What is a space quadrum?
Quadrum refers to square (most of the time), and thus I would assume that a space quadrum would refer to a certain area of space with specific specifications.
For instance, an area which is 1km wide and long. If you were to break the space around Earth into quadrums you'd be able to name each one and simply refer to a specific quadrum if you'd like to pin-point something.
I'm thumb-sucking here so I could be wrong.