x_{1} (line segment) is a neuein/neusis line segment (line element) constructed from directrix x_{2} (curve; not necessarily linear) to catchline x_{3} (curve; not necessarily linear, despite the name) which is inclined toward pole x_{4} (point) such that it has diastema (length) x_{5} (li; nonnegative extended-real number).

Not necessarily unique (specify another point through which it must pass if you wish to make it so, for example). Even better (lower) bounds can be given for the diastema x_{5}. The differences between x_{1} and x_{5} is the same as the difference between a radius (line segment) and the length of the radius (which is a nonnegative extended-real number). This is not a method of geometric construction, but a tool/means/geometric entity which is used in such constructions.