Aristaios of Samos

Aristaios of Samos ( bl. Around 350 BC to 300 BC), also Aristaios the Elder, was a Greek mathematician of the 4th century BC. He was an older contemporary of Euclid and was highly valued by him for his work on conic sections in three dimensions. These were further developed by Apollonios von Perge . He wrote five books on three-dimensional places .

Little is known about him and his writings have not survived. Iamblichus of Chalkis wrongly called him a son-in-law of Pythagoras . Euclid mentions it after Pappos in a lost work on constructions in three dimensions.

Pappos knew his work (in five chapters or books ) about conic sections, especially three-dimensional constructions ( loci (places) with respect to three or four straight lines). Although the title of his book is uncertain, according to Heiberg it is only one work. The references in Euclid and Apollonios suggest that Aristaios did not know the complete solution of the construction with regard to three or four straight lines (in contrast to Apollonios). Euclid and Apollonios, whose work on conic sections made that of Euclid completely obsolete, were more interested in a synthetic representation of the doctrine of conic sections.

Aristaios deals with guidelines ( directrix ) of conic sections, focal points and other properties and the trisection of the angle with the hyperbola.

When the works of Pappos and Apollonios were rediscovered in the Renaissance, efforts were also made to reconstruct the work of Aristaios in the 17th century ( Vinzenco Viviani 1645, Gilles Personne de Roberval ) and later ( Hieronymus Zeuthen ). His work forms a basis in the analytical geometry of the conic sections by René Descartes , whereby this goes over to the general case of construction with regard to any number of straight lines.

Hypsicles mentions an Aristaios in his Euclidean commentary in connection with regular bodies (Book 13 of the Elements of Euclid), but it is possibly a younger Aristaios (that would be an Aristaios the Younger). Eva Sachs (The Five Platonic Solids, Berlin 1917) speaks out against Aristaios the Elder as an author, Thomas Heath in favor.

Its somewhat older predecessor in the treatment of conic sections was Menaichmos .

literature

Kurt Vogel : Aristaeus , in Dictionary of Scientific Biography , Volume 1, pp. 245-246
Entry Aristaios in Guido Walz, Lexicon of Mathematics, Spektrum Verlag

Web links

John J. O'Connor, Edmund F. Robertson : Aristaios of Samos. In: MacTutor History of Mathematics archive .

Individual evidence

↑ Approximate dates of life according to Vogel in his article on Aristaios in the Dictionary of Scientific Biography. In the new edition of the New Pauly by Brill as Aristaios of Samos, around 350 to 330 BC. Chr.

personal data
SURNAME	Aristaios of Samos
ALTERNATIVE NAMES	Aristaios the Elder; Aristaeus
BRIEF DESCRIPTION	Greek mathematician
DATE OF BIRTH	around 370 BC Chr.
DATE OF DEATH	around 300 BC Chr.

[1] Approximate dates of life according to Vogel in his article on Aristaios in the Dictionary of Scientific Biography. In the new edition of the New Pauly by Brill as Aristaios of Samos, around 350 to 330 BC. Chr.