Defined in more basic fencing terms, a riposte is any counterattack made after a defensive maneuver, be it a thrust, slash, whatever.
For example: you are fencing foil. Your opponent lunges. You parry, and quickly thrust at his torso. Your attack would be categorized as a riposte.
The riposte is sometimes called "the echo of the parry" because, like an echo to an actual sound, the two are linked so finely they cannot be separated.  Too, like an echo, the riposte springs instantly from its source.

The riposte is a counterattack launched after a successful parry has been made.  It is, in fact, the most common form of counterattack.  But it is a counterattack that forbids, generally speaking, the use of the lunge.  This is due to the fact that your opponent has already atacked, has lunged himself and is close enough to be hit without generating another such move.

According to the conventions of the foil, once a defending fencer has performed a parry that has deflected an attacker's blade away from his valid target area, he is granted the right-of-way that the attacker initially possessed.  He may then consequently attempt his own offensive, or more precisely, counteroffensive action--the riposte.

But, as has already been mentioned, the riposte, to be legitimate, must be delivered immediately after the parry, without hesitation.  Any pause may end up nullifying your priority in the exchange taking place.

From The Art and Science of Fencing, by Nick Evangelista

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