotus by the Egyptian priests in the 5th century B.C., with the statement of the Lists according to the version of Eusebius establishes this identity. It also establishes two important conclusions. These are,
Now this clashes with the later theory that a Sothic cycle of 1,460 Sothic Egyptians years ended in 139 A.D., which theory is the fundamental basis of the various modern Egyptological chronologies. Why the Egyptians of the 5th century B.C. adopted a theory equally erroneous is a matter that will be dealt with later. The fact of immediate importance is that they knew nothing concerning a Sothic cycle that was due to end in 139 A.D.
The level of the Standard Pyramid circuit 29,220 (Plate XVI, Fig. C) is again defined as follows : — Version Africanus, Human Kings = 4,651. Table B (8), Plate XVI. The level of the circuit 29,220 — 1162.6 above the base — being 4650.4 below the Apex of the Standard Pyramid. Now 1162.6 Primitive inches is the precise level of the axis of the 35th course of masonry in the Great Pyramid. This course is 50 P. inches deep, 25 inches (the Sacred Cubit) above and below the axis of the course at 1162.6 P”. As seen from a distance this 35th course is the most outstanding course in the Pyramid. It occurs after a series of courses generally 26 inches deep. With the exception of the two lowest courses, it is the deepest course in the Pyramid. This sudden increase in depth can only have been for the intention of pointing to the fact that the 35th course axis defines the aroura, and the height of 1162.6 P. inches. This intention is confirmed when we study the accurate Great Pyramid survey data of Professor Petrie in relation to the fact concerning the hollowing-in feature observed by him and discussed in our ¶¶ 18-20. The angle of slope of the Standard Pyramid derived in ¶ 93 (d) is also the angle of slope of the Great Pyramid, 51° - 51’- 14” .3.
The square circuit of the Standard Pyramid base, by data of ¶ 94, is 36,524 P. inches. With 1 P. inch = 1.0011 British inch, as derived in ¶ 81, and independently in ¶ 94, this circuit equals 36,564 British inches. The side of the square base of the Standard Pyramid was, therefore, 9,141 British inches. With the same hollowing-in feature as the Great Pyramid—which is hollowed in to a maximum extent of about 36 inches at the centre of each face slope — the dimension of 9,141 British inches between the centre of one base side and the centre of the opposite base side of the Standard Pyramid would be reduced by 2 × 36 inches, or 72 inches. The distance between centres of face slopes at the base of the Standard Pyramid would be 9,069 British inches (9,059 P. inches). Four values obtained by Petrie for the corresponding dimension in the Great Pyramid are as follows :— 9069.4 B. inches Average value = 9068.8 B. inches ± 0.6 B. inches. The value for the Great Pyramid, then, is identical with the value for the Standard Pyramid of the Dynastological Lists. Now the angle of slope of the Great Pyramid is 51°- 51’- 14” .3, as defined by the existing casing slope. This is identical with the angle of slope derived in ¶ 93 for the Standard Pyramid. The Standard Pyramid of the Dynastologieal Lists, is, therefore, of Gizeh. ¶ 101. THE DIMENSIONS OF THE GREAT PYRAMID. The base circuit of the Great Pyramid then, is 36,524 primitive (or Pyramid) inches. Its base diagonals add 25826.5 Pyr. inches. Its height is 5,813 Pyr. inches, the radius of the circle of 36,524 Pyr. inches circumference. The axis of its 35th course defines the rectangular aroura, and its circuit the measure of 29219.4 Pyramid inches, expressed as 29,220 in the Dynastologieal Lists. The reader will find this matter all clearly explained and diagrammatically illustrated on Plate XVII, where Petrie’s surveyed measurements have been reduced to Pyramid inches. The general appearance of the 35th course is diagrammatically represented by the suddenly thicker course shown on Figs, a, b, and c of Plate XVII. The hollowing in of the core masonry escarpments, prior to the placing of the casing stones, is illustrated in diagrammatic perspective on Plate XVIII. The reader will find a more detailed and precise discussion in Chapter III. In this it will be shown that the extent of hollowing-in is geometrically connected with the displacement of the plane of the Great Pyramid’s Passage System, and that the amount of this displacement (286.1 P”) is a well defined geometrical dimension of the Great Pyramid. As stated on Plate XVII, the resulting value of the Pyramid inch (accurately derived from ¶¶ 81 and 94) divides precisely 500,000,000 times into the Polar Diameter of the Earth, according to the latest determination ‘ of the latter by the U.S.A. surveys of 1906 and 1909. It is a matter for further discussion to show whether the coincidence is due to accident or design. This will be considered further in Chapter III.
