Neusis construction
In geometry, the neusis (νεῦσις; from Ancient Greek νεύειν (neuein) 'incline towards'; plural: νεύσεις, neuseis) is a geometric construction method that was used in antiquity by Greek mathematicians. == Geometric construction == The neusis construction consists of fitting a straight line element of given length (a) in between two given (not necessarily straight) lines (l and m), in such a way that the extension of the line element passes through a given point P. That is, one end of the line element has to lie on l and the other end on m while the line element is "inclined" towards P. Point P is called the pole of the neusis, line l the directrix, or guiding line, and line m the catch line.