Natural Architecture
By Petrus Talemarianus

 

 

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” (pages 1 to 14).

           
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 (pages 14 to 27).

           
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 (pages 27 to 24).

           
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 (pages 34 to 39).

           
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 (pages 39 to 49).

           
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 (pages 49 to 57).

           
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 (pages 57 to 65).

           
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 (pages 65 to 73).


IX. – To this intermediary diagram formed by triangles, he opposes, by complement, another “intermediary diagram on pentalphas,” with eleven elements (pages 74 to 77).

 

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 (pages 77 to 86).


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 (pages 87 to 91).

           
XII. – To test the metaphysical value of the mediating diagram, the Master of the Work studies Egyptian theodicy (pages 91 to 94).


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 (pages 94 to 105).

           
XIV. – The Kabalistic doctrines allow him to divide the mediating diagram according to the divisions in relation to the sephirothic Tree (pages 105 to 112).

           
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 (pages 113 to 120).

           
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 (pages 121 to 127).

           
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 (pages 127 to 134).

           
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 (pages 135 to 147).

           
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 (pages 147 to 152).

           
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 (pages 153 to 159).

           
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 (pages 159 to 179).

           
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 (pages 179 to 194).

           
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 (pages 194 to 204).

           
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 (pages 204 to 213).

            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 (pages 214 to 229).

           
XXVI. – The “Theogony” of Hesiod provides him with further proofs of this concordance (pages 229 to 233).

           
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 (pages 233 to 254).

           
XXVIII. – The “Divine Comedy” of Dante leads in the same way to the alchemical and initiatory science of its author (pages 254 to 261).


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 (pages 261 to 281).


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 (pages 281 to 288).


XXXI. – He extends his work to religious edifices, divided into five types, whose plans he gives (pages 289 to 293).


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 (pages 293 to 304).


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 (pages 305 to 309).


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 (pages 310 to 324).


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 (pages 325 to 330).

 

B. – THE TWELVE APPENDICES

 

            I. – Construction of an approximate pentalpha with the rectangle √g (page 335).

            II. – Table of the approximate numeric values of the eight ratios of ARSENIC●M (page 335).

            III. – Ratio h/g obtained through the regular dodecahedron (page 335).

            IV. – Chinese cosmogonic squares and table of Pythagoras (page 336).

            V. – The magic squares (page 337).

            VI. Khmer arithmological series and Chinese cosmogonic squares (page 338).

            VII. – On √π, 1/√2, and the ratio between the septenary and duodenary (Unpublished study by Francis Warrain) (pages 339 to 341).

            VIII. – Regular polyhedrons and polygons (pages 341 to 360).

            IX. – Quadratures of the circle obtained in the diagrams (page 361).

            X. – The figured numbers (pages 362 to 365).

            XI. – The rhythm of the holy Letters (pages 365 to 370).

            XII. – The divine architectural archetype and its paths (pages 371 to 376).

 

C. – THE ADDED NOTES

 

            We have gathered, at the end of the work (pages 377 and 378), various notes relative especially to the illustration of the “Report” and which could not be placed near the images to which they correspond.

 

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, p. xvii.

 

I

            Untitled engraving, p. 1 – Fig. 1: The arithmetical triangle of Pascal and the Fibonacci series, p. 2 – Fig. 2: The Egyptian triangle, p. 2. – The closed garden, p. 3. – Fig. 3: pascal’s arithmetical triangle limited by the chessboard, p. 4. – Fig. 4: Pentalpha, p. 5. – Fig. 5: Small squares, p. 5. – Fig. 6: The logarithmic spiral resting upon the corners of the turning squares, p. 6. – The humble contemplative before the Virgin, and the four animals, p. 7. – Fig. 7: The key to natural Architecture, p. 8. – Fig. 8: Construction prior to the operative diagram, p. 9. – Fig. 9: The operative diagram, p. 13. – The “Shriyantra,” p. 14.

 

II

            The Holy Trinity, p. 14. – Armes papales, p. 19/ – Fig. 10: The triple triad, p. 20. – Fig. 11: The diagram of Aklishtakar (Plates). – The great Artemis of Ephesus, p. 21. – The Woman, heart of the “Apocalypse,” p. 24. – Kouan-yin with eighteen arms, p. 25. – Fou-hi and his wife Niu koua holding the square and compass, p. 27.

