The first chapter is devoted to illustrate and comment upon the geometrical results belonging to the classical Greek world which present a projective character, or have, in later centuries, prepared for the rising of Projective geometry. So, in Sect. 1.1 we start with the basic theorems from Euclid’s Optics, which in the Renaissance constituted the departing point for the development of mathematical perspective. In the subsequent section, particular attention is given to Apollonius’s treatment of conic sections, as in the first four books of his Conics; and specifically to his theory of diameters and harmonic division property of secants and tangents, which led him to have a first idea of polarity: a concept which only resurfaced in Desargues’s work in the 1630s. The third section is essentially dedicated to the theorem of Menelaus, expressing the condition for three points to be collinear, which was a powerful tool in Desargues’s hands (and later in Carnot’s), and, together with his projection method, allowed him to develop a new approach to the theory of conics. In the final section of the chapter, some propositions of projective character are illustrated which appear in Pappus’s Collection; as for instance the theorem, today bearing his name, which is a particular case of the famous Pascal’s hexagon theorem; and certain Porisms which, since the early eighteenth century, had a part in the rising of Projective Geometry.