Use of The Neusis
Neuseis have been important because they sometimes provide a means to solve geometric problems that are not solvable by means of compass and straightedge alone. Examples are the trisection of any angle in three equal parts, or the construction of a regular heptagon or tridecagon. Mathematicians such as Archimedes of Syracuse (287–212 BC) freely used neuseis. Nevertheless, gradually the technique dropped out of use.
Read more about this topic: Neusis Construction