Category Archives: geometry

Ars Geometrica: Seal…


‘For God created man immortal, and made him in the image of his own eternity.’
– The ‘Twentieth’ Leaf

The preceding image we had to own did not seem to us particularly god-like.

We turned the leaf:

7The Twenty-First Leaf

…Although that description most definitely did.

Finally we came to the last leaf of the little gold-plated book.
It did not come before time.
Already a golden dawn was beginning to blaze through the blinds of our study window.

The Twenty-Second Leaf looked like this:

8We walked to our bedroom in a daze, collapsed on the bed, and fell into a fitful sleep.
We dreamed of two rooms the exact reverse of each other.
One was in shadow.
The other was lit.
We awoke around Noon.
We walked into the living room to find the window open and the little golden book gone.
We fell to our knees and sobbed.

On the study desk were our rough copies of the material we had found in the book.

How had she done it?
Where had she been?
And why didn’t she use the door?

The door may be watched, came the answer.

We remembered our dream and walked back into the bedroom.
We opened one of the mirrored doors to our wardrobe.
There on the floor lay a leaf from the little golden book.
Was it ‘the missing leaf’?
If it was, it was not what we were expecting.

The Twenty-Third Leaf:

9On the back was a seal:


Ars Geometrica: A Corn of Wheat…



‘…then a triangle and finally a circle……’
– The ‘Eighteenth’ Leaf.

…This to our mind pretty much makes the earth feminine and the moon masculine which we expect also makes the sun feminine and the star behind the sun masculine. And that is pretty much how the Egyptian’s had it.
We surmise that at this point there maybe at least one missing leaf to the book delineating in much more detail the geometries of earth and moon.
…But what of the sun?


We turned the ‘Eighteenth’ Leaf…


‘…Except a corn of wheat fall into the ground and die it abides alone…’

The ‘Nineteenth’ Leaf


Which we must assume is referring to the sun.

We turned the ‘Nineteenth’ Leaf aware somewhere in the recesses of our overstretched brain that the moon and sun cycles are conjoint in their nineteenth year.


The ‘Twentieth’ Leaf


‘…But if it dies it brings forth much fruit.’


…Which leaf, incidentally, concludes the geometric designs contained in the book.
The ‘Twenty-First’ Leaf introduced a picture of sorts which to us again appeared to echo some of the Egyptian ideas:


Ars Geometrica: Atalanta…



…The ‘Sixteenth’ and ‘Seventeenth’ Leaves.


‘…From a man and a woman make a circle…’

‘…And then a square…’


We thought again of The Officers Of Law who appeared to see the girl as a man?

‘The Spirit as Inner Fire is ‘Agni’ for the Vedic and ‘Hermes’ for the Greek.

The vessel defines the content which is a perception.

Make the vessel transparent in order to ‘see’ clearly.’

Clearly, this sequence of directions related to a famous alchemical engraving. We dashed to our library…


‘The Flight of Atalanta’ by Michael Maier…


‘The squaring of the circle represents a marriage of opposites. It can be accomplished in two ways, by area or perimeter. The circle is a symbol of the eternal element in creation, whilst the square represents solid matter and human works… The largest squared circle in the natural world is the earth and moon. Earth’s mean radius is 3960 miles and the Moon’s is 1080 miles which makes 5040 miles. With a radius of 5040 the circumference of any sublunary circle is 316180 miles, which is the same as the perimeter of any square containing the earth.’

Blimey, they’re all ‘nines’ save the last which is a ‘one’.

We smile, and then consider that it seems to us somewhat incredible that the planetary bodies should possess such accurate geometric proportions by accident.

‘This combination of heaven and earth, or spirit and matter, is a founding pattern in sacred temples from time immemorial the world over.’


Ars Geometrica: Rose of Sharon…



The ‘Fifteenth’ Leaf.


Operation Three:
‘I am the rose of Sharon as the Lily among thorns
so is my love among the daughters.’
– Song of Songs 2:1


In our mind’s eye we saw her:

She was deep in the earth…
…But far deeper than the deepest imaginable depth.

She moved in a Sanctum of Silence hewn from Living, Breathing Stone.
And she was three:
One was Movement and transcribed the geometric figures in air…
One was Heart and recited the formula with utmost precision of tone…
One was Mind and meditated on all that occurred.

A Fourth there was which oversaw each station and which also took her form.

And what a form it was:
A form transfigured by each Atu…

We were again minded of our studies:


A man is tasked with liberating prisoners.
He finds them deluded.
Their history is prison history, their lives are prison lives.
They think and act accordingly.
Instead of hoarding bread they mould it into dominoes and play games with it.
The rats in prison are treated as pets instead of being trained to communicate with the outside world.
Alcohol is drunk in order to produce hallucinations rather than drug the guards…
The prisoners confuse common words…
‘Provisions’ to them means prison-food…
‘Journey’ means walking to and from cell blocks…
‘Escape’ means avoiding punishment…
When their would-be liberator says, ‘we need provisions for our escape to the outside world,’ he sounds like a madman.
To the inmates their prison is the world.
The liberator dies without accomplishing his task.
Those who tried to understand his words turn them into a prison cult and find questions for the next liberator who comes to set them free…
Nonetheless, occasionally there are some prisoners who escape.
– A Sufi Parable

Is that what she was?
Was she an ‘Escapee’?
The Rose of Sharon…

What did it mean?

