I will have a go at a detailed technical answer for you (but it will probably make things worse

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I'm trying to get this thing down, as a first step to (hopefully) other things, and something has already stumped me. I'm studying from DuQuette's "Magick of Thelema" and he says that when drawing the pentagrams invocation is towards the element, while banishment is away from it, and that the directions are those familiar to me already (earth lower left, fire lower right, etc.).
Well, firstly banishing and invoking other elements is not part of the LBRP. If you want to work with that ritual first it is banishing earth ... and that is it, on all quarters.
Liber O is obscure on this point but not many address it; first we have (in Liber O) a description of some movements then a header GBRP then some pentagram with arrows and virtually no descriptive texts ... It is assumed one puts it together from what is written earlier in Liber O ?
In any case I agree with the first basic DuQuette says - it makes basic sense; away : banish, towards : invoke. But he is being careful with wording; yes that is right ... for an element (but is spirit an element? If we don't mention it there is no problem

also if we just say away from and towards it there is no problem ... until we add 'away from and towards wha't and/or 'to but from where'? Okay lets just comment on the things simply in a book and everyone will assume it is correct ... until they try it out? YOU my dear sir have all the makings of a magical trouble maker !!!

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Thinking myself clever, I tried drawing them in my notebook, and I got it right as far as towards and away is concerned, but not the directions from which this is done.
Unclear what you mean with 'the directions from which it is done'? Do you mean because any point has two lines coming from it, which line does one take?
This may be a silly question, but is the "rule" to invoke from above and banish from below?
Unclear again ; above, below? ... do you mean to invoke draw the line from a point that is a in a higher position in the pentagram? or is that a general statement. Sorry I found some wording confusing ... it could be me ... 'fuzzy' today.
I drew Earth being invoked from Water, which I see by the diagram is wrong.
So; why did you do that ... a variation, a mistake ... ?
Earth is invoked from Spirit, above, and is properly sent back there. Is that how it goes?
Yes, I see it that way.
If so, can Water be invoked from Air? And Air invoked from Water? Why? How?
Because that is the way it is in the book

. How does one's 'magical view of the Universe' justify it? Mine does by seeing air as the 'Mercurius' of water and fire ... if we mix them we get steam (or various gasses) which is of the nature of air, therefore water comes from air ... as does fire; water and fire make air so air contains water and fire; 0=2 therefore 2=0.
But that is just my take on it. One could invoke an element from spirit, to fire to water to air to earth but ... that doesn't work in order on the pentagram. The 'rule' seems to be (when one looks at the pentagram elemental attributions and the diagrams in Liber O) invoke from spirit and banish back there ... but one cant do that on the horizontal air / water line can one?)
But look at the invoking and banishing spirit active and passive ... what's the reason behind that??? Where is it written about ... anywhere?
I have my own way of working that, but one doesn't usually invoke or banish spirit IME. One usually works with the 4 elements.
Often we find discrepancies like these, also not explained or not written about ... I wonder why that is??? As you have found out, if you ACTUALLY start WORKING with the rituals things pop up (e.g. but if my double cube altar IS that ratio size and the Tau is formed from that ratio then I cant fit it in my circle ) I often wonder if the commentators in book ('experts') have actually DONE the rituals?
I am sure DuQuette has ... but he skips over the problems.
Hope my comments helped. Perhaps someone else has a view on this active / passive spirit pentagram drawing? The only thing I can come up with is that the top 'spirit point' of the pentagram is used in the fire and earth invoking and banishing and if one tried to use that for spirit they might invoke or banish earth or fire ??? Maybe makes sense as invoking active or passive spirit is rare?
Then one is left as an alternative: invoke active spirit by first drawing from spirit to fire and passive from spirit to earth? But then one is left with invoking earth from water

(Which is why maybe you did it that way in the first place? Did you come to that conclusion or fluke it?

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Personally I prefer to reassign the elements to other points ... but we better not go there!