Connected with this question of intention is an important question relating to the significance the ancient Egyptians attached to the measurement of 25,826 or 7 Pyramid inches. (Plate XVI, Figs. A and B.) Up to the time of the Persian Conquest, they recognised 25,826 or 7 years to be the duration of the great astronomical cycle known as the period of the Precession of the Equinoxes. As a statement of the period of Precession it is as accurate as any modern determination. Whether, however, it is the precise interval or not does not immediately concern us. The matter of importance is that it is a simple mathematical function of the numerical value of the Solar Year. As such it is a useful constant to which to refer variations in the annual rate of Precession, or variations in the mean rate of Precession over a number of years. Whether it was formerly employed in this manner, and for the purpose stated, will be settled by the evidence discussed later. The period in years = 50√2 times the Solar year in days = 25826.54. Now 78½ Phoenix cycles of 329 years (¶¶ 33, 37, and 38) = 25,826½ years, of the Phoenix cycle or 25,826.54 mean solar years. In this identity the half year of the Phoenix cycle must terminate, in accordance with the Calendar rulings, at Day 1, Month VII of the Calendar Cycle of 103 years. This fixes that ‘the period of 25,826½ years was recognised as a cycle. As shown on Plate XVI, Table D, the division of the Period into 24 — the Babylonian divisions of the ecliptic—indicates that the cycle was identified with the twelve divisions or signs of the Zodiac. The 1,076 years of Eratosthenes would, therefore, represent precession through a half Zodiacal Sign, at the rate of 25,826 years for the 12 signs. One summation of the totals of the Version of Africanus—a summation not shown on Plate XVI — gives 4.305 or 6 years to the beginning of Dynasty XIX. This represents precession through two Zodiacal signs. It seems clear enough from these identifications that the earlier Egyptians, at least, recognised the period of 25,826½ years to be the Period of the Precession of the Equinoxes round the Zodiacal signs.
¶ 103. THE EARLY KNOWLEDGE CONCERNING PRECESSION. Now, although the interval of 25,826½ years is the period—or almost exactly the period—of the Precession of the Equinoxes, the annual rate varies considerably. For this reason, the mean rate between the 48th century and the 4th century B.C., moved the Equinox round 60° of the ecliptic or through two Zodiacal signs in 4,380 years. Now 4,380 Sothic years equal 4,383 vague years. The latter is the stated interval at the time of the 5th to 3rd centuries B.C. for the duration of human kings to the 1st year of Amasis II, 570 B.C. (Plate XVI, Table A, and ¶ 98.) It seems clear enough that a coincidence of this nature could only have originated from a knowledge of the obvious basis of the identity, or from a tradition concerning such knowledge. The knowledge concerning, and the reason for effecting the identity appear to have governed the framing of the List around the year 570 B.C. It is equally certain that this knowledge was lost before the 3rd century B.C., although the identity remained. At least the knowledge was never imparted to the Greeks.
The latter facts are clear from the nature of the list of Africanus, as developed in Plate XVI, Tables A and F. and from the later form of the Old Chronicle of Egypt (Plate XVI, Table E). These both indicate that the cycle of 25,826 years had been confused with a supposed precessional cycle of 36,525 years. This, indeed, is stated by Syncellus, in relating concerning the 36,525 years’ summation of the Old Chronicle. Syncellus states that the period of The statement 36,525 years “relates to the fabled periodical revolution of the Zodiac among the Egyptians and Greeks, that is, its revolution from a particular point to the same again, which point is the first minute of the first degree of that precession, equinoctial sign which they call the Ram, as it is explained in the Genesis of Hermes and in the Cyrannian books.” The sign here taken as datum belongs to later Egyptian times, when the Equinox fell in the Ram (Aries). In earlier times, the sign was Taurus, in which actual sign the Equinox fell from 4,700 B.C. to 1,800 B.C.—since the extent of the sign, as defined by its stars is about 40°. The actual extent of Aries (the Ram) is about 20° — as defined by its stars. The Equinox therefore fell in the Ram between 1,800 B.C. and 320 B.C.1 About 320 B.C., the 1st point of Aries, defined by Syncellus above, therefore marked the diurnal commencement of the Vernal Equinoctial Year. This gives the epoch of the death of Alexander the Great (323 B.C.), and accounts for the origin of the Egypt-theory that ended the alleged precessional period of 36,525 years about this time.
