Galileo proves and uses in the De motu locali the theorem that the trajectory of a horizontal shot describes a semi-parabola downwards. Despite being unable to prove that oblique projection of a body would result in a complete parabolic trajectory (See Damerow et al. 1992 Galileo held the assumption that the trajectory is symmetric, that is, he implicitly assumed that the obliquely projected body runs upward through the same semi-parabola as the corresponding horizontal shot in inverse direction (see folio 106v and 3/07-th-04-cor).