In his paper "On the Need to Rewrite the History of Greek Mathematics" Sabetai Unguru severely criticizes the views of Tannery, Zeuthen, Neugebauer and myself on the "Geometrical Algebra" of the Greeks. Unguru summarizes our position in one sentence: "Greek "geometric algebra' is nothing but "Babylonian algebra' in geometrical attire", and he starts to prove that this position is historically unacceptable. Unguru states his objections very clearly. The object of the present paper is to defend our position against this emphatic attack.