Economic and Stock Market Forecasting, W. D. Gann's Science of Periodicity Sequencing, by Daniel T. Ferrera is a course which presents Gann's science of Mathematical Cyclic Sequencing of Market Pattern Periodicities showing how to use them in conjunction with Gann's cycle theory and to forecast the Global Economy,
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Natural Architecture Table of Contents
A Translation Society Edition
By Petrus Talemarianus
Table of Contents
A. – THE THIRTY-FIVE CHAPTERS OF THE REPORT
I. – The Master of the Work, after having traveled the World in search of the laws of traditional Architecture using natural materials, sees in a dream a “closed Garden”; the entrance is opened to him thanks to the magic word ABRACADABRA, which leads him to discover the ratio h/g linking, in the same circle, the side of a regular pentagon to that of a regular hexagon. He defines the first rules of natural Architecture, whose proportions he has obtained imagining an “operative diagram” with twelve triangles and seven squares; he calculates the elements of the diagram with the aid of “h” and “g”.
II. – The sage AKLISHTAKAR explains to him Hindu doctrines, especially from the aspect of Tantrism, and gives him a diagram. The Master of the Work observes that his operative diagram is generated in the same mode as AKLISHTAKAR’s Tantric diagram.
III. – The study of Chinese Taoism confirms for him the conditions of Hindu doctrines. The Master of the Work can thus attribute numeric correspondences to the different Worlds of Manifestation, and know the existence of the cosmogonic Ennead formed of a Unity ruling eight quantities placed in pairs.
IV. – Chinese wisdom leads him to construct a figure that mediates between the squares and the circle; this figure is the key which yields the form of the Pyramid of CHEOPS. The base of this Pyramid, and its four faces folded upon this base, outline a part of the operative diagram which permits the Master of the Work to discover nine lengths forming eight ratios associated in pairs; these lengths and ratios constitute the constructive aspect of the philosopher’s Stone.
V. – To designate these nine lengths and mark the plans with letters, the Master of the Work seeks the traditional name of the philosopher’s Stone; he acquires the conviction that this word is ARSENIC●M.
VI. – He distributes the nine lengths sought throughout the operative diagram; he makes one of the letters of ARSENIC●M correspond to each of them; he gives a metaphysical attribution to each of the eight ratios; he calculates the numeric quantity for each one. He observes that the succession of values of these ratios forms a geometric progression of ratio h/g, i.e. a mutation of the quinary and senary.
VII. – The study of this progression allows him to find the geometric outline of the interior corridors and chambers of the Great Pyramid, whose dimensions also reveal the proportions of the philosopher’s Stone.
VIII. – The three exterior squares of the operative diagram allow him to imagine an “intermediary diagram on triangles,” with eleven elements, specially marked by the sign of the “Om” (AVM). The Master of the Work makes their elements correspond to the signs of the zodiac and to the planets.
IX. – To this intermediary diagram formed by triangles, he opposes, by complement, another “intermediary diagram on pentalphas,” with eleven elements.
X. – To link these two intermediary diagrams, he imagines the “mediating diagram,” also marked with the seal of the mutations of the quinary and senary, and confirms its primary constructive virtue. He calculates the deformations of the nine lengths of ARSENIC●M obtained in this diagram.
XI. – The calculation allows him to justify the metaphysical attributions given to the eight constructive ratios of the philosopher’s Stone, and to determine the approximate values of these ratios, which bring light to the fundamental role of the mystic numbers 108 and 7 in Tantrism and the Kabala.
XII. – To test the metaphysical value of the mediating diagram, the Master of the Work studies Egyptian theodicy.
XIII. – This study leads him to occupy himself with the Hebraic Kabala, which was the vehicle of Egyptian Science. It leads him to discover the analogy that exists between the constitution of the sephirothic Tree and that of the intermediary diagrams.
XIV. – The Kabalistic doctrines allow him to divide the mediating diagram according to the divisions in relation to the sephirothic Tree.
XV. – Guided by the principle of polarity, the Master of the Work imagines the “complete diagram” where all the elements of the operative diagram are doubled. This complete diagram reveals to him the formal principles of natural Architecture. His geometric studies end with the establishment of a synthetic outline, where the five diagrams he has imagined are placed in a single figure in the form of a tau.
XVI. – Following in this the wise Pythagorean discipline, the Master of the Work then demands of Arithmetic, Astronomy, Harmony, Geometry, and Stereometry a verification of his constructive theories. Through Arithmetic, he finds concordances with the cosmogonic squares of the Chinese.
XVII. – Through Astronomy, he justifies, following a Khmer tradition concerning planetary arithmology, the assignments he has given to the various planets to designate the elements of his diagrams.
