means properly “to knock down.” (French, abattre, whence a battue, i.e., wholesale destruction of game; O.E. a beátan.)
Abate, in horsemanship, is to perform well the downward motion. A horse is said to abate when, working upon curvets, he puts or beats down both his hind legs to the ground at once, and keeps exact time.
Abatement in heraldry, is a mark of dishonour annexed to coat armour, whereby the honour of it is abated.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Abate from Infoplease: