Space and structure are one of the main tool of architecture. Their relationship is not only simple and clear. It depends on different approaches.
Author mentioned that “structure tends to its own geometries.” I think it means that architects use the geometry on the structure for the space’s proportion. Either it is a religious structure or it is a house. Ideal geometry is that suitable geometry for the structure and space. For example, an example in a text, a structure has a performance area which has a regular grid of columns to support the roof. But these columns obstructed everyone’s view of the floor. It is one of the fraught thing that the relation between the space and structure’s ideal geomerty.