XVIII. – The Chinese theory of the twelve musical pipes, completed by the study of the scales of PTOLEMY and PYTHAGORAS, show him the direct resemblance existing between the laws of Harmony and those of natural Architecture.
XIX. – The study of Harmony leads him to that of the sacred alphabets, and allows him to discover that the ratio of the bases of the same exponential law that rules both musical intervals and architectural proportions is √g.
XX. – In Geometry, the Master of the Work is led, by reason of the importance of the logarithmic law in his constructive theories, to study the regular division of the circle, and consequently the rhythmic numbers; he gives the meaning of many universal pantacles.
XXI. – In Stereometry, he studies the regular partition of the sphere, from which proceed the regular polyhedrons; he describes four sorts of correspondences between these solids. He demonstrates that his diagrams are only the projection, on a plane, of some of these correspondences, and that they thus find their justification in the regular partition of the sphere.
XXII. – Having now completed the examination of the traditional sciences, the Master of the Work seeks, in the social applications of metaphysics, new concordances with his constructive doctrines. First, he encounters, in myths and in symbols, the same numeric oppositions, resulting from the laws of the regular partition of the sphere, that he discovered in his diagrams.
XXIII. – He then studies the cults of the Stone and the Waters, dedicated to the two exteriorizations of the Center of the World, and he gives numerous examples drawn from many traditions.
XXIV. – He searches for relationships between the doctrines of the alchemists and his diagrams. He describes notably, with regard to these latter, the constitution of the alchemical Vessel, and follows the development of the four operations or “colors” of the Great Work.
XXV. – The reading of the most famous writings of times past, of a traditional character commonly accepted, allows him to observe that the plan of these works and the numbers that are encountered there confirm his theories about architecture. He first examines, from this point of view, the “Genesis” of MOSES.
XXVI. – The “Theogony” of HESIOD provides him with further proofs of this concordance.
XXVII. – The various myths of PLATO, studied in relation to the “Timaeus,” are in agreement with the constructive doctrines of the Master of the Work.
XXVIII. – The “Divine Comedy” of DANTE leads in the same way to the alchemical and initiatory science of its author.
XXIX. – This secret science is also found in its entirety in RABELAIS’ novel, whose plan the Master of the Work compares with his mediating diagram.
XXX. – Having thus completed the verification of the validity of his doctrines, the Master of the Work uses his diagrams to define the proportions of the houses of habitation erected according to the rules of natural Architecture; he provides plans for six types of houses.
XXXI. – He extends his work to religious edifices, divided into five types, whose plans he gives.
XXXII. – He uses the mediating diagram to describe and link together the two most perfect types of buildings: the philosophical dwelling of an Adept (Domus Talemariana) and the cathedral of a Pontiff (church of type H). He marks, according to his system, the imperial town of Peking with its various Cities.
XXXIII. – Further widening the field of application of his theories, the Master of the Work examines, under their light, the plan of the Island of Atlantis and its royal city, according to the description given by PLATO.
XXXIV. – He finally seeks ultimate concordances in the “Apocalypse” of Saint JOHN, whose visions he analyses. He explores the church of type H, dedicated to “Shekinah” (Cathedral of Amiens), and observes that the divisions of this edifice are in concordance with those of the apocalyptic book.
XXXV. – In conclusion, the Master of the Work, after having summarized the terms of his Report, affirms his faith in the utility, for men, of knowing and loving the rules of natural Architecture, in order to obtain, through the realization of universal Harmony, the great Detachment necessary for their complete felicity.
B. – THE TWELVE APPENDICES
I. – Construction of an approximate pentalpha with the rectangle √g.
II. – Table of the approximate numeric values of the eight ratios of ARSENIC●M.
III. – Ratio h/g obtained through the regular dodecahedron.
IV. – Chinese cosmogonic squares and table of PYTHAGORAS.
V. – The magic squares.
VI. Khmer arithmological series and Chinese cosmogonic squares.
VII. – On √π, 1/√2, and the ratio between the septenary and duodenary (Unpublished study by Francis Warrain).
VIII. – Regular polyhedrons and polygons.
IX. – Quadratures of the circle obtained in the diagrams.
X. – The figured numbers.
XI. – The rhythm of the holy Letters.
XII. – The divine architectural archetype and its paths.
C. – THE ADDED NOTES
We have gathered, at the end of the work, various notes relative especially to the illustration of the “Report” and which could not be placed near the images to which they correspond. Pages 377-378
TABLE OF FIGURES
FIGURES CONTAINED IN THE 35 PARTS OF THE REPORT
Comprising 50 geometric, numeric, and titled designs, of the author, as well as 108 engravings and 7 titled geometric designs of the editor.
