Apollonius Of Perga :: essays research papers fc

Apollonius of Perga Apollonius was a great mathematician, known by his contempories as " The Great Geometer, " whose treatise Conics is one of the greatest scientific works from the ancient world. Most of his other treatise were lost, although their titles and a general indication of their contents were passed on by later writers, especially Pappus of Alexandria. As a youth Apollonius studied in Alexandria ( under the pupils of Euclid, according to Pappus ) and subsequently taught at the university there. He visited Pergamum, capital of a Hellenistic kingdom in western Anatolia, where a university and library similar to those in Alexandria had recently been built. While at Pergamum he met Eudemus and Attaluus, and he wrote the first edition of Conics. He addressed the prefaces of the first three books of the final edition to Eudemus and the remaining volumes to Attalus, whom some scholars identify as King Attalus I of Pergamum. It is clear from Apollonius' allusion to Euclid, Conon of Samos, and Nicoteles of Cyrene that he made the fullest use of his predecessors' works. Book 1-4 contain a systematic account of the essential principles of conics, which for the most part had been previously set forth by Euclid, Aristaeus and Menaechmus. A number of theorems in Book 3 and the greater part of Book 4 are new, however, and he introduced the terms parabola, eelipse, and hyperbola. Books 5-7 are clearly original. His genius takes its highest flight in Book 5, in which he considers normals as minimum and maximum straight lines drawn from given points to the curve ( independently of tangent properties ), discusses how many normals can be drawn from particular points, finds their feet by construction, and gives propositions determining the center of curvature at any points and leading at once to the Cartesian equation of the evolute of any conic. The first four books of the Conics survive in the original Grrek and the next three in Arabic translation. Book 8 is lost. The only other extant work of Apollonius is Cutting Off of a Ratio ( or On Proportional Section ), in an Arabic translation. Pappus mentions five additional works, Cutting off an Area ( or On Spatial Section ) , On Determinate Section, Tangencies, and Plane Loci. Tangencies embraced the following general problem : given three things, each of which may be a point, straight line, or circle, construct a circle tangent to the three. Sometimes known as the problem of Apollonius, the most difficult case arises when the three given things are circles. Of the other works of Apollonius referred to by ancient writers, one, On