Among the mysteries that Frederick Bligh Bond, William Stirling and others unfold for us is the mystery of the Vesica.
There are in numbers a group called irrational numbers. They are real but they are insoluble. The best known of them is Pi – π – which defines the relationship of the Radius to the Circumference of the circle and of all numbers may be said to define the circle since it also is used to determine the area of the circle. For the Greeks working with whole numbers the value of Pi was given as 22/7. In decimal figures this works out to be 3.142857, where the verse that runs “Now I , even I would celebrate…” (http://members.iif.hu/visontay/ponticulus/britannicus/pi-verses.html it runs on from there for 30 places) gives the value as 3.14159. 22/7 is remarkably close. Computers are still trying to resolve this number without success. It is real but not determined by number but by Geometry. There is therefore no reason it should resolve into a whole number.
Similarly the Vesica Piscis is a form which is determined by the intersection of two equal circles whose centres lie on the circumference of the other.
This intersection is said to represent the blending of the Mind of the individual with the Mind of God. We meet again this principle of equality shown elsewhere in Arithmetic.
The form is simple and sometimes encloses a kite, or double equilateral triangle, in which each side of the triangle is the radius of the circles. However the difficulty lies in determining not the width but the height of the long axis of the Vesica. The width is the radius but the height is an unlikely specimen.
But there is a simple way of determining that which is to use Pythagoras theorem that the Square on the hypotenuse is equal to the sum of the squares on the other two sides in a right-angled triangle.
Clearly the vertical axis is at a right angle to the radius that runs between the two centres. But being an equilateral triangle the other two sides are also the length of the radius. The length of one half of the long axis is therefore the square root of the square of the radius minus the square of one half of the radius.
To take a simple example if the circle has a radius of 22 units the square on the radius will be 484, while the square on half the radius (11) will be 121. The length of one half of the long axis is therefore 484 -121 = 363. Now what we see is that 363 is very close to the number of days of the Year. 22 we know demonstrates the circle in its relationship to Pi.
What is the square root of 363? The closest we can come in whole numbers is 19 which gives a square of 361. Thus we can argue that 19 = the Year.
As if that were not enough Bligh Bond tells us that if we take a cube of 64 and tilt it at an angle we are able to see 37 small cube faces. Some cubes show two faces and the centrally placed cube shows 3. These are all outer surfaces of the cube. However some of the faces are hidden from view, those cubes forming the back of the Great Cube.
These number 19 and in the centre of all of these 56 cubes (37+19) is another small cube of 8. Is that not a delight? For further reference read F. Bligh Bond the Apostolic Gnosis where he explores Christian Kabbala and why it was found so acceptable to the Greeks. For a synopsis of the Hebrew and Biblical Kabbala read William Stirling the Canon where he explains other mysteries.