In geometry, the proof of the compatibility of the axioms can be effected by constructing a suitable field of numbers, such that analogous relations between the numbers of this field correspond to the geometrical axioms.

The transition from philosophy to theology, i.e. to the sphere of faith, is presented by Hamilton under the analogous relation between the mind and the body.

Although the fundamental relation of entailment holds between propositions, we shall use the term to refer to an analogous relation between sentences.

Various other relatively simple properties of the functions are also open, including whether it satisfies the traditional exponential functional equation and analogous relations defined for a general exponential by utilizing its inverse, the Artin-Hasse logarithm.

The linkage to AK-47 and helicopter and their rapid response times with respect to their functions may have an analogous relation to fast-paced rap.

An analogous relation holds for the spin operators.

Spin obeys commutation relations analogous to those of the orbital angular momentum:

And this spirit appears to stand to the soul-centre or original in a relation analogous to that between the point in a joint which moves being moved and the unmoved.

In the modern society of China, institutional, customary and legal reform (a rule of law that embodies universal rules uniformly enforced by a centralised and bureaucratic state) is necessary to govern legal relations; analogous to gesellschaft.

Gerhard Richter's large, partly reflective sheet of glass floated a few inches in front of the wall suggests analogous relations between the mirror, the window and painting.