Hidden Geometry in Da Vinci, Rennes le Chateau, and Maranatha Et in Arcadia Ego: Guest Post by Hayward Gladwin
Hayward perseveres in the search for Truth. His determination and dedication for this quest is something to greatly admire. It is a privilege to be able to share part of his journey and thoughts here. Please feel free to leave comments or questions for him below.
Soon after I picked up a copy of Maranatha in 2010 (and I’m not really sure how I was initially lead to it), I had discovered a tilted hexagram on the second image in the book. It was probably because it seemed that the staffs in that image were quite obviously framing the outline of a particular visual shape on their own. When holding this page up to the light, and with the transparent image showing through the page on the other side, it seemed to become even more clear to me. I used the staffs as lines and extended them to try to draw a shape. The result seemed probable, but too irregular. I put the hexagram to the side and forgot about it for awhile.
It wasn’t until later, after realizing that a certain passage of text in the book was actually referring to the hexagram, that I began to see how to make it accurately. This too proved to be momentarily interesting until sometime last year I went back to review the book from the beginning step by step and found something really interesting. Below is what I found.
(I recommend, if possible, to go through these steps by yourself. You can do it in Photoshop as I did, or you can use a compass and square. It is one thing to see this geometry displayed and laid out here, but really the most convincing way is in witnessing how it all fits together through the process first-hand. Believe me, it is more rewarding that way.)
To begin with, start with looking at Image #1 in the book, often referred to as “Hermes & Time”. It is important to remember a few clues given by the authors here. “In the circle of Hermes, can Time be squared”. And there were also the final two clues given which were more explicit , “Draw a circle around Hermes using his feet as its edge”, and “Draw a Square around Time using his back as the edge”.
Using the little “point” where Hermes’ sleeve and the staff meet (at the nook there- click to enlarge image), place the point of the compass there and widen the arc to the point of the encircled “+” sign there in the upper right. Completing this whole circle, Hermes’ feet touch the edge of the circle just as prescribed. Next, we go on to produce the square with the back of Time used as the edge.
There is a small bump in his garment where to begin with the upper left corner of the square. You’ll know that this line is correct as it splits his hourglass in the middle and crosses the point where the serpents on Hermes’ staff meet. The right edge of the square meets encircled “+” sign where the circle had previously been drawn. The bottom edge of the square and the circle touch at the bottom.
Ok, just to point it out, for anyone else who notices, this is precisely the same square
and circle found in Leonardo Da Vinci’s “Vitruvian Man”. Since this image was also found on the back of the book we can be sure then that his was intended.
Moving on, let’s go to Image #2 to find the hexagram.
In the section entitled “Solis Sacerdotibus”, these are the instructions that I found that lead to the construction of the tilted hexagram.
“See to the first Joseph the prince the shepherd of Canaan. He leans and prays upon his staff. His gaze through the all seeing eye of wisdoms guidance falls like a treasure to his kin to the very heel and toe of Aaron.” (I understood the figure at top, the lion-headed figure, to represent “Joseph”. The all-seeing eye, I understood as his eye passing through the crook of the staff, and passing also through the eye of the dragon. The line continues through the back heel and front right toe of the dragon figure on lower left. The connection to the staff is at a point with a sprouting bud.)
Step 2 “…Mosis the Priest the shepherd of Midian born again into the royal house until he rose above that death and gazed down with the aid of his brother and revealed the secret mark of Josephs wisdom.” (I understood Mosis as being the remaining figure to the bottom right, since Joseph and Aaron have already been mentioned in the text. His “gaze down” is reflected by joining his eye to the same point on the staff as below. “The aid of his brother” is indicated by the fact that the dragon “Aaron” pointed out where the connection was through his eye.)
Step 3: Join the two lines using the staff of the figure above using Joseph’s Wisdom (Joseph’s wisdom” is pointed out by following the staff previously referred to as “wisdom’s guidance”).
