On The Mathematical Elements Of The Almagest

OntheMathematicalElements oftheAlmagest (Abstract) 爪eA加哈estbyholemyisaveryimpo比mt砒hlevementlnthehlstoryofsclence．U卯nto no风 Howeve． there are卜wpaPers inChinese providing a幻刀dyon It due tothe shoftofrClatlve ma柏＂als andthel峋纠istic obstacle ofits onginal ie刀t．This paPaPerh二esto Overcomethese difficult and give abriefsurvey onthe m印hematical elemen匕 ofMeAImImq非上,which Is Inits English edition,topro。de for furtherstudies such as comparingamgthethOUghtS In ltwlththeM ethods ofanclent Chinese ma山ematlcal SSTt8STtonomy ARer recounting the sketch of how it came down through山e gges,仇e paper比gm todlsc旧s PtoPtolemy's Philosophical opinions ofmathematics and the m讪ematlcal Problems imPliedIn this book．During the course,neoteric mathematical tecMique isa加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 A加pt,we can seePtolemy'sP卜！losophlcal opinion of mathematics,which to IUm Is a vecy general sc！ence compnsing帖tronomtas aPttandleadsto劝soMelycertainnnthsthatwlIIneverbe suqectedtodoubt．On theother hand,although Ptolemy said geometry is all the mathematical prerequlsdes of the＼vllole 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 tab］e has a significant status In the hGtory ofh口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 pnm叼 concept of undame成altrlsonometflc function In theA加昭est．In some waX we preferic conslderthe chordtable s allllear InterPolatlve approxim3tionto thehctlon relation be仙een chords and arcs． Geomet丁Is onlq one p刮d叶山e theoretical equipment of PtoPtolemyT卜e A沁ages t aboundsIn numerical calculations．Besides purely arithmetical operations we can discern In汕e A加ags tat［eastthe rudiments ofatheoryoffunctlons which叩peared as forms．In负ctkolemyhadyrcsupposed a great n咖rer of practical methops for dealing wig functions of many differentklnys,such as thatthe linear interpolation was emp［oyed to determine the Ins咖咖eous an…＼cloclV which thow a new light on the ancient Greek tTadltlonal毗ematlcs．...