The modern mathematician finds the space of three dimensions, in which our visible universe is containled, entirely too contracted for his conceptions, and is obliged to imagine a space of “n” dimensions in order that his fancy may find room to disport itself. But it is a new idea, on the part of the novelist, to make the conceptions of transcendental geometry the basis for an amusing story.

The very short article goes on to compare “Flatland” with “Through the Looking Glass” and their use of geometry as speculative and imaginative.

In trying to find more about this term, it appears that sadly the intelligent design crowd has laid claim to it.  The most I could find (in an admittedly short search) was this related Wikipedia article on “Complex Geometry“:

In mathematics, complex geometry is the study of complex manifolds and functions of many complex variables. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric chapters of complex analysis.