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oriental¡¡spirit¡£¡¡They¡¡were¡¡under¡¡the¡¡spell¡¡of¡¡tradition£»¡¡and£»¡¡in¡¡the¡¡main£»¡¡what¡¡they¡¡accepted¡¡from¡¡the¡¡Greeks¡¡they¡¡regarded¡¡as¡¡almost¡¡final¡¡in¡¡its¡¡teaching¡£¡¡There¡¡were£»¡¡however£»¡¡a¡¡few¡¡notable¡¡exceptions¡¡among¡¡their¡¡men¡¡of¡¡science£»¡¡and¡¡to¡¡these¡¡must¡¡be¡¡ascribed¡¡several¡¡discoveries¡¡of¡¡some¡¡importance¡£¡¡The¡¡chief¡¡subjects¡¡that¡¡excited¡¡the¡¡interest¡¡and¡¡exercised¡¡the¡¡ingenuity¡¡of¡¡the¡¡Arabian¡¡scholars¡¡were¡¡astronomy£»¡¡mathematics£»¡¡and¡¡medicine¡£¡¡The¡¡practical¡¡phases¡¡of¡¡all¡¡these¡¡subjects¡¡were¡¡given¡¡particular¡¡attention¡£¡¡Thus¡¡it¡¡is¡¡well¡¡known¡¡that¡¡our¡¡so¡­called¡¡Arabian¡¡numerals¡¡date¡¡from¡¡this¡¡period¡£¡¡The¡¡revolutionary¡¡effect¡¡of¡¡these¡¡characters£»¡¡as¡¡applied¡¡to¡¡practical¡¡mathematics£»¡¡can¡¡hardly¡¡be¡¡overestimated£»¡¡but¡¡it¡¡is¡¡generally¡¡considered£»¡¡and¡¡in¡¡fact¡¡was¡¡admitted¡¡by¡¡the¡¡Arabs¡¡themselves£»¡¡that¡¡these¡¡numerals¡¡were¡¡really¡¡borrowed¡¡from¡¡the¡¡Hindoos£»¡¡with¡¡whom¡¡the¡¡Arabs¡¡came¡¡in¡¡contact¡¡on¡¡the¡¡east¡£¡¡Certain¡¡of¡¡the¡¡Hindoo¡¡alphabets£»¡¡notably¡¡that¡¡of¡¡the¡¡Battaks¡¡of¡¡Sumatra£»¡¡give¡¡us¡¡clews¡¡to¡¡the¡¡originals¡¡of¡¡the¡¡numerals¡£¡¡It¡¡does¡¡not¡¡seem¡¡certain£»¡¡however£»¡¡that¡¡the¡¡Hindoos¡¡employed¡¡these¡¡characters¡¡according¡¡to¡¡the¡¡decimal¡¡system£»¡¡which¡¡is¡¡the¡¡prime¡¡element¡¡of¡¡their¡¡importance¡£¡¡Knowledge¡¡is¡¡not¡¡forthcoming¡¡as¡¡to¡¡just¡¡when¡¡or¡¡by¡¡whom¡¡such¡¡application¡¡was¡¡made¡£¡¡If¡¡this¡¡was¡¡an¡¡Arabic¡¡innovation£»¡¡it¡¡was¡¡perhaps¡¡the¡¡most¡¡important¡¡one¡¡with¡¡which¡¡that¡¡nation¡¡is¡¡to¡¡be¡¡credited¡£¡¡Another¡¡mathematical¡¡improvement¡¡was¡¡the¡¡introduction¡¡into¡¡trigonometry¡¡of¡¡the¡¡sinethe¡¡half¡­chord¡¡of¡¡the¡¡double¡¡arcinstead¡¡of¡¡the¡¡chord¡¡of¡¡the¡¡arc¡¡itself¡¡which¡¡the¡¡Greek¡¡astronomers¡¡had¡¡employed¡£¡¡This¡¡improvement¡¡was¡¡due¡¡to¡¡the¡¡famous¡¡Albategnius£»¡¡whose¡¡work¡¡in¡¡other¡¡fields¡¡we¡¡shall¡¡examine¡¡in¡¡a¡¡moment¡£¡¡Another¡¡evidence¡¡of¡¡practicality¡¡was¡¡shown¡¡in¡¡the¡¡Arabian¡¡method¡¡of¡¡attempting¡¡to¡¡advance¡¡upon¡¡Eratosthenes'¡¡measurement¡¡of¡¡the¡¡earth¡£¡¡Instead¡¡of¡¡trusting¡¡to¡¡the¡¡measurement¡¡of¡¡angles£»¡¡the¡¡Arabs¡¡decided¡¡to¡¡measure¡¡directly¡¡a¡¡degree¡¡of¡¡the¡¡earth's¡¡surfaceor¡¡rather¡¡two¡¡degrees¡£¡¡Selecting¡¡a¡¡level¡¡plain¡¡in¡¡Mesopotamia¡¡for¡¡the¡¡experiment£»¡¡one¡¡party¡¡of¡¡the¡¡surveyors¡¡progressed¡¡northward£»¡¡another¡¡party¡¡southward£»¡¡from¡¡a¡¡given¡¡point¡¡to¡¡the¡¡distance¡¡of¡¡one¡¡degree¡¡of¡¡arc£»¡¡as¡¡determined¡¡by¡¡astronomical¡¡observations¡£¡¡The¡¡result¡¡found¡¡was¡¡fifty¡­six¡¡miles¡¡for¡¡the¡¡northern¡¡degree£»¡¡and¡¡fifty¡­six¡¡and¡¡two¡­third¡¡miles¡¡for¡¡the¡¡southern¡£¡¡Unfortunately£»¡¡we¡¡do¡¡not¡¡know¡¡the¡¡precise¡¡length¡¡of¡¡the¡¡mile¡¡in¡¡question£»¡¡and¡¡therefore¡¡cannot¡¡be¡¡assured¡¡as¡¡to¡¡the¡¡accuracy¡¡of¡¡the¡¡measurement¡£¡¡It¡¡is¡¡interesting¡¡to¡¡note£»¡¡however£»¡¡that¡¡the¡¡two¡¡degrees¡¡were¡¡found¡¡of¡¡unequal¡¡lengths£»¡¡suggesting¡¡that¡¡the¡¡earth¡¡is¡¡not¡¡a¡¡perfect¡¡spherea¡¡suggestion¡¡the¡¡validity¡¡of¡¡which¡¡was¡¡not¡¡to¡¡be¡¡put¡¡to¡¡the¡¡test¡¡of¡¡conclusive¡¡measurements¡¡until¡¡about¡¡the¡¡close¡¡of¡¡the¡¡eighteenth¡¡century¡£¡¡The¡¡Arab¡¡measurement¡¡was¡¡made¡¡in¡¡the¡¡time¡¡of¡¡Caliph¡¡Abdallah¡¡al¡­Mamun£»¡¡the¡¡son¡¡of¡¡the¡¡famous¡¡Harun¡­al¡­Rashid¡£¡¡Both¡¡father¡¡and¡¡son¡¡were¡¡famous¡¡for¡¡their¡¡interest¡¡in¡¡science¡£¡¡Harun¡­al¡­Rashid¡¡was£»¡¡it¡¡will¡¡be¡¡recalled£»¡¡the¡¡friend¡¡of¡¡Charlemagne¡£¡¡It¡¡is¡¡said¡¡that¡¡he¡¡sent¡¡that¡¡ruler£»¡¡as¡¡a¡¡token¡¡of¡¡friendship£»¡¡a¡¡marvellous¡¡clock¡¡which¡¡let¡¡fall¡¡a¡¡metal¡¡ball¡¡to¡¡mark¡¡the