Apollonius Of Perga :: essays research papers fc

Apollonius of Perga     Apollonius was a great mathematician, known by his contempories as " TheGreat Geometer, " whose treatise Conics is wholeness of the greatest scientific worksfrom the ancient world. Most of his other treatise were lost, although theirtitles and a general indication of their contents were passed on by laterwriters, 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. Hevisited Pergamum, capital of a Hellenistic kingdom in westbound Anatolia, where auniversity 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 ofConics. He addressed the prefaces of the first troika books of the final editionto Eudemus and the remaining volumes to Attalus, whom some scholars identify asKing Attalus I of Pergamum .     It is clear from Apollonius allusion to Euclid, Conon of Samos, andNicoteles 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 andMenaechmus. A number of theorems in Book 3 and the great part of Book 4 arenew, however, and he introduced the terms parabola, eelipse, and hyperbola.Books 5-7 are clearly veritable. His genius takes its highest flight in Book 5,in which he considers normals as minimum and maximum straight lines drawn fromgiven points to the curve ( independently of tangent properties ), discusses howmany normals can be drawn from particular points, finds their feet byconstruction, and gives propositions determine the center of curvature at anypoints 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 thenext three in Arabic translation. Book 8 is lost. The only other extant workof Apollonius is Cutting Off of a Ratio ( or On Proportional Section ), in anArabic 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 circletangent to the three. Sometimes known as the problem of Apollonius, the mostdifficult case arises when the three given things are circles.     Of the other works of Apollonius referred to by ancient writers, one, On