Step 4: “It was as his staff turned on the other serpents under Josephs guidance did it consume its tip to assure perfection allowing this son of Hermes to climb the mount and hear the laws of creation.” (At this point, we begin using the transparency of image #1. Joseph’s Wisdom “turns” at its end, indicating that the image “turns’ over from the other side. Viewing this, we can see how the staff of time on the reverse side passes through Joseph’s Wisdom staff and ends at the point of Mosis’ (griffin) below).
Step 5: “But look to the preying face of the demons for like the fiery serpents they obscure the undulating moving of the divine truth swaying in the breath of Zeus. Such then is the need to solidify the wisdom to dispel these beasts and offer firm understanding.” (A line is now drawn from the last point toward the direction of Aaron (dragon).)
The “preying face of the demons”:
The “fiery serpents” (upside down):
Step 6: “Such then is the need to solidify the wisdom to dispel these beasts and offer firm understanding.” (Join the lines near the Preying Face and the Fiery Serpents)
Step 7: “For mortal endeavour now do we learn of the third son of Hermes and his staff Aaron the Levite the shepherd of Mizraim. For from the tip of his staff does he find the divine balance of the wisdom of Mosis and Joseph. See him Kneeling before his own tomb on the mount for wasn’t his staff that was laid to rest in the Sacred Ark a talisman to ward away the rebel beasts.” (From here, it is apparent that the tip of the staff that Aaron (dragon) is “pointing” (reaching out to) to is used to balance the “wisdom” of the lines drawn from Joseph (Lion), and Mosis (Griffin). The fact that his staff is set to “rest” in the Ark/talisman (hexagram) suggests that it should lie all within the shape. For this, I have scaled up the image to incorporate this. You can see how the points made on the right side of the hexagram have been kept in place.
Now, I realize at this point, that this is a step might seem somewhat arbitrary at first. Having already gone through the various steps to produce a hexagram (which seemed convincing on its own) only to then have to alter the entire shape like this to get to the next point, seems tenuous. The reason why I did this will make sense in a moment, and you will see why it is important.
Combining the Geometry from Image #1 with Image # 2
When I saw that the two shapes produced on opposite sides of the page closely related to each other but were just slightly away from aligning, the obvious question of “how do the two shapes interact with each other” came about. This proximity seemed to be suggesting that the two need to go together, but perhaps not exactly as they are drawn. I decided to try scaling up the hexagram, using Aaron’s (dragon) staff tip as the new point for the lower point of the hexagram it all fell into place. The result is a very peculiar anomaly.
The interaction between these two shapes now seems quite obvious. One point of the hexagram touches the circle, and one point touches the square. In addition, a crossing point of two lines on the hexagram also intersects with the square and circle at the bottom. The three shapes really seemed to “key” together here. If this seems interesting, there is something else that will confirm the relationship between these shapes.
If one were to draw a line from each corner of the square to its opposite corner, these lines intersect at an upper intersection of two lines on the hexagram. Also, one of these lines follows the right edge of the hexagram in its full length as the other passes through a third intersecting point on the hexagram.
Such a harmonious interaction between shapes was never expected. Even when I look at it know it still produces a sense of awe; something hard not to keep looking at.
A Further Step to Make
After considering the above shape at length, the only problem that remained was how to account for other images in the book in relation to it. Clearly, (as the logic followed) if something was to be found in two of the images, then there would be something in another image that would correspond in some way. One of the prominent images that stood out in this regard was Image #5, the entwined serpents with the staff of Tiresias.
In the chapter “Terribilis Est Locus Iste”, there is a line that states “Then seek the meaning of the Staff of Tiresias the relic of Hermes. For through its power it transmuted that which it touched beyond the value of gold.” Thinking about this, it became obvious that Hermes’ circle in image #1 was about the same size as the shape of one of the serpents in image #5. Then with the “value of gold” relating to an idea about the Golden Ratio, I began to see how the two serpents appeared as interlocking circles such as found in a Vesica Piscis. This is not a standard form for a Vesica Piscis however, in which the arc of each circle passes through the center of the other, they are slightly off.
Considering this shape, it only made sense to incorporate the two circles together the previous geometry. This exact relationship between the two circles fits together with the square as such. The top of the new circle meets the top of the square as the bottom of the previous met with the square’s bottom edge.
