The Counter-Earth is a hypothetical body of the Solar system first hypothesized by the presocratic philosopher Philolaus

Philolaus

Philolaus was a Greek Pythagorean and Presocratic philosopher. He argued that all matter is composed of limiting and limitless things, and that the universe is determined by numbers. He is credited with originating the theory that the earth was not the center of the universe.-Life:Philolaus is...

 to support his non-geocentric cosmology

Cosmology

Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

, in which all objects in the universe revolve around a Central Fire. The Greek word "Antichthon" means "Counter-Earth."
By 500 BC most contemporary philosophers considered the Earth to be spherical — there was obvious evidence for this from the behavior of objects near the horizon.