Neusis construction

In geometry, a neusis is a construction method used by the mathematicians of ancient Greece in which a line segment of a given length is positioned between two given curves so that, when extended, it passes through a specified point. Prominent mathematicians including Archimedes, Pappus of Alexandria, and much later Isaac Newton used neusis constructions in their work. The method can accomplish tasks that compass and straightedge construction alone cannot, such as trisecting an angle or doubling the cube, though it cannot square the circle, since neusis constructions produce only algebraic ratios rather than the transcendental values that task requires. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/