It is clear that the confusion arose first from the period of 4,380 years. Originally this was identified correctly as the number of years taken by the Equinox, between 4,700 B.C. and 320 B.C. to travel backwards through 60° of the ecliptic, from 1st point of Gemini, through Taurus and Aries, to 1st point of Aries. The termination of this period was then prematurely attached to 570 B.C., the 1st year of Amasis II, and identified as three Sothic cycles of 1,461 vague years, = 4,383 vague years, = 4,380 Sothic years. 25 of these Sothic cycles = 36,525 vague years ; whereas the Sothic cycle fails to divide into the Precessional period of 25,826½ years. The latter, however, contains 78½ Phoenix cycles of 329 years. The Phoenix cycle in the Hebrew Chronology is associated with a period of 1,461 solar years (¶ 39), and from this originated the erroneous identification — noted by Tacitus (¶ 39) — that the Phoenix cycle was a period of 1,461 years. This sequence of error was obviously the origin of the late conception that the period of Precession was 36,525 years.
Apart, however, from the sequence noted, tradition obviously held that the true period of Precession was given by the Pyramid base, tradition failed to preserve the knowledge that the numerical value of the period was contained in the sum of the diagonals of the base square. The later Egyptians, therefore, adopted the circuit of the base square as giving the period of Precession. They passed this period of 36,525 years on to the Greeks. The period is equal to an annual rate of Precession of 35.5 secs., of angle. Hence Hipparchus (circ. 150 B.C.) “determined“ the rate of Precession as 36 secs, of angle. The period was also reckoned as containing not only 25 Sothic Cycles, but 24 nominal Solar cycles of 1521.875 vague years. (Refer ¶ 59.) The nominal Solar year of 365.24 days was reckoned to travel completely backwards round the nominal Sothic year of 365.25 days in 36,525 years. The vague year also travelled backwards completely round the nominal solar year in 1521.875 vague years. This gives the complete explanation of the late conceptions concerning Precession. Hence the system of Africanus (Plate XVI, Table A) gave the Divine and Human Dynasties as of the duration of 20 nominal solar cycles of 1521.8 years, or 30,437 years.
It was obviously of no recent derivation or migration of science that Zonares1 wrote, in treating of arithmetic and astronomy, when he stated— “It is said that these came from the Chaldees to the Egyptians, and thence to the Greeks.” The truth in this remark is monumentally confirmed by the lasting name of the monument perpetuating the early knowledge to which Zonares refers. For the name “Pyramid “ — like all the constructional conceptions embodied in the Great Pyramid — is primarily of Euphratean derivation. The Egyptian name for the Great Pyramid is “Khuti“—”the Lights.” In the Semitic languages the equivalent name is “Urim“—”the Lights.” In Phrygian and Greek, the root “Ur “ (light) became successively “Pur“ and “Pyr“ (fire), and “ Pyra “ (a plural) “ beacon fires.” Thus Plato, in his “Cratylus“ (Taylor’s translation), says, “Do you know on what account ‘Pur‘ (Pyr) was so called? Consider whether this is not of barbaric origin — for it is by no means easy to adopt this to the Greek tongue; and it is manifest that the Phrygians thus denominate ‘fire‘ with a trifling deviation.” Thus ‘Pur‘ (Pyr) is a form of the Hebrew ‘Ur‘—’ light.’ The addition of the labial ’p‘—as also ‘b‘ and ‘i,’ hence ‘burn‘ and ‘furnace‘— is a frequent change observed in roots passing from one language to another. Hence ‘Uri’ = ’fiery.’ Here both words contain the same original root. Again in Hebrew, ‘middin’ = ‘measures,’ ‘madadu’ = ’to measure’; in Sanscrit, ‘ma,’ ’mad,’ = ’to measure’; in Zend, ‘meete,’ ‘mate’; Latin, ‘modus,’ ‘a measure’; Greek, ‘metron’; Anglo-Saxon, ‘ metan,’ ‘ to measure.’ Examples—’ Aga-medes,’ Semitic, ‘ The Great Measurer,’ or Greek, ‘ the very wise ‘Phoenician, ‘ Baal-middoh,’ ‘ the Lord of the measures.’ In Chaldee and Hebrew, ‘ Urim’ = ’Lights,’ with the labial ‘p,’ as in Phrygian, ‘Urim‘ = ‘Purim‘ = ’Lights.’ Greek ‘Pyra‘ = ‘beacon fires‘ (lights). In Chaldee and Hebrew, ‘middin’ = ’measures.” Hence the Chaldee-Hebrew name for the Great Pyramid—in Egyptian, ‘Khuti,’ ‘the Lights’ — is ‘Urim-middin‘ (Parim-middin) — ‘Lights-Measures.’ In Greek this becomes ‘ Pyra-midos,’ ‘ Pyra-mid.’
