There is a nice recent article about Cauchy's contribution to integral geometry which is probably what you mean by Cauchy's Crofton formula:

Hyksova, M.; Kalousova, A.; Saxl, I. ``Early history of geometric probability and stereology.'' Image Anal. Stereol. 31, (2012), no. 1, 1--16. See [this link](http://go.galegroup.com/ps/i.do?id=GALE%7CA331004426&sid=googleScholar&v=2.1&it=r&linkaccess=fulltext&issn=15803139&p=AONE&sw=w&authCount=1&u=barilan&selfRedirect=true).