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Francois Ziegler
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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 stereologyEarly history of geometric probability and stereology.'' Image Anal. Stereol. 31, (2012), no. 1, 1--16. See this link.

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.

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.

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Mikhail Katz
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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.