L’analogie et la symétrie

The design of temples depends on symmetry, the rules of which architects should be most careful to observe. Symmetry arises from proportion, which the Greeks call "analogia". Proportion is a due adjustment of the size of the different parts to each other and to the whole; on this proper adjustment symmetry depends. Hence no building can be said to be well designed which wants symmetry and proportion. In truth they are as necessary to the beauty of a building as to that of a well formed human figure.

Vitruvius, On Architecture, Book III

Two examples of portrayals of symmetry linked to the notion of measurement
(after di Giorgio Martini and Martin)

The violin family offers many examples of constructions where analogy and symmetry are unambiguously related to proportionality. Could the violin outline shed light on the hitherto obscure definitions of the two design principles inherited from the Greek and Roman era called analogia and symmetria?

Drawing on Euclid's definitions, the Traité de Lutherie puts forward new and unusual mathematical keys which explain how these concepts of proportion may be put into practice.