autograph:  Greek auto- was a prefixal use of the adjective autós, meaning ‘same, self’. Many of the commonest auto- words in English, including autograph itself and also autocrat , automatic  (a derivative of automaton , which was formed from a hypothetical base *men- ‘think’ related to mental and mind), autonomy , and autopsy  (originally meaning ‘eye-witness’, and derived from Greek optós ‘seen’, source of English optic), are original Greek formations.
But the 19th and particularly the 20th century have seen a mass of new coinages, notably in scientific and technical terminology, including such familiar words as autism, autobiography, autoerotic, autofocus, autogiro, autoimmune, automotive, autosuggestion, and of course automobile (originally a French formation of the 1870s). Automobile has itself, of course, given rise to a completely new use for the auto- prefix, with the general connotation of ‘motorized transport’, as in autobus, autocar, autocycle, and the German autobahn.
"a person's signature," 1791, from Latin autographum, from Greek autographon, neuter of autographos "written with one's own hand," from autos- "self" (see auto-) + graphein "to write" (originally "to scratch;" see -graphy). Used earlier (1640s) to mean "author's own manuscript."