concoquo is a latin word meaning something literal like cook together. it comes from cum+coquo. we get our english word cook from coquo, which could have either come directly through vulgar latin during the roman occupation of england or via a dialect of anglo-norman (french). the cum prefix gets assimilated to con- which gives us the form concoct we see today from the perfect passive participle concoctus. in a more metaphorical sense it means to consider well.