We present an approach for solving proportional analogies of the form A : B :: C : D where a plausible outcome for D is computed. The core of the approach is E–Generalization. The generalization method is based on the extraction of the greatest common structure of the terms A, B and C and yields a mapping to compute every possible value for D with respect to some equational theory. This approach to analogical reasoning is formally sound and powerful and at the same time models crucial aspects of human reasoning, that is the guidance of mapping by shared roles and the use of re-representations based on a background theory. The focus of the paper is on the presentation of the approach. It is illustrated by an application for the letter string domain.