Many here will be aware that the ‘Toys’ page in Johann Bessler’s Maschinen Tractate was numbered MT 138, 139, 140 and 141. I suggested that the drawings he destroyed or buried were replaced by this curious page of what appear to be toys, but perhaps there was another reason.
The previous page was numbered MT137, which was the logical number for the preceding page. As I pointed out previously MT137 contains the musical ‘circle of fifths’, plus if you use two radii to divide a circle according to the golden ratio it yields sectors of approximately 137° (1.618, the golden ratio) and 222°, hence the number 137.
So 360/1.618 = 222.5 . 360-222.5=137.5 Curiously 1/137.5 = 00727272727 etc. 5x72=360.
The pentagram is of course constructed with numerous examples of the golden ratio.
I should add there is a huge amount of discussion in scientific circles about the mystery of the number 137. https://en.m.wikipedia.org/wiki/137_(number)
The final number on the Toys page is 141, is an interesting choice. The number of Bible references in Bessler’s Declaration of Faith also number 141. Only 3 and 47 are divisors of 141. This brings to mind Euclid’s 47th problem. MT47 has a curious feature, the number 47 is repeated upside down within the drawing.
Bessler seems to be underlining the importance of the number 47. It could suggest the requirement for a 3:4:5 right angle in his wheel?
Other reasons occur to me which could explain Bessler’s inclusion of these numbers but it would be too much speculation at this point.
I’m aware of suggestions that Bessler was involved with FreeMasonry and so I offer the following information gleaned from
https://bricksmasons.com/blogs/masonic-education/the-47th-problem-of-euclid
“The 47th Problem of Euclid or 47th Proposition of Euclid is also known as the Pythagorean Theorem. It is represented by three squares.
The symbol of the 47th problem of Euclid looks mysterious to the uninitiated, and a lot of them often ponder on what this Masonic symbol means.
Some Masonic historians describe the 47th Problem of Euclid as something that connotes a love of the sciences and the arts. But that definition leaves a lot unsaid. In this article, we’ll shed more light on the 47th Problem of Euclid. Our explanation will include the Masonic Square along with Pythagoras’s Theory.
Euclid
Euclid is known as the Father of Geometry. He lived several years after Pythagoras, and he continued the work of Pythagoras. Euclid focused mainly on the 3:4:5 ratio puzzle. Some sources have it that he had to make a sacrifice of 100 cattle or oxen before he could solve the puzzle. Some other sources have it that the Egyptians had long solved the puzzle before he did.
The Pythagoras Theorem
The Pythagoras theorem states that in a right-angled triangle, the sum of the squares on the two sides is equal to the square of the hypotenuse. So, for a right-angled triangle with lengths of sides in the ratio 3:4:5, ‘5’ represents the hypotenuse or the longest side.
3: 4: 5
32: 42: 52
9: 16: 25
9 + 16 = 25
The first four numbers are 1, 2, 3 and 4. Let us write down the squares of these numbers.
12:22:32:42
1: 4: 9: 16
When you subtract each square from the next one, you get 3, 5, 7.
4-1 = 3
9-4 = 5
16-9 = 7
The ratio 3: 5: 7 is very important. The ratio represents the steps in Freemasonry. They are the steps are the exact number of brothers that form the number of Master Masons needed to open a lodge.
3 Master Mason
5 Fellow Craft
7 Entered Apprentice
3: 5: 7 represents the steps in the Winding Stair that leads to the Middle Chamber.
The 47th Problem of Euclid is necessary for constructing a foundation that is architecturally correct as established by the use of the square. This is important to Operative Masons as well as Speculative Masons.
The 47th Problem of Euclid is a mathematical ratio that allows a Master Mason to square his square when it is out of square.
In the old days, old wooden carpenter squares had one longer leg because they were created using the 3: 4: 5 ratio from the 47th problem of Euclid. But carpenters of today use squares that have equal legs.
If you have four sticks and a piece of string, you can work out the 47th Problem of Euclid on your own. You will be able to create a perfect square with these. The string should be about 40 inches in length, and the four sticks must be strong enough to stick into soft soil. You will also need a black marker to mark the rope.”
I remain unconvinced of Bessler’s membership of the Masons, but he seems to have had some knowledge or interest in them.
JC
