Apollonius of Perga developed a systematic theory of conic sections. His surviving Conics studies the geometry of the ellipse, parabola and hyperbola, including their tangents and diameter relations.[ref]
Treatise on Conic Sections by Apollonius of Perga (Heath edition). Primary Conics text, Book I; edition introduction distinguishes the ancient work from modern notation
A single construction—cutting a cone by a plane—produces these different families of curves. Apollonius's work organizes their properties through geometric relations rather than modern Cartesian equations. Translating between those viewpoints helps explain why an equation such as describes a parabola without attributing coordinate notation to the ancient author.
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Apollonius of Perga (circa 262 – circa 190 BCE) was a Greek mathematician and astronomer, known primarily for his work in geometry. He is often referred to as "The Great Geometer" for his significant contributions to the field, particularly in the study of conic sections.