Apollonius Of Perga :: essays research papers fc

Apollonius of Perga     Apollonius was a great mathematician, know by his contempories as " TheGreat Geometer, " whose treatise Conics is one of the greatest scientific kit and caboodlefrom the ancient world. Most of his early(a) treatise were lost, although theirtitles and a general indication of their contents were passed on by laterwriters, especially Pappus of Alexandria.     As a youthfulness 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 western 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 iii books of the final editionto Eudemus and the remaining volumes to Attalus, whom some scholars identify as powerfulness A ttalus 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. bind 1-4 stock a systematic account of the essential principles of conics,which for the most part had been antecedently set forth by Euclid, Aristaeus andMenaechmus. A number of theorems in disc 3 and the greater part of Book 4 arenew, 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 haggard fromgiven points to the curve ( independently of tangent properties ), discusses howm any normals can be drawn from particular points, finds their feet by createion, and gives propositions determining the center of curvature at anypoints and leading at once to the Cartesian equation of the evolute of any conic.     The firs t four books of the Conics survive in the original Grrek and thenext ternion in Arabic translation. Book 8 is lost. The only other living workof Apollonius is neat 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 task given third 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