Etymology

The word quadrature comes from the latin word, quadrare which means "make square-shaped".

Mathematical Quadrature

In mathematics, integration by quadrature may refer to either

• the quadrature of the circle, a subject of geometry, deemed impossible or
• the symbolic evaluation of a definite integral, but more commonly refers to the numerical approximation of an integral, i.e. a synonym of numerical integration.

Telecommunications Concept of Quadrature

In telecommunications, the term quadrature has the following meanings:

1. The state of being separated in phase by 90° (π/2 radians).

2. Pertaining to the phase relationship between two periodic quantities varying with the same period, that is, with the same frequency or repetition rate, when the phase difference between them is one-quarter of their period.

Source: from Federal Standard 1037C and from MIL-STD-188