Rodrigues, Olinde: "Des lois géométriques qui régissent les déplacements d'un système solide...", translation and commentary

Abstract: I provide for the first time in English a line-by-line translation of the entire text of the monumental 1840 memoir of Olinde Rodrigues, "On the geometrical laws governing the motions of a solid system..." published in French in the Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. I accompany the translation with copious notes in italics, in which I explicate some passages whose meaning is obscure in the direct translation, supply detailed proofs, where lacking, of assertions in the original, and clarify the overall organization of the memoir and the relation of its sections to one another.