This paper deals with the transfer of Arab visual theory in the Middle Ages, as it is believed that the cultural significance of this transfer needs a new emphasis. Mathematical perspective was invented in Florentine Renaissance Art. However, except in the history of science, it is a little known fact that this visual theory was based on the Book of Optics, written by Ibn al Haithan, also known as Alhazen, and was translated, probably in Spain, with the Latin title Perspectiva. We therefore can speak of a double history of perspective, as visual theory and as pictorial theory. The main argument is to identify the importance of images, which separate Arab thought from Western thinking. It was the transformation of mathematics into art, in the Western sense, that allows us to distinguish two different cultures. In this process, the invention of mathematical space by Biagio Pelacani was an important step. Thereafter, the gaze and its looking space became a new concern of the Renaissance.