Cavalieri was a mathematician that was trying to solve a number of problems involving volumes and areas. He never did any work that is employed in stereology unless you want to consider crediting him with an initial attempt at calculus. Like many other contemporaries such as Galileo and Roberval he was attempting to come up with a theory of infinitesimals. He and others understood that there were problems with their approaches.

Buffon solved a number of problems involving geometry and probability. Unlike previously solved probability problems his work involved continuous values. Cards, dice, and coin flips are discrete events with a countable number of outcomes such as 6 outcomes for the roll of a die.

Neither Cavalieri or Buffon applied their work to areas considered in stereology. Later mathematicians saw how these ideas could be applied. Steinhaus and Tomkeieff and others extended the ideas.

Delesse and Rosiwal produced ideas but the implementations were onerous. They did not prove, but were pretty sure their ideas worked. Most of the rest of the geological community was skeptical.

It would take the Shand recorder to provide the first usable instance of a stereological procedure. You might say that Shand’s device marks the start of actual stereological research. With his device comes the first published works using what are recognized today as stereological methods.