Tangent to a parabola by Archimedes (~250BCE)
Complete
Proposition: If from a point …1… on a parabola a straight line…2.. be drawn which parallel or equal to the axis, and if the segment …3.. is a chord parallel to the tangent to the parabola at ..1.. and meeting …2.. in M, then …4…
Conversely, if …4… , then the chord …3.. will be parallel to the tangent at …1…