Understanding Agrippa's Scale of Four.
Agrippa's scale of four is a simplified scheme of Great Chain of Being.
It starts off with Original World. This is the world the First Mover aka God.
It then moves into the Intellectual World. The Intellectual World is the world of Angelic beings.
Flowing from there we enter the Celestial World, the home of the celestial bodies which imparts the virtue upon the Elemental World below. Not all neoplatonists separate the celestial and intellectual worlds, but Agrippa does. Below the Elemental world comes the Infernal world, home of the evil and destructive demons(though that doesn't mean they can't be put to good use).
Now currently there is some discussion in the blogosphere about whether or not the demons are in a sense elemental spirits, as RO puts it here: http://headforred.blogspot.com/2013/04/demonic-agendas.html
But this theory does not fit in with Agrippa's scheme, the grimoires of the renaissance, nor the Elizabethan world view.
Let's go back to Agrippa's Scale of Four for illustration.
The argument that the demons/infernals must be elemental in nature because Agrippa lists "Four Princes of Devils, offensive in the elements", doesn't hold much water.
Because if you notice, (in Agrippa Book II, Scale of Four) you will see that the "Rulers of the Elements" also appear in the intellectual world. Does that mean that the angels of the intellectual world are elementals? Absolutely not.
Notice also that the Intellectual World and the Infernal World are opposite reflections of each other. For instance:
In the Intellectual world you first have the Four Angels ruling over the four corners of the world, then you have the Four Angelic rulers of the Elements.
In the Infernal World you have the four princes(which also means ruler) offensive in the elements, followed by the four princes ruling over the four angles of the world.
See how they are inverse reflections?
What that tells us is that the Demons/Infernals are not elementals any more than Angels are, only that the elements have roots in both directions from the elementary world, a world in which Agrippa refers to as where the law of generation and corruption is.
So the Elemental world being a middle ground between the Angelic and the Infernal makes much more sense for terrestrial being of mixed nature, the kind mentioned in the the Theurgia-Goetia of the Lemegeton.