The Treatise "On teh Section of a Cylinder" of Serenus of Antinoeia and the Apollonian Tradition

We approach three aspects of the works of Serenus of Antinoeia: the historical, the mathematical and the logical. The comparisons between the treatise “On the Section of a Cylinder of Serenus of Antinoeia” and the treatises “The Mathematical Collection” of Pappus, “Commentary on the Conics” and “Commentary on the Sphere and the Cylinder” of Eutocius, “The Conics” of Apollonios, “The Elements”, “Phenomena” and “Optics” of Euclid and “On Spheroids and Conoids” and “On the Sphere and the Cylinder” of Archimedes permit us to conclude the membership of the propositions 1 to 28 of his treatise to the Apollonian tradition. We examine, also, the transmission of the treatise in the Byzantine and the Arabic scientific circles.