The Greeks were known to have extensive knowledge of geometry, producing many great geometers. With this and other contributions in mathematics, the Greeks profoundly changed the approach and character of the entire mathematical field. It is thought that Thales of Miletus (c. 625-c. 550 B.C.E.; Ionian) first introduced geometry to the Greeks. As a merchant traveler, he was exposed to the Babylonian concept of measurement, from which practices sprang geometry. Thales used his geometric knowledge to solve problems such as the height of the pyramids and the distance of ships from the shoreline.

Greek geometer Hippocrates of Chios (470-410 B.C.E.) was one of the first to present an axiomatic approach to geometry, as well as the first to work on the elements almost a century before Euclid (see below). Hippocrates may have worked on geometry and such problems as squaring the circle, but he lacked common sense and was duped by many people.

Zeno of Elea (c. 490-c. 425 B.C.E.) raised questions about lines, points, and numbers—all part of geometry—with his many paradoxes (for more information about Zeno and his paradoxes, see “Foundations of Mathematics”). Another important figure is Eudoxus of Cnidus (408-355 B.C.E.), who worked on geometric proportions and theories for determining areas and volumes.

Others followed these geometers, including Archimedes (c. 287-212 B.C.E.; Hellenic), who worked on mechanics and took the first steps toward integral calculus. Apollonius of Perga (262-190 B.C.E.), or the “great geometer,” first named and presented theories on conic sections in his book Conics, and he introduced the terms “parabola,” “ellipse,” and “hyperbola.” There was also Pappus of Alexandria (290–350), who presented the basis for modern projective geometry (the geometry that deals with incidences, or whether elements such as lines, planes, and points coincide or not).