Firstly a good call by Niel A on the 0.25" CP form.
Circular Pitch isn't used much nowadays and even when it was it was usually used on linear movement.
DP always has Pi somewhere in the calculations but CP is a fixed linear move.
Ideally racks on machine tools should be in CP as then the hand wheels will relate to proper numbers. a 16 tooth pinion in 0.25" CP will move exactly 4" per rev.
Anyway to get back to the original problem. If James wants to make a cutter using the method outlined in the Gears and Gear cutting book then the following diagram should help.

The red which is hard to see as the green overlays it is one tooth of a 37T gear @14.5 PA and 0.25" CP or 12.5664DP the circle on the left is how the size was drawn using two chords on the curve to find the centre and mirrored to the other side.
So James wants two buttons at 0.700" diameter, spaced at 0.799" apart and a blank cutter of 0.250" wide.
Once the buttons come into contact with the edges of the blank he needs to infeed 0.224" to form the shap but when cutting the gear he only needs to infeed the cutter 0.175" deep.
This is a slightly different way to how Ivan Law does it in the gears book. He touches the OD of the buttons on the face of the blank and then moves across, then feeds in.
The method above is the one devised by Grant in Victorian times and resurrected by Unwin in the 1980's.