they soon returned to paris and cauchy's father was active in the education of young augustin-louis. laplace and lagrange were visitors at the cauchy family home and lagrange in particular seems to have taken an interest in young cauchy's mathematical education.

How would the previous sentence be correctly capitalized?
They soon returned to Paris and Cauchy's father was active in the education of young Augustin-Louis. Laplace and Lagrange were visitors at the Cauchy family home and Lagrange in particular seems to have taken an interest in young Cauchy's mathematical education.