lune of Hippocrates

Nevertheless, for some figures (for example a lune of Hippocrates) a quadrature can be performed.

The quadrature of the lune of Hippocrates is the special case of this result for an isosceles right triangle.

See Lune of Hippocrates.

In this fragment the area is calculated of some so-called Hippocratic lunes - see Lune of Hippocrates.

Hippocrates of Chios squared certain lunes, in the hope that it would lead to a solution - see Lune of Hippocrates.

For example, a quadrature of the circle, Lune of Hippocrates, The Quadrature of the Parabola.

In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.

All such lunes can be specified by the two angles formed by the inner and outer arcs on their respective circles; in this notation, for instance, the lune of Hippocrates would have the inner and outer angles (90 ,180 ).

Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.