Not a slide rule, but an old style "flight computer"
Your post inspire me to look on eBay where I found a Concise Circular sliderule that I bought. Concise still has a website and still sells circulars. This one is a model 300 with a 4” diameter which makes it have the roughly same resolution as a 12” stick sliderule.
There are two kinds of circulars that I have found. The first a Post uses two connected cursors. Place one on the index’s point of the scale and the other on the number then use them together preserving the angle to find the second number and at the other end you’ll find the answer.
The concise uses two rotating discs where you move one the smaller disk index point to the first number and then line the cursor on the second number on the smaller disk and read the answer on the larger disk under the cursor.