In the fourth book, the inverse propositions of certain propositions from the third book are examined and proven using the method of reductio ad absurdum. Also examined are the points of intersection of conic sections with each other or with the circumference of a circle. The fifth book, which is preserved in Arabic, deals with the topic of "minima" and "maxima", that is, with the maximum and minimum lines that one can draw towards the perimeter of conic sections from various points either on the axis or between the axis and the intersection or outside the intersection.