Hippocrates of Chios

Born              :  ca 470

Died              : 410 BC

Country         : Greece

Hippocrates (no known relation to Hippocrates of Cos, the famous physician) wrote his own Elements more than a century before Euclid. Only fragments survive but it apparently used axiomatic-based proofs similar to Euclid's and contains many of the same theorems. Hippocrates is said to have invented the reductio ad absurdem proof method. Hippocrates is most famous for his work on the three ancient geometric quandaries: his work on cube-doubling (the Delian Problem) laid the groundwork for successful efforts by Archytas and others; his circle quadrature was of course ultimately unsuccessful but he did prove ingenious theorems about "lunes" (certain circle fragments); and some claim Hippocrates was first to trisect the general angle. Hippocrates also did work in algebra and rudimentary analysis.

(Doubling the cube and angle trisection are often called "impossible," but they are impossible only when restricted to compass and unmarkable straightedge. There are ingenious solutions available with other tools. Construction of the regular heptagon is an
other such task, with solutions published by four of the men on this List.)