ABSTRACT
Algebraic geometry came to light as a proper chapter of mathematics when al-Khayyam gave himself the theoretical means of a two-fold translation: to reduce geometrical problems notably solids and super solids, to algebraic equations, and to solve the latter by the intersection of conic curves. Some mathematicians notably Kamal al-Din ibn Yunus, Athir al-Din al-Abhari, etc., and also members of the school of Isfahan in the 19th century followed the tradition of al-Khayyam and al-Tusi. This chapter includes the Ad locos planos et solidos isagoge. The author of the obituary tells us that it is an analytical work written independently of Descartes's Geometrie. Fermat's starting point is not the theory of algebraic equations, but research on geometrical loci. In the Mathematical Collection, Pappus reproduces certain propositions from this lost book of Apollonius. The propositions treat pointwise transformations, an effective tool in the research on loci. But this research on pointwise transformations is new in relation to Hellenistic geometry.