¡¡hours¡£¡¡This¡¡mechanism£»¡¡which¡¡is¡¡alleged¡¡to¡¡have¡¡excited¡¡great¡¡wonder¡¡in¡¡the¡¡West£»¡¡furnishes¡¡yet¡¡another¡¡instance¡¡of¡¡Arabian¡¡practicality¡£¡¡Perhaps¡¡the¡¡greatest¡¡of¡¡the¡¡Arabian¡¡astronomers¡¡was¡¡Mohammed¡¡ben¡¡Jabir¡¡Albategnius£»¡¡or¡¡El¡­batani£»¡¡who¡¡was¡¡born¡¡at¡¡Batan£»¡¡in¡¡Mesopotamia£»¡¡about¡¡the¡¡year¡¡850¡¡A¡£D¡££»¡¡and¡¡died¡¡in¡¡929¡£¡¡Albategnius¡¡was¡¡a¡¡student¡¡of¡¡the¡¡Ptolemaic¡¡astronomy£»¡¡but¡¡he¡¡was¡¡also¡¡a¡¡practical¡¡observer¡£¡¡He¡¡made¡¡the¡¡important¡¡discovery¡¡of¡¡the¡¡motion¡¡of¡¡the¡¡solar¡¡apogee¡£¡¡That¡¡is¡¡to¡¡say£»¡¡he¡¡found¡¡that¡¡the¡¡position¡¡of¡¡the¡¡sun¡¡among¡¡the¡¡stars£»¡¡at¡¡the¡¡time¡¡of¡¡its¡¡greatest¡¡distance¡¡from¡¡the¡¡earth£»¡¡was¡¡not¡¡what¡¡it¡¡had¡¡been¡¡in¡¡the¡¡time¡¡of¡¡Ptolemy¡£¡¡The¡¡Greek¡¡astronomer¡¡placed¡¡the¡¡sun¡¡in¡¡longitude¡¡65¡¡degrees£»¡¡but¡¡Albategnius¡¡found¡¡it¡¡in¡¡longitude¡¡82¡¡degrees£»¡¡a¡¡distance¡¡too¡¡great¡¡to¡¡be¡¡accounted¡¡for¡¡by¡¡inaccuracy¡¡of¡¡measurement¡£¡¡The¡¡modern¡¡inference¡¡from¡¡this¡¡observation¡¡is¡¡that¡¡the¡¡solar¡¡system¡¡is¡¡moving¡¡through¡¡space£»¡¡but¡¡of¡¡course¡¡this¡¡inference¡¡could¡¡not¡¡well¡¡be¡¡drawn¡¡while¡¡the¡¡earth¡¡was¡¡regarded¡¡as¡¡the¡¡fixed¡¡centre¡¡of¡¡the¡¡universe¡£¡¡In¡¡the¡¡eleventh¡¡century¡¡another¡¡Arabian¡¡discoverer£»¡¡Arzachel£»¡¡observing¡¡the¡¡sun¡¡to¡¡be¡¡less¡¡advanced¡¡than¡¡Albategnius¡¡had¡¡found¡¡it£»¡¡inferred¡¡incorrectly¡¡that¡¡the¡¡sun¡¡had¡¡receded¡¡in¡¡the¡¡mean¡¡time¡£¡¡The¡¡modern¡¡explanation¡¡of¡¡this¡¡observation¡¡is¡¡that¡¡the¡¡measurement¡¡of¡¡Albategnius¡¡was¡¡somewhat¡¡in¡¡error£»¡¡since¡¡we¡¡know¡¡that¡¡the¡¡sun's¡¡motion¡¡is¡¡steadily¡¡progressive¡£¡¡Arzachel£»¡¡however£»¡¡accepting¡¡the¡¡measurement¡¡of¡¡his¡¡predecessor£»¡¡drew¡¡the¡¡false¡¡inference¡¡of¡¡an¡¡oscillatory¡¡motion¡¡of¡¡the¡¡stars£»¡¡the¡¡idea¡¡of¡¡the¡¡motion¡¡of