 

III

            The pair of opposites (oriental and occidental Alchemies), pp. 28 and 29. – Fig. 12: The generation of the Pa Koua,” p. 30. – Shiva on the cow Nandi, p. 31. – Dice players, p. 32. – Fig. 13: Triangular numbers, p. 32. – Fig. 14: Square numbers, p. 33. – Fig. 15: Pentagonal numbers, p. 33. – Fig. 16: the “Shrivatsa,” p. 34.

 

IV

            Fig. 17: The constitutive triangles of the pyramid of Cheops, p. 36. – Fig. 18: The essential dimensions of the Great Pyramid, p. 37. – Fig. 19: The constitutive triangles of a pyramid linked to the “materia” squares, p. 38. – Chinese “Ming t’ang,” p. 38. – Lotus flower, p. 39.

 

V

            The ten Sibyls, p. 45.

 

VI

            The cow Nouit and the supporting gods, p. 50. – Assyrian ennead, p. 51. – Untitled engraving, p. 55. – Fig. 20: Quadrilateral of Hermes, p. 56.

 

VII

            The twelve signs of the zodiac, p. 58. – The seven planets, p. 59. – Fig. 21: Outline of the interior chambers and corridors of the Great Pyramid (Plates). – The coffer of the Virgin, p. 63. – Fig. 22: Magic rectangle of the Great Pyramid, p. 64. – Pentagon and pentalpha, p. 65.

 

VIII.

            Fig. 23: Construction prior to the intermediary diagram on triangles, p. 66. – Fig. 24: The intermediary diagram on triangles, p. 67. – The head and tail of the Dragon, p. 68. – The Egg of the World, p. 70. – The Tibetan “Om,” p. 71. – Fig. 25: The intermediary diagram on triangles in correspondence with the “Om,” p. 72. – Pectoral of the archgallus, p. 73.

 

IX

            Fig. 26: The intermediary diagram on pentalphas, p. 75. – The mediating Sovereign, p. 76. – Pentagonal lamp, p. 77.

 

X

            Fig. 27: The mediating diagram, p. 78. – The zodiacal hermaphrodite, p. 79. – Fig. 28: Construction relating to the lower part of the mediating diagram, p. 82. – The alchemical Work, p. 86.

 

XI

            Untitled engraving, p. 91.

 

XII

            The Ogdoad of Hermopolis, p. 93.

 

XIII

            Aleph, p. 95. – Fig. 29: The sephirothic Tree, p. 97. – Cybele, the Mother of the gods, p. 98. – Michael, the “Metatron,” p. 99. – The Candelabra of the Tabernacle, p. 102. – The Table of the twelve loaves of showbread, p. 103.

 

XIV

            Nouit, Shu, and Seb, p. 106. – Meditating Taoist, p. 107. – Untitled engraving, p. 108. – Hindu “Lingam,” p. 110. – “Aum mani padme houm,” p. 112.

 

XV

            Fig. 30: Construction prior to the complete diagram, p. 113. – The Annunciation, p. 115. – Fig. 31: The complete diagram, p. 116. – Fig. 32: Geometric properties of the complete diagram, p. 117. – Fig. 33: The geometric Tau, p. 118. – Crucifixion between the Sun and Moon, p. 119.

 

XVI

            Fountain of science, p. 121. – Fig. 34 a and b: The “Ho-t’ou” and the “Lo chou,” pp. 122 and 123. – Fig. 35 a and b: Chinese cosmogonic squares of 6 and 5, p. 123. – Fig. 36 a and b: The eight Trigrams (arrangements of Fou-hi and King Wen), p. 124. – Fig. 37 a and b: Cosmogonic square of 5 (separating directions of Fou-hi and King Wen), p. 124. – Chinese tower with eleven stories, p. 125. – Fig. 38 a and b: “Svastikas”  on the cosmogonic square of 6 and 5, p. 126. – The goddess of the rainbow, p. 127.