The Master of the work.
Fig. 1: The arithmetical triangle of PASCAL and the FIBONACCI series.
Fig. 2: The Egyptian triangle.
The closed garden.
Fig. 3: PASCAL’s arithmetical triangle limited by the chessboard.
Fig. 4: Pentalpha.
Fig. 5: Small squares.
Fig. 6: The logarithmic spiral resting upon the corners of the turning squares.
The humble contemplative before the Virgin, and the four animals.
Fig. 7: The key to natural Architecture.
Fig. 8: Construction prior to the operative diagram.
Fig. 9: The operative diagram.
The Holy Trinity.
Fig. 10: The triple triad.
Fig. 11: The diagram of AKLISHTAKAR (Plates)
The great ARTEMIS of Ephesus.
The Woman, heart of the “Apocalypse”.
KOUAN-YIN with eighteen arms.
FOU-HI and his wife NIU KOUA holding the square and compass.
The pair of opposites (oriental and occidental Alchemies).
Fig. 12: The generation of the “Pa Koua”.
SHIVA on the cow NANDI.
Fig. 13: Triangular numbers.
Fig. 14: Square numbers.
Fig. 15: Pentagonal numbers.
Fig. 16: the “Shrivatsa”.
Fig. 17: The constitutive triangles of the pyramid of CHEOPS.
Fig. 18: The essential dimensions of the Great Pyramid.
Fig. 19: The constitutive triangles of a pyramid linked to the “materia” squares.
Chinese “Ming t’ang”.
The ten Sibyls.
The cow Nouit and the supporting gods.
Fig. 20: Quadrilateral of HERMES.
The twelve signs of the zodiac.
The seven planets.
Fig. 21: Outline of the interior chambers and corridors of the Great Pyramid (Plates).
The coffer of the Virgin.
Fig. 22: Magic rectangle of the Great Pyramid.
Pentagon and pentalpha.
Fig. 23: Construction prior to the intermediary diagram on triangles.
Fig. 24: The intermediary diagram on triangles.
The head and tail of the Dragon.
The Egg of the World.
The Tibetan “Om”.
Fig. 25: The intermediary diagram on triangles in correspondence with the “Om”.
Pectoral of the archgallus.
Fig. 26: The intermediary diagram on pentalphas.
The mediating Sovereign.
Fig. 27: The mediating diagram.
The zodiacal hermaphrodite.
Fig. 28: Construction relating to the lower part of the mediating diagram.
The alchemical Work.
The Ogdoad of Hermopolis.
Fig. 29: The sephirothic Tree.
CYBELE, the Mother of the gods.
MICHAEL, the “Metatron”.
The Candelabra of the Tabernacle.
The Table of the twelve loaves of showbread.
NOUIT, SHU, and SEB.
“Aum mani padme houm”.
Fig. 30: Construction prior to the complete diagram.
Fig. 31: The complete diagram.
Fig. 32: Geometric properties of the complete diagram.
Fig. 33: The geometric Tau.
Crucifixion between the Sun and Moon.
Fountain of science.
Fig. 34 a and b: The “Ho-t’ou” and the “Lo chou”.
Fig. 35 a and b: Chinese cosmogonic squares of 6 and 5.
Fig. 36 a and b: The eight Trigrams (arrangements of FOU-HI and King WEN).
Fig. 37 a and b: Cosmogonic square of 5 (separating directions of FOU-HI and King WEN).
Chinese tower with eleven stories.
Fig. 38 a and b: “Svastikas” on the cosmogonic square of 6 and 5.
The goddess of the rainbow.
Fig. 39: The Khmer arithmological and planetary squares.
MITRA-PHANES emerging from the pyrogenic Egg of the World.
Egyptian Gnostic cross.
Fig. 40: The rose of the twelve musical pipes.
Chinese bell with phoenix heads.
AMPHION, son of JUPITER, building “hundred-gated” Thebes.
Fig. 41: Alphabetical wheels based of ARSENIC●M.
Ritual of the dedication of a church.
The rose on the façade of the cathedral of Exeter.
Plan of the upper story of the statues of the “screen” of Exeter.
The union of the macrocosm and the microcosm.
Architecture and music.
Fig. 42 a and b: Constitutive quadrilaterals of the equilateral triangle and the square.
Fig. 43 a, b, and c: Equilateral triangle and squares with their constitutive triangles.
Fig. 44: Pentagon with constitutive triangles.
Notre-Dame de Tournai.
Fig. 45 a, b, c, d, and e: The planar projections of the “Yin” correspondences of the platonic solids superimposed on the complete diagram.