¡¡the¡¡solar¡¡system¡¡not¡¡being¡¡permissible¡£¡¡This¡¡assumed¡¡phenomenon£»¡¡which¡¡really¡¡has¡¡no¡¡existence¡¡in¡¡point¡¡of¡¡fact£»¡¡was¡¡named¡¡the¡¡¡¨trepidation¡¡of¡¡the¡¡fixed¡¡stars£»¡¨¡¡and¡¡was¡¡for¡¡centuries¡¡accepted¡¡as¡¡an¡¡actual¡¡phenomenon¡£¡¡Arzachel¡¡explained¡¡this¡¡supposed¡¡phenomenon¡¡by¡¡assuming¡¡that¡¡the¡¡equinoctial¡¡points£»¡¡or¡¡the¡¡points¡¡of¡¡intersection¡¡of¡¡the¡¡equator¡¡and¡¡the¡¡ecliptic£»¡¡revolve¡¡in¡¡circles¡¡of¡¡eight¡¡degrees'¡¡radius¡£¡¡The¡¡first¡¡points¡¡of¡¡Aries¡¡and¡¡Libra¡¡were¡¡supposed¡¡to¡¡describe¡¡the¡¡circumference¡¡of¡¡these¡¡circles¡¡in¡¡about¡¡eight¡¡hundred¡¡years¡£¡¡All¡¡of¡¡which¡¡illustrates¡¡how¡¡a¡¡difficult¡¡and¡¡false¡¡explanation¡¡may¡¡take¡¡the¡¡place¡¡of¡¡a¡¡simple¡¡and¡¡correct¡¡one¡£¡¡The¡¡observations¡¡of¡¡later¡¡generations¡¡have¡¡shown¡¡conclusively¡¡that¡¡the¡¡sun's¡¡shift¡¡of¡¡position¡¡is¡¡regularly¡¡progressive£»¡¡hence¡¡that¡¡there¡¡is¡¡no¡¡¡¨trepidation¡¨¡¡of¡¡the¡¡stars¡¡and¡¡no¡¡revolution¡¡of¡¡the¡¡equinoctial¡¡points¡£¡¡If¡¡the¡¡Arabs¡¡were¡¡wrong¡¡as¡¡regards¡¡this¡¡supposed¡¡motion¡¡of¡¡the¡¡fixed¡¡stars£»¡¡they¡¡made¡¡at¡¡least¡¡one¡¡correct¡¡observation¡¡as¡¡to¡¡the¡¡inequality¡¡of¡¡motion¡¡of¡¡the¡¡moon¡£¡¡Two¡¡inequalities¡¡of¡¡the¡¡motion¡¡of¡¡this¡¡body¡¡were¡¡already¡¡known¡£¡¡A¡¡third£»¡¡called¡¡the¡¡moon's¡¡variation£»¡¡was¡¡discovered¡¡by¡¡an¡¡Arabian¡¡astronomer¡¡who¡¡lived¡¡at¡¡Cairo¡¡and¡¡observed¡¡at¡¡Bagdad¡¡in¡¡975£»¡¡and¡¡who¡¡bore¡¡the¡¡formidable¡¡name¡¡of¡¡Mohammed¡¡Aboul¡¡Wefaal¡­Bouzdjani¡£¡¡The¡¡inequality¡¡of¡¡motion¡¡in¡¡question£»¡¡in¡¡virtue¡¡of¡¡which¡¡the¡¡moon¡¡moves¡¡quickest¡¡when¡¡she¡¡is¡¡at¡¡new¡¡or¡¡full£»¡¡and¡¡slowest¡¡at¡¡the¡¡first¡¡and¡¡third¡¡quarter£»¡¡was¡¡rediscovered¡¡by¡¡Tycho¡¡Brahe¡¡six¡¡centuries¡¡later£»¡¡a¡¡fact¡¡which¡¡in¡¡itself¡¡evidences¡¡the¡¡neglect¡¡of¡¡the¡¡Arabian¡¡astronomer's¡¡discovery¡¡by¡¡his¡¡immediate¡¡successors¡£¡¡In¡¡the¡¡ninth¡¡and¡¡tenth¡¡centuries¡¡the¡¡Arabian¡¡city¡¡of¡¡Cordova£»¡¡in¡¡Spain£»¡¡was¡¡another¡¡important¡¡centre¡¡of¡¡scientific¡¡influence¡£¡¡There¡¡was¡¡a¡¡library¡¡of¡¡several¡¡hundred¡¡thousand¡¡volumes¡¡here£»¡¡and¡¡a¡¡college¡¡where¡¡mathematics¡¡and¡¡astronomy¡¡were¡¡taught¡£¡¡Granada£»¡¡Toledo£»¡¡and¡¡Salamanca¡¡were¡¡also¡¡important¡¡centres£»¡¡to¡¡which¡¡students¡¡flocked¡¡from¡¡western¡¡Europe¡£¡¡It¡¡was¡¡the¡¡proximity¡¡of¡¡these¡¡Arabian¡¡centres¡¡that¡¡stimulated¡¡the¡¡scientific¡¡interests¡¡of¡¡Alfonso¡¡X¡£¡¡of¡¡Castile£»¡¡at¡¡whose¡¡instance¡¡the¡¡celebrated¡¡Alfonsine¡¡tables¡¡were¡¡constructed¡£¡¡A¡¡familiar¡¡story¡¡records¡¡that¡¡Alfonso£»¡¡pondering¡¡the¡¡complications¡¡of¡¡the¡¡Ptolemaic¡¡cycles¡¡and¡¡epicycles£»¡¡was¡¡led¡¡to¡¡remark¡¡that£»¡¡had¡¡he¡¡been¡¡consulted¡¡at¡¡the¡¡time¡¡of¡¡creation£»¡¡he¡¡could¡¡have¡¡suggested¡¡a¡¡much¡¡better¡¡and¡¡simpler¡¡plan¡¡for¡¡the¡¡universe¡£¡¡Some¡¡centuries¡¡were¡¡to¡¡elapse¡¡before¡¡Copernicus¡¡was¡¡to¡¡show¡¡that¡¡it¡¡was¡¡not¡¡the¡¡plan¡¡of¡¡the¡¡universe£»¡¡but¡¡man's¡¡interpretation¡¡of¡¡it£»¡¡that¡¡was¡¡at¡¡fault¡£¡¡Another¡¡royal¡¡personage¡¡who¡¡came¡¡under¡¡Arabian¡¡influence¡¡was¡¡Frederick¡¡II¡£¡¡of¡¡Sicilythe¡¡¡¨Wonder¡¡of¡¡the¡¡World£»¡¨¡¡as¡¡he¡¡was¡¡called¡¡by¡¡his¡¡contemporaries¡£¡¡The¡¡Almagest¡¡of¡¡Ptolemy¡¡was¡¡translated¡¡into¡¡Latin¡¡at¡¡his¡¡instance£»¡¡being¡¡introduced¡¡to¡¡the¡¡Western¡¡world¡¡through¡¡this¡¡curious¡¡channel¡£¡¡At¡¡this¡¡time¡¡it¡¡became¡¡quite¡¡usual¡¡for¡¡the¡¡Italian¡¡and¡¡Spanish¡¡scholars¡¡to¡¡understand¡¡Arabic¡¡although¡¡they¡¡were¡¡totally¡¡ignorant¡¡of¡¡Greek¡£¡¡In¡¡the¡¡field¡¡of¡¡physical¡¡science¡¡one¡¡of¡¡the¡¡most¡¡important¡¡of¡¡the¡¡Arabian¡¡scientists¡¡was¡¡Alhazen¡£¡¡His¡¡work£»¡¡published¡¡about¡¡the¡¡year¡¡1100¡¡A¡£D¡££»¡¡had¡¡great¡¡celebrity¡¡throughout