After the two illustrations discussed in my previous post I have decided to offer my findings in another of the illustrations; this time the ‘Andere Figura’ and the ‘Secunda Figura in ‘Das Triumphans’. Again I am discussing the numbering used in them. I have placed a copy of the drawing below. Again a single click on the picture will bring up an enlarged version so you can see the numbering more clearly.
The first thing to
note in the pictures shown above, is that the right side of the
left picture has been truncated slightly. In the book they are separated by a small gap filled with thin black and white lines, clearly designed to allow for the inner margins being partially enclosed by the book binding. These lines allow you to bring the edges of the two illustrations close together as shown above.
In the drawing above you can see that the left circle can be completed and joins at the circumference of the right circle. Notice that the circle I've drawn in, does not follow the original one as it leaves the left page. This is due to the page being pulled inwards at the central binding which has slightly deformed the printed circle. I always thought that the two pages were intended to be joined and I tested the theory with my original copy of DT, by pressing the pages flat with a piece of glass and adjusting the right page until the thin black and white dividing lines were hidden. It was then possible to draw in the complete circle to show that it did indeed abut the right circle. As a check, note that the left half of my added circle aheres closely to the original one and that it only diverges as the bend in the paper aproaches the central crease.
In the above picture you can see yet aother pentagram inside the left picture. Notice how the extension of one of the chords of the pentagram runs through the middle of the right picture. This extension to the pentagon is governed by the close proximity of the two pictures so one must assume that the extension is intentional. The main supporting pillar forms a perfect angle of 72 degrees with the extended chord, thus indicating the rotational angle of a second pentagon.
I've included the additional pentagram in the above picture, which may seem more speculative and I must admite that although it looks possible, I have found it difficult to draw in a perfect pentagram so please add a pinch of salt to this particular suggestion.
In the right side picture above, the large triangular pendulum has some curious properties
which seem to be additional clues. They
are 30 degrees for the bottom angle, and 78 and 72 degrees for the upper left
and right angles respectively. The 72 degree
angle obviously fits in with the hidden pentagon, but is there an additional
clue there? Of course!
The second thing is that the right picture seems to have an excess of the number eight (four). This over-labelling looks suspiciously like the same technique I have described for the two first wheel pictures. Could this be another indication of a grand total being sought?
Yes - the numbers in the left picture add up to 28; those in the right, 62, to total 90. There are 15 numbers used and 90 divided by 15 is six. But this does not seem to be a significant number, however Bessler’s favourite number 5, divides exactly 18 times into 90 – 5 and 18; the ubiquitous pentagonal numbers again. Secondly the numbers used, 1 to 10, add up to a total of 55 – the other Bessler number.
In the drawing above you can see that the left circle can be completed and joins at the circumference of the right circle. Notice that the circle I've drawn in, does not follow the original one as it leaves the left page. This is due to the page being pulled inwards at the central binding which has slightly deformed the printed circle. I always thought that the two pages were intended to be joined and I tested the theory with my original copy of DT, by pressing the pages flat with a piece of glass and adjusting the right page until the thin black and white dividing lines were hidden. It was then possible to draw in the complete circle to show that it did indeed abut the right circle. As a check, note that the left half of my added circle aheres closely to the original one and that it only diverges as the bend in the paper aproaches the central crease.
In the above picture you can see yet aother pentagram inside the left picture. Notice how the extension of one of the chords of the pentagram runs through the middle of the right picture. This extension to the pentagon is governed by the close proximity of the two pictures so one must assume that the extension is intentional. The main supporting pillar forms a perfect angle of 72 degrees with the extended chord, thus indicating the rotational angle of a second pentagon.
I've included the additional pentagram in the above picture, which may seem more speculative and I must admite that although it looks possible, I have found it difficult to draw in a perfect pentagram so please add a pinch of salt to this particular suggestion.
The second thing is that the right picture seems to have an excess of the number eight (four). This over-labelling looks suspiciously like the same technique I have described for the two first wheel pictures. Could this be another indication of a grand total being sought?
Yes - the numbers in the left picture add up to 28; those in the right, 62, to total 90. There are 15 numbers used and 90 divided by 15 is six. But this does not seem to be a significant number, however Bessler’s favourite number 5, divides exactly 18 times into 90 – 5 and 18; the ubiquitous pentagonal numbers again. Secondly the numbers used, 1 to 10, add up to a total of 55 – the other Bessler number.
10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.
