OntheMathematicalElements oftheAlmagest (Abstract) 爪eAåŠ å“ˆestbyholemyisaveryimpo比mtç ’hlevementlnthehlstoryofsclence.Uå¯nto no风 Howeve. there areåœwpaPers inChinese providing a幻刀dyon It due tothe shoftofrClatlve maæŸï¼‚als andthelå³‹çº istic obstacle ofits onginal ie刀t.This paPaPerh二esto Overcomethese difficult and give abriefsurvey onthe må°hematical elemen匕 ofMeAImImqéžä¸Š,which Is Inits English edition,topro。de for furtherstudies such as comparingamgthethOUghtS In ltwlththeM ethods ofanclent Chinese maå±±ematlcal SSTt8STtonomy ARer recounting the sketch of how it came down throughå±±e gges,仇e paper比gm todlscæ—§s PtoPtolemy's Philosophical opinions ofmathematics and the m讪ematlcal Problems imPliedIn this book.During the course,neoteric mathematical tecMique isaåŠ pied In a history podd ofview thus some old statements are realgued,and some new conclusions are drawn· From what was sasd and what was done h 爪e AåŠ pt,we can seePtolemy'sPåœï¼losophlcal opinion of mathematics,which to IUm Is a vecy general scï¼ence compnsing帖tronomtas aPttandleadstoåŠsoMelycertainnnthsthatwlIIneverbe suqectedtodoubt.On theother hand,although Ptolemy said geometry is all the mathematical prerequlsdes of theï¼¼vllole st'Udy of astronomyy es did not impede him aing advantage of other mathematical1llCthodS,Wb1Ch We Will eXp1Ore In thC latef two ChaPte fsfS· Ptolemry's chord tabï¼½e has a significant status In the hGtory ofhå£yonometry nd has beenrcyarded as atable ofslne unction.Butan investigation Intothe aPplying ofthetable will showtilat It Is not always such a thing.we can not ind any pnmå¼ concept of undameæˆaltrlsonometflc function In theAåŠ æ˜est.In some waX we preferic conslderthe chordtable s allllear InterPolatlve approxim3tionto thehctlon relation beä»™een chords and arcs. Geometä¸Is onlq one p刮då¶å±±e theoretical equipment of PtoPtolemyTåœe Aæ²ages t aboundsIn numerical calculations.Besides purely arithmetical operations we can discern In汕e AåŠ ags tatï¼»eastthe rudiments ofatheoryoffunctlons whichå©peared as forms.Inè´Ÿctkolemyhadyrcsupposed a great nå’–rer of practical methops for dealing wig functions of many differentklnys,such as thatthe linear interpolation was empï¼»oyed to determine the Inså’–å’–eous an…\cloclV which thow a new light on the ancient Greek tTadltlonal毗ematlcs....
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