What we have done now is made a shape in which the hexagram touches 3 different shapes: The Square, The Circle, and the other Circle. I don’t find this to be coincidental, considering that it also fits precisely with Davinci’s geometry. The new circle is a mirror of the previous one.
The Dagobert Parchment of Rennes Le Chateau fame also contains a similar form.
The steps for finding this are as follows:
Starting with the raised “R” in the center of the document, use this point as the center point. Using a compass, widen the arc to the “+” to upper right (in front of “mandu”) then complete the circle. Next draw a line from the “+” you just used through the next “+” symbol a little lower to the left. End the line at the circle’s edge. Next, use this last point to draw a line to the “crook” in the shape on the parchment in the upper right. Then simply join these last two points. This is you first equilateral triangle.
The next triangle is not as easy to find. Start by drawing a line from the bottom point of the first triangle back through the center point of the circle “R”. Stop the line at the circle edge. From this point, draw a line through the last “+” sign in the lower left portion of the document (after “batis”). Finally, use this last point to draw a line through the space in between the “S” and “I” of the vertical word “SION” written with the last letter of each line (there is a little dot there in the original document to indicate this). Here is the result:
But what, of course, does this explain other than simply this shape has been found (or inserted) in various places to be found? It seems as though it is part of a larger whole, with other parts perhaps still missing. Or should there be reason to accept it in this form as complete in any way?
To draw further relationship, there is also another curious connection between the two circles found in the Maranatha book and the parchment here. As Henry Lincoln had presented his own geometry found in the Dagobert parchment (referred to as the document’s “geometric substructure”), there are two circles there which correspond to exact ratio as those found in Image #5 of Maranatha.
Here is what the Dagobert Parchment with Lincoln’s geometry look like overlapped:
It seems clear in any event that the authors of Maranatha were somehow corresponding with the geometry presented by Lincoln as well as discovered in the Dagobert Parchment. And in addition, although there is no immediate relationship between the hexagram and the geometry with two circles on the parchment, they can be integrated in the same way as presented above using the square in appropriate proportion. It would appear that the geometry as discovered by Lincoln somehow establishes the relationship of the two circles. Notice also how the circles in the Parchments are skewed in a similar manner as the serpents in Image #5 (I had to flip the parchment horizontally in the picture to overlap the images,but they fit together upright without rotating).
This is my recreation of Lincoln’s geometry over the Dagobert Parchment.
The geometry, as it stands alone, is again something quite intriguing to look at and think about.
It should be noted that any deviation from the exact proportions between Davinci’s original square and circle causes these other shapes to NOT relate to each other in any way. It is clear from this that the interaction between geometric shapes is a product only of this specific Square and Circle. Considering the introduction of the hexagram throughout this story, it thus seems also not a coincidence that this might appear.
One question now might be, “does the hexagram as seen here act as a missing element that ‘solves’ the problem of the Square and Circle originally presented in the Davinci geometry?” Perhaps, in this light, the reverse steps of producing the circle or square using the hexagram and one of the others is the solution to get there.
Yet there are a few other ways to “solve” this problem using correspondences to addition shapes.
By taking the size of the original square and rotating it 45 degrees using the same center point, another interesting relationship occurs.
As you can see, the bottom point of the new square corresponds to the radius of the circle that touches the top edge of the other square.
So of course, placing the other circle of the geometry, an exact reflection of the same relationship occurs. Yet still, there is even something else interesting to look at.
Using two diagonal corners of the first square as the points of an even larger hexagram, two points of this shape also touch the outer two circles. It would appear that scaling these events again and again, we might replicate the same pattern and relationship between shapes. If this is the solution to “squaring the circle”, it might be additionally significant in providing a rational formula of proportional growth provided by the circle, square and hexagram (rotated 15 degrees) in successive fashion.
One thing that seems clear to me know with all of this is that, even though the geometry was hidden, these relationships between the shapes actually does occur. And although we don’t have the full meaning of it yet, my hope is that, through either intention or grace to be able to figure out more.
The “jewel that fell from the crown of Rex Mundi?”