A full review is provided in this chapter of the mathematical texts Cusanus writes between 1445 and 1459 on the vexata quaestio of the squaring of the circle and of the straightening of the curve: De geometricis transmutationibus, De arithmeticis complementis, De circuli quadratura, Quadratura circuli, De mathematicis complementis, Declaratio rectilineationis curvae, De una recti curvique mensura, Dialogus de circuli quadratura, De caesarea circuli quadratura, De mathematica perfectione, Aurea propositio in mathematicis. Detailed information on their context, genesis, and content is provided for each text.