Greek and Roman artillery pieces had dovetailed slider to which the triggering mechanism was attached. This article describes various ways to make such a slider and the side pieces inside which it moves.
Making a slider with a circular saw Edit
Probably the simplest modern method for making a slider is the one described below. Although it was used to make a Cheiroballistra slider, the process should work equally well for any artillery piece.
Start from a rectangular wooden plank that is a little wider than the top of the stock (or case) of the ballista. Make sure it's as thick as the dovetailed portion of the slider:
Adjust the circular saw to the correct angle. This is probably somewhere around 20 degrees:
The idea is to cut away sides of the plank at an angle. These cut-out pieces will form the female part of the dovetail joint, the slider being the male part. Adjust the width of the cut so that these side pieces are sufficiently wide at the bottom and that the slider is of correct width. It's best to test the process using pieces of scrap wood.
Once you're sure the circular saw is adjusted just right, cut one side of the plank, rotate it and cut the other side. The results should look like this:
After this you can glue in the attach the top part of the slider to the dovetailed, lower part.