 

XVII

            Fig. 39: The Khmer arithmological and planetary squares, p. 128. – Mitra-Phanes emerging from the pyrogenic Egg of the World, p. 131. – Egyptian Gnostic cross, p. 132. – Alchemical putrefaction, p. 133.

 

XVIII

            Fig. 40: The rose of the twelve musical pipes, p. 135. – Chinese bell with phoenix heads, p. 141. – Amphion, son of Jupiter, building “hundred-gated” Thebes, p. 147.

 

XIX

            Fig. 41: Alphabetical wheels based of ARSENIC●M, p.149. – Ritual of the dedication of a church, p. 150. – The rose on the façade of the cathedral of Exeter, p. 152.

 

XX

            Plan of the upper story of the statues of the “screen” of Exeter, p. 154. – The union of the macrocosm and the microcosm, p. 156. – Double-headed eagle, p. 159.

 

XXI

            Architecture and music, p. 162. – Fig. 42 a and b: Constitutive quadrilaterals of the equilateral triangle and the square, p. 164. – Fig. 43 a, b, and c: Equilateral triangle and squares with their constitutive triangles, p. 164. – Fig. 44: Pentagon with constitutive triangles, p. 168. – Notre-Dame de Tournai, p .171. – Fig. 45 a, b, c, d, and e: The planar projections of the “Yin” correspondences of the platonic solids superimposed on the complete diagram, p. 174. – The quintuple hexahedron, p. 177. – Cubic Stone, p. 179.

 

XXII

            Image of the Moon and image of the Sun, p. 182. – Hayagriva, p. 184. – Avalokiteshvara with eleven heads and eight arms, p. 185. – Fig. 47: Descent of the sephirothic Tree into the different Worlds of Manifestation, p. 190. – Ascent of “Kundalinî” through the seven “chakras” of the human being, p. 191. – The prophet Zechariah, p. 194.

 

XXIII

            Black Virgin, p. 197. – Jacob’s ladder, p. 199. – The story of Œdipus, p. 201. – The two Dioscures at the service of the Goddess, p. 202. – The pinecone of the Vatican, p. 203.

 

XXIV

            Alchemical laboratory, p. 205. – The upper, middle, and lower parts of the furnace, p. 208. – Alchemical credence, p. 209. – Ulysses healing Telephus, p. 211. – Pyrogenic vessel, p. 213.

 

XXV

            The Ark of the covenant, p. 217. – The Tabernacle of Moses and its courtyard, p. 225. – Nubian tau, p. 229.

 

XXVI

            The tomb of King Midas the alchemist, p. 231. – Cybele, her two assistants, and her two lions, p. 233.

 

XXVII

            The Great alchemical Work (humid path), p. 239. – The Great alchemical Work (dry path), p. 249. – The labyrinth at Chartres cathedral, p. 253.

 

XXVIII

            Tree of Raymond Lull, pp. 258 and 259.

 

XXIX

            The rocks of Bogaz-Kheui, pp. 264 and 265. – The magical lintel of the octagonal chapel of Montmorillon (interior face and exterior face), pp. 268 and 269. – The Pontiff, p. 277. – The Virgin in her cloak, p. 279.

 

XXX

            The Virgin in her glory, p. 282. – Fig. 48 a and b: Plans of houses at the interior of the gardens, pp. 284 and 285. – Plan of the palace of Versailles, superimposed on the Monad of John Dee, p. 287. – Fig. 49: Mediating plan, p. 288.

 

XXXI

            Fig. 50: Split arch, p. 289.

 

XXXII

            Feet of Buddha, p. 294 and 295. – Cybele between the Sun and Moon, p. 297. – The two powers and their synthesis, p. 301. – Diagram of the itinerary to follow for acquiring the faculty of flying through the air, p. 303. – Untitled engraving, p. 304.

 

XXXIII

            Schematic plans of the island of Atlantis and its royal city (Plates). – Mithras cutting the bull’s throat, p. 307. – Saint Christopher, p. 309.

 

XXXIV

            “Ecclesia templariis,” p. 311. – “Templum Ezekiel,” p. 313. – The vision of the throne of God and the Lamb, p. 317. – Keystone of the absidial vault of the cathedral of Amiens, p. 319. – Saint John at Pathmos, p. 324.