It is of importance to observe that the Greek name is not derived from two Greek roots, but is the Grecianised form (Pyramidos) of the Semitic name ‘ Urim-middin,’ or possibly of a composite Phrygian and Phoenician form of the name—’ Purim-middoh.’ 1Lib.I,vi.
In the compilation of the ancient Egyptian King Lists, Egyptologists recognise three main periods when such compilations were made. These are, in order,
In the evolution of the Egyptian Sacred writings, Egyptologists recognise three similar periods as follows :—
To the latter recension belongs the version entitled “The Book of the Master of the Hidden House,” in which, as Mr.’Marsham Adams1 has shown, the soul of the departed is pictured as following the passages and chambers allegory of the of the Great Pyramid. In this version the Pyramid itself is pictured as an allegory in stone of the ways and trials of the future life.
As a result of Mr. Adams’ researches, Sir Gaston Maspero concluded that “The Pyramids and the ‘Book of the Dead‘ reproduce the same original, the one in words and the other in stone.”2 In quoting the preceding, Mr. Adams refers to “the prevalence of a tradition among the priests of Memphis,” a fact which he says he “learned later from the same authority,” supporting his “contention that the Secret House was the scene where the neophyte was initiated into the mysteries of Egypt.” Accordingly every possible attempt was made by the compilers of the Egyptian various chapters of the Book of the Dead to refer back the origin of the ritual and symbolism to the Pyramid Kings of Memphis — the builders of the Pyramids of Gizeh. Thus a passage in the cxxxviith chapter of the Book of the Dead states that that chapter was found by Heru-tat-ef, son of Khufu, the builder of the Great Pyramid.
Now it was during the XXVIth (Sa’ite) Dynasty that the order of chapters Book of the Dead was drawn up, and when, as Breasted states,3 Hence in the Saite system of Dynastology, preserved in the version of Africanus, the duration of years stated to Psammetichos, the first actual king of Dynasty XXVI (Sai’te), is given as 5,271, the length of the arc of the 36,525 the arc of circumference, measuring the angle of slope of the Standard Pyramid. Reduced to modern angular measure this angle of slope is 51°- 51’- 14”.3, the angle of slope of the Great Pyramid of Gizeh. It was during the reign of Psammetichos (Psamtek I) — as Herodotus states — that Greek colonists first settled in Egypt.4 For the significance of this settlement, and its date in relation to the history of Greek Geometry and Astronomy, the reader is referred to Section II of this chapter, and Table X. ¶110. COPTIC CHRISTIANITY AND “ THE BOOK OF THE DEAD.” Thus it is that from the remotest periods of authentic history, an atmosphere of mystery has enshrouded all expression of thought and opinion concerning the Pyramids of Gizeh. Essentially geometrical in form, Pyramids, by influencing the expression of theological conceptions, supplied religious allegory with an unfailing source of geometrical symbolism. It is this pyramid allegory of which a corrupt survival exists in the Egyptian Book of the Dead. It is from the Book of the Dead that the Coptic descendants of the ancient “The Book of Egyptians derived the mystical and allegorical element which was introduced influences into early Christian gnosticism. The literature of early Christian gnosticism Christianity abounds in mystical pyramid figures and associated astronomical conceptions and constellations. To the Copts is due the survival, to the present day, of the ancient Egyptian Calendar and month names. To them we owe the retention of a dialect of Coptic in the ancient Egyptian language, and with it, much that has tended to facilitate the and elucidate the translation of ancient hieroglyphic texts. Hence the importance and value attaching to any traditions concerning the Great Pyramid that can be reliably identified as of Coptic origin.
