L. A. Braun - Da Vinci’s Divine Proportion (Da Vincis REAL Secrets)

The life-giving watersof the sacred fountainhead flow in a divine proportion.

About This Book

Luca Pacioli himself, in thebeginning of the 1509 book De DivinaProportione, had stated that the Golden Ratio was a divine secret of thesacred Wisdom. This book elucidates the evidence supporting that statement. Ourbooks typically offer a summary of a wide-based assortment of mysterious sacredsecrets that wed found hidden within the Masters Art. However, this book chartsa slightly different course. It, instead, hones in exclusively on Leonardo DaVinci's sacred geometry, which he had illustrated in De Divina Proportione ofLuca Pacioli. That treatise had specifically addressed the Golden Ratio.Herein, well take a look at the basics on the geometry and mathematics of thevarious solids set forth in the manuscript.

After that, well furtherextrapolate upon Da Vincis geometry clues to gauge the rebus evidence of aunique Stairway pattern that he had embedded within his works, which we callthe Stairway to Heaven. While demonstrating its direct correlation to theGolden Ratio, well link the geometry secret into the work of the greatMasters Art to try to uncover the deeper meaning.

SECTION ONE

If no maththen no art had been LucaPaciolis working mantra. Within this book, well assess the geometric andmathematic patterns of the magical Golden Ratio, as it had been set forth inPaciolis De Divina Proportione (TheDivine Proportion). The coveted manuscript, quite revolutionary in its freshgeometric concepts, was illustrated by Leonardo Da Vinci, a pupil of Pacioli,in Milan in 1498. The treatise was then later published in Venice in 1509.

Paciolis books subject hadcovered mathematical and artistic proportion, especially when using thecalculated measure of the Golden Ratio. The treatise had explicitly examinedvarious calculated applications of the Golden Ratio, referring to the mathematicalmeasure as the Divine Proportion. The distinctive focus was on the structure ofgeometric shapes. Hed personally averredthat the perfect circle, combined with the equilateral square, had underlinedall great art and architecture. Over sixty different illustrations, created byDa Vinci, had been presentedstarting with the sphere and ending with apolyhedron of seventy-two faces. The multi-shaped diversities had advancedthrough all of the imaginable machinations along the way.

Two versions of Paciolisoriginal manuscript are still extant, although three had been originallyproduced; one is exhibited in the Biblioteca Ambrosiana in Milan, while theother is displayed in the Bibliothque Publique et Universitaire in Geneva. The Title Page (1509) of 16 lines (astitle and description):

After wevebecome acquainted with Paciolis book, then well look at a conspicuous yetmysterious geometric pattern of a Stairway that appears throughout the rebuspictograms of the Great Masters. Frankly, we were first intrigued when weddiscovered that a geometric stepladder shape had popped up all over the work ofLeonardo Da Vinci. Its footprint was randomly placed in the oddest of places.Wed dubbed Da Vincis tantalizing geometric phenomenon as the Stairway toHeaven and set out to explore its perimeters to better understand itsimportance. After taking a look at the Divine Proportion, it became clearthat Da Vincis recurring Stairway pattern was intricately connected to theDivine Proportion of the Golden Ratio. It was a part of the sacred geometry.

Within our books,weve searched the Masters Artupside and down--to isolate and assess thesacred secrets of the Philosophers Stone. Wed first uncovered a number of secretshidden inside of the artwork of Da Vinci. In fact, his work alone had producedan enormous cache of outrageous surprises. The secrets were ensconced withinthe rebus picture words (using picture symbols for words). Our quest has beento unravel the import of these rebus secrets. In fact, each of our books is athread-gathering effort to solve the conundrums. Today, well demonstrate howthe recurrent manifestation of astairway-shaped secret within the Masters Art was connected to the GoldenRatio. Indeed, well reveal how it was linked to the fractal geometry of the SierpiskiTriangle (which is foundationally linked to the Fibonacci Sequence, based onthe Golden Ratio).

Da Vinci had been living withhis math tutor Pacioli at the time that the Divine Proportions drawings werecreated. A painting usually attributed to Jacopo de' Barbari (1495) portraysPacioli wearing the monk robe with a mathematicians tools. There was adodecahedron resting upon a book bearing his initials. Up above was a hangingrhombicuboctahedron (which is a convex 26-faced solid consisting of 18 squaresand 8 triangles).

Paciolis work had primarilyfocused on the use of the Golden Ratio ( = 1.618034 ) . In mathematics, two quantitiesare in the Golden Ratio if their ratio is the same as the ratio of their sum tothe larger of the two quantities. The line segments of the Golden Ratio (when bx 1.618034 = a):

The Golden Ratio turns upfrequently in geometry, particularly in figures with pentagonal symmetry. Asone example, the length of a regular pentagon's diagonal is times its side. As another example, the vertices of a regular icosahedron arethose of three mutually orthogonal golden rectangles (based on ) .

The Golden Ratio had playedan important role in the geometry of pentagrams. For example, each intersectionof edges sections other edges in the Golden Ratio. Also, the ratio of thelength of the shorter segment to the segment bounded by the two intersectingedges (a side of the pentagon in the pentagram's center) is :

Know thy self to know God.

The mathematic makeup underscoringPaciolis Golden Ratio and the Fibonacci Sequence are closely interconnected.In the Fibonacci Sequence, each number is the sum of the two preceding ones:

1, 1, 2, 3, 5, 8, 13, 21, 34,55, 89, 144, 233, 377, 610, 987, ...

After the first severaldigits, the ratio between the progressive numbers becomes PHI1.618034. To present a visually illustrative example, the closed-formexpression for the Fibonacci Sequence directly involves the Golden Ratio:

The fractal geometry of the SierpiskiTriangle had been craftily veiled within the great Masters Art works (and itwas innately connected to the mathematics of the Fibonacci Sequence, based uponthe Golden Ratio).

There has been muchdiscussion over whether Da Vinci had then went on, after illustrating Paciolisvery important book on the Golden Ratio, to incorporate the principles of the DivineProportion directly into his own artworks. Certainly, lots of suggestive but arbitraryGolden Rectangles can be drawn within the various masterpieceshowever, theconclusions are suspicious.