 In his Supplement of geometry (1593), François Viète also addresses the outstanding problems of geometry that were solvable by curves that could not constructed by straightedge and compass. He claims that at least some such problems could be solved by properly geometrically means by adopting as his postulate that the so-called neusis problem could be solved. That is, he assumed that given two lines, a point \(O\), and a segment \(a\), it was possible to draw a straight line through \(O\) intersecting the two lines in points \(A\) and \(B\) such that \(AB = a\) (Bos 2001, 167–168). In the Supplement, Viète shows that once we accept as a fundamental geometrical postulate that the neusis problem is solvable, then we can, by legitimately geometrical means, solve the problems of trisecting a given angle and of constructing the two mean proportional between two given line segments. Specifically and importantly, we generate these solutions without having to rely on the construction of conics or higher-order curves, such as the spiral or quadratrix (Bos 2001, 168).