Regarding the Coptic traditions, Dr. Sprenger, in Appendix to Vyse’s “Pyramids of Gizeh,” vol. II, observes that “the traditions of the ancient Egyptians were preserved by their descendants, the Copts, who were held in great esteem by the Arabs.................It may be remarked that the Arabian authors have given the same accounts of the Pyramids, with little or no variation, for above a thousand years ;” and that they appear to have repeated the traditions of the ancient Egyptians, mixed up with fabulous stories and incidents, certainly not of Mahometan invention.” The account of Masoudi (died 345 A.H. = 957 A.D.), in the Arabic MS. of the Akbar-Ezzeman, at Oxford, relates that “Surid one of the kings of Egypt before the flood, built the two great Pyramids.” In this narration the Great Pyramid is referred to as “ the Eastern Pyramid.” Dr. Sprenger states that “ Masoudi affirms, in the Akbar-Ezzeman that he wrote his account of Surid from a Coptic modern history.” The narration of Masoudi is as follows :—
“He (Surid) also ordered the priests to deposit within them (the Pyramids), written accounts of their wisdom and acquirements in the different arts and sciences with the writings of the priests containing all manner of wisdom, the names and properties of medical plants, and the Arithmetic and sciences of arithmetic and geometry, that they might remain as records, for the benefit of those who could afterwards comprehend them.” ”In the Eastern Pyramid (the Great Pyramid) were inscribed the heavenly spheres, and figures representing the stars and planets....” “ The king,’ also, deposited the positions of the stars and their cycles ; together with the history and chronicle of time past, of that which is to come, and every future event which would take place in Egypt.” Similarly the MS. of Makrizi states that “ the first (the Great) Pyramid was especially dedicated to history and astronomy ; the second (Pyramid) to medical knowledge.” Tohfat Alagaib states that the Great Pyramid contained “plans of the stars, and historical and prophetic records.”
According to the ‘accounts of Masoudi and Al Kodhai, a papyrus, found in the monastery of Abou Hormeis, and said to have been inscribed with ancient “Coptic“ characters, gave the following account of the Pyramids :— “ Upon the walls were written the mysteries of science, astronomy, geometry, physics, and much useful knowledge, which any person, who understands our writing, can read.” The Pyramids of Gizeh, we know, contain no such hieroglyphic inscriptions as the traditions imply. It is only such texts as that of the Book of the Dead, which picture the passages and chambers of the Standard Pyramid of the of Dynastological Lists, or Secret House of the Book of the Dead as lined with with instructions and formulae, and with mythical figures and stars. It is to these that the traditions refer, and from such texts as these that the traditions obtained authority for identifying the Standard Pyramid of the Dynastological Texts with the Great Pyramid of Gizeh. The fact therefore remains that Coptic tradition associates the Great Pyramid with the symbolising of astronomical and geometrical figures, just as the Egyptian Ancestors of the Copts associated the Great Pyramid with their ideal secret house in the Book of the Dead, and with their geometrical Dynastology, cosmical year circle, and Sothic cycle mythology.
¶ 113. PREVIOUS CONCLUSIONS AND NEW DATA. In the Summary and Conclusions of Chapter I (Section I, ¶¶ 40-46), it was seen that a high state of civilisation flourished in times classified as “prehistoric.” The culture of this civilisation was seen to have reached an advanced stage of scientific knowledge. It was not suggested that scientific development had proceeded along the same lines as modern scientific research. It was, however, suggested, by the evidence, that results had been attained in the science of astronomy in no way inferior to the results of modern gravitational astronomy. In one particular line of inquiry, the indications pointed clearly to an advanced knowledge concerning the elements of the planetary orbits. These indications suggested that this knowledge had been recognised to be capable of simple expression as a system of Natural Law ; the system being capable of complete definition in solid geometrical form. This was indicated as of Pyramidal form.
