- Wilbur R. Knorr
- and Reviel Netz
In geometry he was first to show that the cube duplication is equivalent to finding two mean proportionals between lines in the given ratio. He also constructed rectilinear figures equal to three forms of ‘lunules’ (mēniskoi), figures bounded by two circular arcs, alone or in combination with a circle (a problem related to the quadrature of the circle). A long fragment from *Eudemus on these quadratures is reported by Simplicius (in Phys. 1. 2, ed. Diels, 60–9). According to Proclus, Hippocrates was first to compile an ‘Elements’ of geometry, which would appear to have anticipated substantial parts of *Euclid's books 1, 3, and 6. In *astronomy, Hippocrates was known for a theory of comets, reported by Aristotle (Mete. 1. 6).