associre

Associre is an obsolete term used in the history of mathematics, particularly in the context of Euclid's Elements. In this context, associre referred to a geometric method used by Euclid to demonstrate the possibility of constructing a regular polygon by associating a given point with a series of smaller polygons.

The method of associre is described in the 14th book of Euclid's Elements, where it is applied to the construction of a hexagon. In this construction, Euclid uses a series of smaller hexagons to show how a given point can be associated with a regular hexagon. The method relies on geometric invariants and proportional relationships between the sides of the polygons.

The term associre is derived from the Latin words "associo," meaning "to associate," and "motus," referring to the movement or operation involved in the method. This term was likely used to describe the associative process of linking a given point to smaller polygons in order to construct a regular polygon.

While the method of associre is an important historical contribution to the field of geometry, its applicability has largely been surpassed by more advanced mathematical techniques. Nevertheless, the concept of associre continues to be studied by historians and mathematicians interested in the development of mathematical thought and methodology.

The term "associre" has largely fallen out of use in modern mathematical notation and has been replaced by more descriptive terms. However, its historical significance remains, providing insight into the evolution of geometric thought and the methods used by Euclid in his influential work, the Elements.