The evidence discussed afforded reliable grounds for tentatively accepting the hypothesis that the Great Pyramid of Gizeh was the structural expression of this system of Natural Law. It suggested that the Pyramid was constructed to perpetuate this knowledge at a time when the remote founders of the Euphratean, Egyptian, and Mediterranean civilisations were reconstructing their systems of national life upon the fragments of oral tradition remaining from the former civilisation. the discussion of the new evidence adduced in the present chapter indicates New Data that the hypothesis suggested by the preliminary data is confirmed by the systems of oral traditions concerning the Great Pyramid, by its association with the Tradition, and original scientific system of primitive measures, and by its external measures Measures and principal features.
The evidence upon which the preceding conclusion is based leads to the further inference that the external features of the Great Pyramid are primarily concerned with a geometrical representation of the dimensions and motions of the Earth and its orbit. The unit for the geometrical representation of dimensions must necessarily be a simple function of (a) the Earth’s Polar diameter, (b) the Sun’s diameter, or (c) the Earth’s mean distance from the Sun. Otherwise the representation can have no meaning or application. It seems to be clearly evident that of the three possible units that derived from the Earth’s Polar Diameter is the most suitable for representing the other two dimensions in terms tangible to the Earth’s scientific inhabitants. Intentionally, or by accident, the Great Pyramid unit of measurement— the Primitive inch—is the simplest possible function of the Earth’s Polar Diameter. The Earth’s Polar Diameter measures exactly 500 million Primitive inches. The value giving this result was derived from three independent sources :—
The three independent sources agree in associating the Primitive inch value with the representation of cyclic functions of the Earth’s motion in its orbit. This tends to confirm that the simple relationship between the Earth’s Polar Diameter and the Primitive inch can scarcely have been an accidental relationship. It cannot, however, be established that the relationship was intentional until the Pyramid’s geometrical system is shown to extend the relationship to the Sun’s diameter, the mean Sun distance, and the variations in the eccentricity of the Earth’s orbit. These values should be confirmed, as to intention, by the representation of independent heliocentric or geocentric angular measurements where possible. At least, this is what one would expect to find in a geometrical system of the nature inferred, and in which the Designer’s express purpose was to establish the certainty of his intentions.
The Primitive inch—the inferred Polar diameter inch—is the basal unit of the Primary Metrological system of the former civilisation. An important unit of this system was the Sacred Cubit of 25 P. inches. The latter has been preserved by the measurements of the Great Pyramid, and by the Hebrews. It never occurs in Egypt except during periods of Semitic domination. Apparently from the half cubit (12½) of this system originated the 12½|” foot of ancient Roman remains, and of ancient British and Medieval English remains. Of the same origin is the old Rhineland foot, and the foot in Switzerland and Austria. The Primitive inch (1.0011 B”) is also the original of the British Inch, of the old German, Austrian and Swiss Zoll, of the Danish tomme, and Scandinavian turn, and of the old French pouce. This origin, at least for the British Inch, is confirmed by the connection between the sacred half-cubit and the decimal division of the Hebrew unit of 10 acres in ancient Cornwall, where the side of the 10 acres square occurred as a furlong of 8,000 inches. ¶¶ 85 and 86.)
¶ 116. THE SECONDARY METROLOGICAL SYSTEM. The Secondary Metrological System of the former civilisation is very clearly defined. It appears to have been formulated to avoid in calculations the use of the ratio = 3.14159. A Standard Year Circle of 3652.42 Primitive inches was adopted. The Standard Diameter of this circle was divided into Diametric Digits, Diametric Feet, and Diametric Cubits. The Standard Circumference was divided into Circumferential Digits, Circumferential Feet, and Circumferential Cubits. These linear units have all been preserved by the Egyptians. A standard of Square Measure was formulated as follows : — A Rectangle of length equal to the circumference of the Standard Circle, and of breadth equal to the diameter of the Standard Circle was the standard unit of square measure. It was equal in area to the area of four standard Circles. The Standard Rectangle was transformed into a square of equal area. The side of this square was divided into a hundred parts. The linear unit thus obtained was adopted as the cubit for measuring sides of rectangular figures. This cubit has been preserved by the Egyptians as their common cubit of 20.63 Simple rule-of-thumb relations connected the diametric and circumferential units with the linear units of rectangular figures. The Secondary system Uncultured was obviously formulated at a time when the uncultured many were organised to carry out highly skilled work under the intermittent direction of a cultured few. The system appears in use in ancient Egypt in the earliest Dynastic times — and possibly in pre-dynastic times — before the Pyramids were built.
