Serenus of Antinoöpolis (Ancient Greek:Σερῆνος; c. 300 – c. 360 AD) was aGreek mathematician from theLate AntiqueThebaid inRoman Egypt.
Serenus came either fromAntinoeia or fromAntinoöpolis, a city inEgypt founded byHadrian on top of an older settlement. Two sources confirm that he was born in Antinoöpolis. It was once believed that he was born inAntissa, but this has been shown to have been based on an error.
Serenus wrote a commentary on theConics ofApollonius, which is now lost. We hear fromTheon of Alexandria that the main result of the commentary was that of a number of angles that are subtended at a point on a diameter of a circle that is not the center, then with equal arcs of that circle, the angle nearer to the center is always less than the angle farther away from the center.[1] But he was also a prime mathematician in his own right, having written two works entitledOn the Section of a Cylinder andOn the Section of a Cone, works that came to be connected to Apollonius'Conics. This connection helped them to survive through the ages.
In the preface ofOn the Section of a Cylinder, Serenus states that his motivation for writing this work, as summarized by Heath, was that "many persons who were students of geometry were under the erroneous that the oblique section of a cylinder was different from the oblique section of a cone known as an ellipse, whereas it is of course the same curve."[1] The work consists of thirty-three propositions.
In propositions one though fifty-seven ofOn the Section of a Cone, Serenus deals largely with the areas of triangular sections of right and scalene cones that are created by planes passing through the vertex. He shows when the area of a triangle of a certain class of triangles is at its maximum. Propositions fifty-eight through sixty-nine form a separate section of the book and deal with the volumes of right cones in relation to their heights, their bases and the areas of triangular sections through the axis.