¡¡the¡¡mediaeval¡¡period¡£¡¡The¡¡original¡¡investigations¡¡of¡¡Alhazen¡¡had¡¡to¡¡do¡¡largely¡¡with¡¡optics¡£¡¡He¡¡made¡¡particular¡¡studies¡¡of¡¡the¡¡eye¡¡itself£»¡¡and¡¡the¡¡names¡¡given¡¡by¡¡him¡¡to¡¡various¡¡parts¡¡of¡¡the¡¡eye£»¡¡as¡¡the¡¡vitreous¡¡humor£»¡¡the¡¡cornea£»¡¡and¡¡the¡¡retina£»¡¡are¡¡still¡¡retained¡¡by¡¡anatomists¡£¡¡It¡¡is¡¡known¡¡that¡¡Ptolemy¡¡had¡¡studied¡¡the¡¡refraction¡¡of¡¡light£»¡¡and¡¡that¡¡he£»¡¡in¡¡common¡¡with¡¡his¡¡immediate¡¡predecessors£»¡¡was¡¡aware¡¡that¡¡atmospheric¡¡refraction¡¡affects¡¡the¡¡apparent¡¡position¡¡of¡¡stars¡¡near¡¡the¡¡horizon¡£¡¡Alhazen¡¡carried¡¡forward¡¡these¡¡studies£»¡¡and¡¡was¡¡led¡¡through¡¡them¡¡to¡¡make¡¡the¡¡first¡¡recorded¡¡scientific¡¡estimate¡¡of¡¡the¡¡phenomena¡¡of¡¡twilight¡¡and¡¡of¡¡the¡¡height¡¡of¡¡the¡¡atmosphere¡£¡¡The¡¡persistence¡¡of¡¡a¡¡glow¡¡in¡¡the¡¡atmosphere¡¡after¡¡the¡¡sun¡¡has¡¡disappeared¡¡beneath¡¡the¡¡horizon¡¡is¡¡so¡¡familiar¡¡a¡¡phenomenon¡¡that¡¡the¡¡ancient¡¡philosophers¡¡seem¡¡not¡¡to¡¡have¡¡thought¡¡of¡¡it¡¡as¡¡requiring¡¡an¡¡explanation¡£¡¡Yet¡¡a¡¡moment's¡¡consideration¡¡makes¡¡it¡¡clear¡¡that£»¡¡if¡¡light¡¡travels¡¡in¡¡straight¡¡lines¡¡and¡¡the¡¡rays¡¡of¡¡the¡¡sun¡¡were¡¡in¡¡no¡¡wise¡¡deflected£»¡¡the¡¡complete¡¡darkness¡¡of¡¡night¡¡should¡¡instantly¡¡succeed¡¡to¡¡day¡¡when¡¡the¡¡sun¡¡passes¡¡below¡¡the¡¡horizon¡£¡¡That¡¡this¡¡sudden¡¡change¡¡does¡¡not¡¡occur£»¡¡Alhazen¡¡explained¡¡as¡¡due¡¡to¡¡the¡¡reflection¡¡of¡¡light¡¡by¡¡the¡¡earth's¡¡atmosphere¡£¡¡Alhazen¡¡appears¡¡to¡¡have¡¡conceived¡¡the¡¡atmosphere¡¡as¡¡a¡¡sharply¡¡defined¡¡layer£»¡¡and£»¡¡assuming¡¡that¡¡twilight¡¡continues¡¡only¡¡so¡¡long¡¡as¡¡rays¡¡of¡¡the¡¡sun¡¡reflected¡¡from¡¡the¡¡outer¡¡surface¡¡of¡¡this¡¡layer¡¡can¡¡reach¡¡the¡¡spectator¡¡at¡¡any¡¡given¡¡point£»¡¡he¡¡hit¡¡upon¡¡a¡¡means¡¡of¡¡measurement¡¡that¡¡seem

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