The methods of solution presented here are likely to seem strange to a modern reader. We have several involving motion, two involving the use of conic sections (which themselves ultimately derive from motion, since they derive from a cone), and several that involve motion in a way that has a *mechanical* feeling, suggesting their adaptability to practical computation. A reader who has previously studied Greek mathematics may have come across the term *neusis* to describe a particular type of solution to various problems. In the usual sense, *neusis* involves finding a line from a given point, so that the segment cut off by two given lines is equal to a given segment. The two lines could be either straight or curved.

For example, in the following figure, we have two curved lines, and a given point A. We seek the particular configuration where the segment between the two curves is equal to some given length. There is a bit of a Goldilocks feel here: some segments, like BC, are too large; others, like DE, are too small; but one, say FG, is *just right*.

Above: The general setup of a *neusis* construction.

The point G is movable.

The reader will note however that the methods below do not precisely fit this mold. For this reason, the term *neusis*-like (coined by Fried and Unguru, in [6]), seems an apt choice. Nicomedes’ solution, for example, is built around a curve that is defined in such a way that *all* the segments between it and a straight line are equal to some given segment. Hence using the curve so generated (which Nicomedes calls a *conchoid line*) in the usual method of *neusis* would not be particularly illuminating on its own. But the method of *generating* it was clearly inspired by the method of *neusis*; thus, Fried and Unguru’s term *neusis*-like.