Ars Geometrica: White World…


We turned the ‘Eleventh’ leaf of the book:


Operation Two:
’… to him that overcomes will I give a white stone, and
in the stone a new name written…’
– Revelation 2:17


…The ‘Twelfth’ Leaf.

Albedo: A White World.

Was it a coincidence?
Twelve Tribes of Israel… Twelve Jewels on the High Priest’s Ephod…
Twelve Disciples of the Christ…
…Twelve Gates into the New Jerusalem.
Twelve Months of the Old Year.

It certainly suggested that thus far the leaves were in fact in the correct order.
Scratch that.
All it really suggested was that the Twelfth leaf was in the correct place.

But why this headlong career though the leaves of the book?
And why did we feel the need to so hastily transcribe its contents?
Something told us it was not ours to keep.


The ‘Thirteenth’ Leaf:


‘…One becomes Two, Two becomes Three…’


In terms of number symbolism alone that really was very clever…

We decided to be audacious;
‘Why are you wanted by The Officers Of Law?’
We did no more than frame the question in our mind.

Silence…Nothing… and then:

‘Because the Dead Letter always seeks to contain the Spirit,
Whilst the Living Word seeks only to set it free.’


The ‘Fourteenth’ Leaf:


‘…And out of the Third comes One as the Fourth…’


…As Indeed was that.

And that is without even considering the geometric forms.
The one here certainly resembles a seed…
…A Diamond seed sown at the heart of conjunction.

Our brain was now again beginning to fire yet simultaneously to tire.

It was all we could do to get the thing down as accurately as we could.
We were onto the Third Operation already…

And finally we saw her…


Ars Geometrica: Ask…


‘…We shall all be changed for this mortal,
must put on immortality.’
– The ‘Eleventh’ Leaf.

…Our respect for the stranger at our door grew.
This little device appeared to effectively marry the elements and directions in a four-fold equilibrium…
And as any aspiring psychoanalyst or psychologist knows the four-fold equilibrium of the psyche represents optimum health for the individual…
…Butterflies as souls.
We thought again of the girl whose book we now perused but who had appeared much too young to know this…
And then her voice rang out clear in our mind.

‘There is a sense in which one is one self:
There is a sense in which one is also every one else.
Such thinking is alien to the personality:
Cultivate it!’

It could have been an auditory hallucination.
We had been studying now long into the early hours.
It certainly made very little sense in conventional terms.
As if to compound our possible insanity we answered her back:
‘We will follow your instruction if you can answer a question.’

Nothing… Silence…and then…
‘Why the Blind Seer?’ we said, thinking ourselves very clever.

‘Not difficult,’ was the response, ‘If one already knows what is to happen one hardly need see it transpire.’

It was a good answer.
It was an exceptionally good answer…


Ars Geometrica: Six…


…The rest of the Night and into the Dawn is something of a blur for us.

One can only take in so much after all.

We continued to turn the leaves of the little book…

Leaf ‘Six’:

Operation One:

‘…O Daughters of Jerusalem,

I am black as the tents of Kedar yet

comely as the curtains of Solomon.’

Song of Songs 1:5


We took in the contents or at least we hoped we did…

The Sun and its Shadow…?

Or, more accurately, the precise relationship between the two.

We did our best to transcribe their contents as faithfully as possible, albeit somewhat crudely considering the exquisite craftmanship of the originals…

Even so it is extremely likely there are mistakes.

Should ‘tents’ and ‘curtains’ have borne capital initial letters?

Each image and phrase played out in a rapture of increasing intensity.

Could the compilers of, ‘The Book’ be complicit in The Work?


Ars Geometrica: Great Work…


…Not that we were going to let that stop us.

The next two leaves of the book can be taken together and it was these entries more than any others perhaps which gave us inkling that the book may be describing a ritual.

Leaves ‘Three’ and ‘Four’:


Certainly one of the things the Alchemists could seemingly never agree upon was the number of actual operations leading to the successful culmination of their art… Three, Five or Seven were the usual candidates but here in this ‘little book’ we had a possible solution to the conundrum and what is more, by giving these operations a spatial direction in the round, as it were, they had also been reduced to a whole.

Where else could the Nigredo commence or the Rubedo finish?

Perfect… Crystalline…Complete.

Our admiration for our unsteady and elusive visitant grew immeasurably…

“…Great Work…” she had whispered before collapse.

Great Work indeed!

…and we had not even considered the ‘Fourth’ Leaf yet…

We recognised immediately the titles of the Atu from our studies yet it had never, and probably never would have, occurred to us that they could be the overseers of the Alchemical Operations.

As a test to the validity of this arrangement one need only consider the following:

The Black Phase is overseen by Atu XXI, the White Phase by Atu IXX!

