Influences

Fermat had many influences such as Apollonius, who wrote Conics, which introduced terms such as parabola and hyperbola, and Beaugrand, who published books on geostatics and mathematics.

Apollonius

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Apollonius of Perga was known as 'The Great Geometer'. Little is known of his life but his works have had a very great influence on the development of mathematics, in particular his famous book Conics introduced terms which are familiar to us today such as parabola, ellipse, and hyperbola.
In his day, Apollonius was a popular name, so you shouldn't confuse The Apollonius of Perga with a different one.The only other pieces of information about Apollonius's life is to be found in the writings of the various books of Conics. We learn that he had a son, also called Apollonius, and in fact his son took the second edition of book two of Conics from Alexandria to Eudemus in Pergamum. We also learn from the preface to this book that Apollonius introduced the geometer Philonides to Eudemus while they were at Ephesus. Apollonius was also an important founder of Greek mathematical astronomy, which used geometrical models to explain planetary theory.

Beaugrand

Jean Beaugrand was, it is believed, the son of Jean Beaugrand who was an author of the works La paecilographie and Escritures and the calligraphy teacher to Louis XIII who was king of France from 1610 to 1643. Very little is known about the life of Jean Beaugrand, we don't even have a picture of him to show, but what we do know has been pieced together from references to him in the correspondence of Descartes, Fermat and Mersenne. It is said that he was a pupil of Viète but since Viète died in 1603 this must have been at a very early stage in Beaugrand's education.