In Chapters III and IV it will be seen that the Great Pyramid contains a single comprehensive system of geometry representing the complete derivation of the Secondary System of Measures in terms of the Solar year to the scale of 1 P. inch to a day. From this, and the data in the present chapter, it follows that the Great Pyramid represents the geometry of the year circle to three decimal scales,
Its 35th course defines the Sacred Cubit of 25 P. inches, and the aroura rectangle of 3652.4 P. inches by 1162.6 P. inches. The Square circuit of any horizontal plane of the Pyramid is equal to the circumference of a circle of radius equal to the Pyramid height above the horizontal plane considered ; and the area of the right vertical section of the Pyramid above this horizontal plane is equal to the area of the quadrant of the circle defined. The datum of this representation is the Pyramid’s base circuit of 36524. 2 +P. inches, representing the value of the solar year on the scale of 100 P. inches to a day.
It was at a comparatively late period of Egyptian history that the Egyptians constructed their various systems of fictitious chronology. This they did by substituting years of alleged Egyptian history for Pyramid inches in important measurements of the Great Pyramid. The principle upon which they proceeded in such cases was outlined by Dr. Sprenger about a century ago. Sprenger stated, regarding the Egyptians, that, with them, “an idea, a period of time, or any remarkable occurrence, were frequently connected with ideal persons in mythology, and when any similarity existed, received the same appellation.”1 The idea” in the particular case under consideration was that oral tradition associated the Pyramid’s measures with astronomical cycles and orbital motions. This supplied the data for their various “periods of time,” and for identification with “remarkable occurrences” in history and astronomy. So extensively did the Egyptians adopt the outstanding measurements of the Great Pyramid in their fictitious systems of chronology that the Great Pyramid’s external features, dimensions, and units can be derived without any prior reference to the Great Pyramid. Were the Great Pyramid not now in existence its external form, dimensions, and units, together with its principal external features, could be reconstructed entirely from the Dynastological Lists of the Egyptians.
The unsystematic manner in which the Egyptians adopted Pyramid measurements as the basis of astronomical periods in their King Lists clearly indicates that they had nothing but a general vague tradition to guide them. They proceeded to extract measurements without regard to sequence or principle. Scientific principle demands that a graphical representation of a period of time cannot be made along an axis defining radii and diameters, and at the same time be made round a circuit defining a circumference. The latter method of representation is possible, the former unlikely, but both together are impossible in a scientific representation. The compilers of the King Lists, however, added the measurements of radii to the measurements of arcs, horizontal distances to vertical distances, and totalled measurements in cubits together with measurements in inches. The single idea they did adhere to was that the Pyramid base circuit contained a representation of the Period of Precession. One school adopted the sum of the base diagonals as giving the period in inches for years. Another school adopted the base circuit in inches for years, as defining the Period. The Base Diagonals difference between the two conceptions amounted to 10,698 years, or twice the duration of the human kings given in one summation of the Lists preserved by Africanus. (Plate XVI, Table C (4).) Nevertheless, in their oral tradition, possibly without much understanding of the facts, the Egyptian priests retained many valuable items of astronomical knowledge. This is indicated by the manner and sequence in which the Greeks derived their knowledge of science from the Egyptians. (Refer Section II of this Chapter — and Table X.)
The traditional association of the Pyramid’s base with the idea Precession leads to a further possible inference. The difference between the solar year and the siderial year is the annual amount of precession measured in time. This and the Pyramid base connection suggest that while the base square circuit gives the value of the Tropical year, the perimeter of the hollowed in base may have been intended to give the value of the Siderial year. By following up this suggestion, the reader will find the intention of the Pyramid rapidly developing in Chapter III. From this suggestion, the external features, dimensions, and units of the Great Pyramid, when studied in plan, of inquiry will be found to give, precisely and accurately, every essential value of the Earth’s orbit, and its motions. These will be found to include the values of Anomalistic, Siderial and Solar years, the mean Sun distance, the Sun’s diameter (independent linear and angular representations), and the maximum and minimum values of the eccentricity of the Earth’s orbit. From these representations the reader will be able to appreciate how and why Pythagoras — having studied the science of the Egyptians—was enabled to enunciate, over 2,000 years before the truth was generally realised, that the planets revolve round the Sun. (Refer Section II, ¶ 126 and 129 to 133, Astronomy. and Table X.)
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