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 “
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
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
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
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
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 “
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”
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
XX
Plan of the upper story of the
statues of the “screen” of
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
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
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
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
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
XXXV
The central tympanum of the main
door of the cathedral of
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
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
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 Cheops (§ i 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.)