 

XXXV

            The central tympanum of the main door of the cathedral of Bourges, p. 325. – Untitled engraving, p. 329.

 

The Holy Bottle (§ xxxvi), p. 330.

The Pilgrim, p. 331.

 

 

FIGURES AND TABLES CONTAINED IN THE TWELVE APPENDICES OF THE WORK

 

            Tibetan engraving, p. 333. – Plan of the Lamaic cathedral at Lhasa, p. 334.

 

I

            Construction of an approximate pentalpha with the rectangle √g, p. 335.

 

II

            Table of the approximate numeric values of the eight ratios of ARSENIC●M, p. 335.

 

III

            Ratio h/g obtained through the regular dodecahedron, p. 335.

 

IV

            Chinese cosmogonic squares and table of Pythagoras, p. 336.

 

V

            The magic squares and their planetary correspondences, pp. 337 and 338.

 

VI

            Khmer arithmological series and Chinese cosmogonic squares: Fig. I, p. 338. – Fig. II a, b, c, and d, p. 338. – Fig III a, b, and c, p. 339.

 

VII

            Bell curve, p. 340.

 

VIII

            Regular polyhedrons: surfaces and volumes, pp. 341 and 342. – Fig. I a, b, c, and d, p. 343. – Fig. II, III, and IV, p. 345. – Table of the classification of the types of polyhedrons, pp. 346 and 347. – Nomenclature of the polyhedrons, pp. 348 and 349. – Table of the elements of the polyhedrons, pp. 350 to 353. – Construction of the faces of the polyhedrons, pp. 354 and 355. – Correspondence of the polyhedrons with the “Sephiroth,” pp. 356, 360, and 361.

 

IX

            Quadrature of the circle obtained in the operative diagram, p. 361.

 

X, XI, and XII

            Figured numbers, p. 364.

 

 

THE TWENTY-TWO TITLED TABLES CONTAINED IN THE REPORT

 

            Table of the numeric values corresponding to t he letters of the Hebrew and Greek alphabets, p. 41.

            Table I, p. 55. – Table II, p. 87. – Table III, p. 89. – Table IV, p. 89. – Table V, p. 90. – Table VI, p. 105. – Table VII, p. 114.

            Table of Khmer planetary arithmology, p. 129.

            The 10 antediluvian kings of Babylon, p. 134.

            Starred Table of the twelve Chinese musical pipes, p. 136.

            Circular Table of the twelve Chinese musical pipes, p. 137.

            Generation of the diatonic scale of Ptolemy, p. 142.

            Diatonic distances between the musical intervals of Ptolemy, p. 143.

            Generation of the diatonic scale of Pythagoras, p. 145.

            Ratios between the sides of various polyhedrons, p. 157.

            Table of the elements of the regular polyhedrons, p. 160.

            Properties of the parts of the whorl seen by Er the Pamphylian, p. 243, in note.

            Proportions of the eighteen models of houses of habitation, p. 286.

 

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[1]

 

–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 Cheopsi to vii).

– The intermediary diagrams and the mediating 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).

Astronomy. – Khmer planetary arithmology (§ xvii).

Harmony. – The Chinese theory of the twelve musical pipes, and the Greek scales; the universal alphabets (§ xviii and xix).

Geometry. – The regular division of the circle: the rhythmic numbers and the traditional pantacles (§ xx).

Stereometry. – The regular partition of the sphere: the regular polyhedrons and their reciprocal correspondences (§ xxi).

in the social applications of metaphysics

The writings and representation of mythical, alchemical, and sacred character (§ xxii to xxix).

Natural Architecture in the West, the East, and in mystical accounts. Atlantis and the Apocalypse (§ xxx to  xxxiv).

– The Great Renunciation and the Return to Unity through the divine Mother (§ xxxv).

 

the master of the work

“...Antiquam exquirite matrem.”

(Virgil: Aeneid, III, 96.)



[1] Here we reproduce the plan of the Work found in the Author’s notes. We have simply added to it the indication of the sections given in the Table of Materials.