Early history of geometric probability and stereology

Abstract

This paper provides an account of the history of geometric probability and stereology from the time of Newton to the early 20 th century. It depicts the development of two parallel paths. On the one hand, the theory of geometric probability was formed with minor attention paid to applications other than those concerning spatial chance games. On the other hand, practical rules for the estimation of area or volume fraction and other characteristics, easily deducible from the geometric probability theory, were proposed without knowledge of this branch. Special attention is paid to the paper of J.-É. Barbier, published in 1860, which contained the fundamental stereological formulas, but remained almost unnoticed by both mathematicians and practitioners.