[ gdw]
The editor of Marie Fresne suggests the sense ‘divisé, ramifié en quatre’ (glossary, p. 312). However, the sense ‘divide into four’ is not attested by any of the other dictionaries, and the verb always seems to have referred to the action of making square, i.e. of providing with four sides or angles.
For the p.p. used as a., see the article quarré.