  This is a translation of Proceedings of 22 th Symposium on History of
Mathematics, Tsuda University 2011, on the work of Benjamin Olinde Rodrigues
and on his life. His chef-d'oeuvre is the work on Euclidean motion group in
1840. He invented Rodrigues expression of rotation and give explicit
calculation formula for product of two rotations, which might be considered as
a discovery of quaternion product rule ahead of Hamilton. We follow a new proof
of E. Cartan in his book on spineurs in 1938 for Rodrigues formula, which was
called as Euler-Olind-Rodrigues formula mistakenly. We add as Appendix
important parts of Lecture Note on applications of quaternion. Description of
rotation in Rodrigues expression and an interesting compact formula for time
derivative of rotation, applicable in many purposes.
