The treatise on conic sections by the Hellenistic mathematician Apollonius from Perga is regarded as a supreme achievement of Greek mathematics and maintained its authority right up to the 18th century. This new edition is the first to consider all Greek and Arabic sources, with the Arabic texts being presented in the first ever critical edition. Both versions of the text are accompanied by a French translation, an extensive mathematical commentary, numerous philological notes and a complete glossary. The four volumes of the edition are intended to be completed in 2009.