The quintuple hexahedron.
Image of the Moon and image of the Sun.
AVALOKITESHVARA with eleven heads and eight arms.
Fig. 47: Descent of the sephirothic Tree into the different Worlds of Manifestation.
Ascent of “Kundalinî” through the seven “chakras” of the human being.
The prophet ZECHARIAH.
The story of ŒDIPUS.
The two Dioscures at the service of the Goddess.
The pinecone of the Vatican.
The upper, middle, and lower parts of the furnace.
ULYSSES healing TELEPHUS.
The Ark of the covenant.
The Tabernacle of MOSES and its courtyard.
The tomb of King MIDAS the alchemist.
CYBELE, her two assistants, and her two lions.
The Great alchemical Work (humid path).
The Great alchemical Work (dry path).
The labyrinth at Chartres cathedral.
Tree of Raymond LULL.
The rocks of Bogaz-Kheui
The magical lintel of the octagonal chapel of Montmorillon (interior face and exterior face).
The Virgin in her cloak.
The Virgin in her glory.
Fig. 48 a and b: Plans of houses at the interior of the gardens.
Plan of the palace of Versailles, superimposed on the Monad of John DEE.
Fig. 49: Mediating plan.
Fig. 50: Split arch.
Feet of BUDDHA.
CYBELE between the SUN and MOON.
The two powers and their synthesis.
Diagram of the itinerary to follow for acquiring the faculty of flying through the air.
Schematic plans of the island of Atlantis and its royal city (Plates).
MITHRAS cutting the bull’s throat.
The vision of the throne of GOD and the Lamb.
Keystone of the absidial vault of the cathedral of Amiens.
Saint JOHN at Pathmos.
The central tympanum of the main door of the cathedral of Bourges.
The Holy Bottle (§ XXXVI).
FIGURES AND TABLES CONTAINED IN THE TWELVE APPENDICES OF THE WORK
Plan of the Lamaic cathedral at Lhasa.
Construction of an approximate pentalpha with the rectangle √g.
Table of the approximate numeric values of the eight ratios of ARSENIC●M.
Ratio h/g obtained through the regular dodecahedron.
Chinese cosmogonic squares and table of PYTHAGORAS.
The magic squares and their planetary correspondences.
Khmer arithmological series and Chinese cosmogonic squares:
Fig. II a, b, c, and d.
Fig III a, b, and c.
Regular polyhedrons: surfaces and volumes.
Fig. I a, b, c, and d.
Fig. II, III, and IV.
Table of the classification of the types of polyhedrons.
Nomenclature of the polyhedrons.
Table of the elements of the polyhedrons.
Construction of the faces of the polyhedrons.
Correspondence of the polyhedrons with the “Sephiroth”.
Page 356, Pages 360- 361
Quadrature of the circle obtained in the operative diagram.
X, XI, XII
THE TWENTY-TWO TITLED TABLES CONTAINED IN THE REPORT
Table of the numeric values corresponding to the letters of the Hebrew and Greek alphabets.
Table of Khmer planetary arithmology.
The 10 antediluvian kings of Babylon.
Starred Table of the twelve Chinese musical pipes.
Circular Table of the twelve Chinese musical pipes.
Generation of the diatonic scale of PTOLEMY.
Diatonic distances between the musical intervals of PTOLEMY.
Generation of the diatonic scale of PYTHAGORAS.
Ratios between the sides of various polyhedrons.
Table of the elements of the regular polyhedrons.
Properties of the parts of the whorl seen by ER the Pamphylian
Page 243, in note
Proportions of the eighteen models of houses of habitation.
THE FIVE FIGURES FORMED OF ALPHABETICAL CHARACTERS
are on Pages 2, 4, 48, 140 (in note), and 148.
THE SEVEN UNTITLED GEOMETRIC FIGURES
are in notes on Pages 35, 36, 106, 125, 166, 212, and 289.
THE TWO ORNAMENTAL LETTERS
are on Pages 1 and 325.
PLAN OF THE WORK
–The magic word ABRACADABRA provides the key to natural Architecture.
THE “GOLDEN RULE”
Its three aspects
– The operative diagram, verified by Tantric and Taoist doctrines, and applied to the geometric outline of the Pyramid of CHEOPS (§ i to vii).
– The intermediary diagrams and themediating diagram, in concordance with the Pythagorean and Kabalistic doctrines (§ viii to xiv).
– The complete diagram, leading to the establishment of a geometric tau (§ xv).
Its seven correspondences
in the traditional sciences
Arithmetic. – The Chinese cosmogonic squares (§ xvi).
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