No wonder she swooned.
It is almost too perfect to bear.

Dare we turn another leaf?
It would be foolish not too…

Leaf ‘Five’:


But that is too much by far…
As a summary of the first four leaves it is exquisite.
It leaves us expressionless…


Ars Geometrica: ABC’s…


‘…The secret of the magic of life consists in using action in order to attain non-action…’
– The Book of Heavenly Consciousness

For the next few hours we were as if transported.
We went nowhere, bodily, yet the vistas contained in that little book.
And yet it was little more and in some respects much less even than a book.
The twenty or so pages held within its gold plated covers were unnumbered and loose leafed and were exquisitely hand drawn, written and coloured on the finest parchment.
There was no way of telling the order in which they were supposed to be read.
Our studies helped with some of it if only to render us a foot-hold.
We recognised a number of the lists and had previously come across broadly similar ideas.
For example it had recently been posited in one of our meetings that some of the Christian Miracles related to geometrical constructs and that the land of Atlantis, as meticulously described by Plato, could also be similarly viewed but to what purpose or to what end?
What we had here, though, was more like an ‘ABC’ of such concepts.

It will be as much as we can do to reproduce as accurately as we may some of its contents.
The ‘First’ Leaf:


Beneath this deceptively simplistic geometrical construction was the following Alchemical Maxim which appeared in the loose leaves of the book as given here below.


Had we realised that ‘over’ is contained in govern? We had not.
You will notice that the maxim is contained in the final shape of the previous plate and also that in order to achieve this shape from their start points the two triangles have to, as it were, traverse the alternative realm, that is, ‘heaven’ must become ‘earth’ and vice versa.

We assume that as there are three statements and also three shapes, they are meant to be related to each other. We may of course be quite wrong in this assumption yet the immediately following leaf of the book appeared to confirm such a proposition giving as it did what can only be regarded as an Alchemical Key to the Work which was couched in broadly similar terms.

The ‘Second’ Leaf:
3. Gold: the result when Art perfects Nature…
2. Art: the state we seek to create…
1. Nature: the state we find ourselves in…

‘Three Sevens…’ We marvelled to ourselves, and then ‘Gold as a Hidden Third.’
But enough already…
Upon reaching this stage in our studies, we found to our surprise that the sun had already set and darkness had descended…


Ars Geometrica: China my China…


‘In its essentials, Indian alchemy is the same as Western, and Chinese alchemy, although set in a completely different spiritual climate, can throw light on both…’
– Titus Burckhardt

… We took up the collapsed form in our arms and carried it up the stairs kicking back open the door to our flat with a precariously lifted foot.
The sofa bed along the far wall of the living room presented an ideal and welcome put down point and as we laid the form to rest, as it were, those delicate lips again parted and let out a soft moan.
Thinking that it would not be long before our unexpected visitant returned to full consciousness we retired to the kitchen in order to make coffee.
Upon our return to the living room some minutes later we found the girl gone!
Nowhere to be found…
Were we dreaming?
In her stead, on our study desk in the corner of the room to one side of the sofa bed, there now lay what we took to be a gold plated cigarette case.
Upon closer inspection the cigarette case proved to be a book… of sorts.

Its title, engraved centrally upon the front leaf of the gold plate looked like this;

On its back leaf, again engraved centrally into the gold plate, was a symbol:

8We just had time to wonder to ourselves how far the vertical ray extended and whether it too eventually culminated in a chalice and if so which way up it was when we heard a loud banging on the front door.
Our immediate thought was that the girl had returned.
As the loud banging continued with more force we knew this not to be the case.
Inserting the ‘Golden Book’ into our top pocket we exited the living room and descended the stairs in a rather more circumspect fashion than some minutes before.
Two tall bulky forms could be discerned through the frosted glass.
We opened the door and were presented with an I.D. card proclaiming the door’s assailants to be Officers of Law.
“We know he’s in here!” said one…
“Been tracking him for days,” said the other.
And together they pushed passed us and swiftly traversed the stairs.
We followed behind them, slowly, thinking, ‘He?’
And then, ‘Him?’
We had barely reached the top of the stairs when one of the Officers charged back out of our flat, barged past us again and disappeared out of the front door at the foot of the stairs.
“…Given us the slip yet again,” he yelled as he went.
Regaining our feet and our composure we re-entered our flat to find the second Officer peering somewhat forlornly out of the now open living room window.
We stood alongside him and peered too; at the tarpaulin roof of the bay window of the flat below and at the drainpipe which ran alongside.
“He could of been out and down and off in two bounds,” said the Officer.
“Sprightly chap was he?” we enquired and then found ourselves pressed firmly against, and halfway up, the living room wall with a judicious arm held tightly over our windpipe.
“Didn’t leave anything did he?” said the Officer in a rather menacing tone and with a most unsavoury glint in his eye.
We shook our head and by the time we had regained our balance back on the ground the first Officer too was gone.
“We’ll be watching you,” he called from the stairs as we pushed the door to and with something approaching relief re-attached the door chain.
We walked back to the window pulled that shut too and then reached for our top pocket…