neusis

Neusis, also known as the method of neusis construction or "inclination," is a geometric construction technique that uses a marked ruler. It was employed by ancient Greek mathematicians, including Archimedes, to solve problems that were impossible with only an unmarked straightedge and compass, such as trisecting an angle.1

The method involves maneuvering a measured length into a specific position to complete a geometric figure. While not strictly adhering to the classical Greek rules of construction, neusis provided a way to tackle complex geometric challenges. It is distinct from the abstract, theoretical approach to geometry that the Greeks, particularly through Euclid's Elements, largely championed.123