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ut¡¡this¡¡interpretation¡¡upon¡¡the¡¡theory£»¡¡conceiving¡¡the¡¡various¡¡spheres¡¡as¡¡actual¡¡crystalline¡¡bodies¡£¡¡It¡¡is¡¡difficult¡¡to¡¡imagine¡¡just¡¡how¡¡the¡¡various¡¡epicycles¡¡were¡¡supposed¡¡to¡¡revolve¡¡without¡¡interfering¡¡with¡¡the¡¡major¡¡spheres£»¡¡but¡¡perhaps¡¡this¡¡is¡¡no¡¡greater¡¡difficulty¡¡than¡¡is¡¡presented¡¡by¡¡the¡¡alleged¡¡properties¡¡of¡¡the¡¡ether£»¡¡which¡¡physicists¡¡of¡¡to¡day¡¡accept¡¡as¡¡at¡¡least¡¡a¡¡working¡¡hypothesis¡£¡¡We¡¡shall¡¡see¡¡later¡¡on¡¡how¡¡firmly¡¡the¡¡conception¡¡of¡¡concentric¡¡crystalline¡¡spheres¡¡was¡¡held¡¡to£»¡¡and¡¡that¡¡no¡¡real¡¡challenge¡¡was¡¡ever¡¡given¡¡that¡¡theory¡¡until¡¡the¡¡discovery¡¡was¡¡made¡¡that¡¡comets¡¡have¡¡an¡¡orbit¡¡that¡¡must¡¡necessarily¡¡intersect¡¡the¡¡spheres¡¡of¡¡the¡¡various¡¡planets¡£¡¡Ptolemy's¡¡system¡¡of¡¡geography¡¡in¡¡eight¡¡books£»¡¡founded¡¡on¡¡that¡¡of¡¡Marinus¡¡of¡¡Tyre£»¡¡was¡¡scarcely¡¡less¡¡celebrated¡¡throughout¡¡the¡¡Middle¡¡Ages¡¡than¡¡the¡¡Almagest¡£¡¡It¡¡contained¡¡little£»¡¡however£»¡¡that¡¡need¡¡concern¡¡us¡¡here£»¡¡being¡¡rather¡¡an¡¡elaboration¡¡of¡¡the¡¡doctrines¡¡to¡¡which¡¡we¡¡have¡¡already¡¡sufficiently¡¡referred¡£¡¡None¡¡of¡¡Ptolemy's¡¡original¡¡manuscripts¡¡has¡¡come¡¡down¡¡to¡¡us£»¡¡but¡¡there¡¡is¡¡an¡¡alleged¡¡fifth¡century¡¡manuscript¡¡attributed¡¡to¡¡Agathadamon¡¡of¡¡Alexandria¡¡which¡¡has¡¡peculiar¡¡interest¡¡because¡¡it¡¡contains¡¡a¡¡series¡¡of¡¡twenty¡seven¡¡elaborately¡¡colored¡¡maps¡¡that¡¡are¡¡supposed¡¡to¡¡be¡¡derived¡¡from¡¡maps¡¡drawn¡¡up¡¡by¡¡Ptolemy¡¡himself¡£¡¡In¡¡these¡¡maps¡¡the¡¡sea¡¡is¡¡colored¡¡green£»¡¡the¡¡mountains¡¡red¡¡or¡¡dark¡¡yellow£»¡¡and¡¡the¡¡land¡¡white¡£¡¡Ptolemy¡¡assumed¡¡that¡¡a¡¡degree¡¡at¡¡the¡¡equator¡¡was¡¡500¡¡stadia¡¡instead¡¡of¡¡604¡¡stadia¡¡in¡¡length¡£¡¡We¡¡are¡¡not¡¡informed¡¡as¡¡to¡¡the¡¡grounds¡¡on¡¡which¡¡this¡¡assumption¡¡was¡¡made£»¡¡but¡¡it¡¡has¡¡been¡¡suggested¡¡that¡¡the¡¡error¡¡was¡¡at¡¡least¡¡partially¡¡instrumental¡¡in¡¡leading¡¡to¡¡one¡¡very¡¡curious¡¡result¡£¡¡¡¨Taking¡¡the¡¡parallel¡¡of¡¡Rhodes£»¡¨¡¡says¡¡Donaldson£»£§5£§¡¡¡¨he¡¡calculated¡¡the¡¡longitudes¡¡from¡¡the¡¡Fortunate¡¡Islands¡¡to¡¡Cattigara¡¡or¡¡the¡¡west¡¡coast¡¡of¡¡Borneo¡¡at¡¡180¡¡degrees£»¡¡conceiving¡¡this¡¡to¡¡be¡¡one¡half¡¡the¡¡circumference¡¡of¡¡the¡¡globe¡£¡¡The¡¡real¡¡distance¡¡is¡¡only¡¡125¡¡degrees¡¡or¡¡127¡¡degrees£»¡¡so¡¡that¡¡his¡¡measurement¡¡is¡¡wrong¡¡by¡¡one¡¡third¡¡of¡¡the¡¡whole£»¡¡one¡sixth¡¡for¡¡the¡¡error¡¡in¡¡the¡¡measurement¡¡of¡¡a¡¡degree¡¡and¡¡one¡sixth¡¡for¡¡the¡¡errors¡¡in¡¡measuring¡¡the¡¡distance¡¡geometrically¡£¡¡These¡¡errors£»¡¡owing¡¡to¡¡the¡¡authority¡¡attributed¡¡to¡¡the¡¡geography¡¡of¡¡Ptolemy¡¡in¡¡the¡¡Middle¡¡Ages£»¡¡produced¡¡a¡¡consequence¡¡of¡¡the¡¡greatest¡¡importance¡£¡¡They¡¡really¡¡led¡¡to¡¡the¡¡discovery¡¡of¡¡America¡£¡¡For¡¡the¡¡design¡¡of¡¡Columbus¡¡to¡¡sail¡¡from¡¡the¡¡west¡¡of¡¡Europe¡¡to¡¡the¡¡east¡¡of¡¡Asia¡¡was¡¡founded¡¡on¡¡the¡¡supposition¡¡that¡¡the¡¡distance¡¡was¡¡less¡¡by¡¡one¡¡third¡¡than¡¡it¡¡really¡¡was¡£¡¨¡¡This¡¡view¡¡is¡¡perhaps¡¡a¡¡trifle¡¡fanciful£»¡¡since¡¡there¡¡is¡¡nothing¡¡to¡¡suggest¡¡that¡¡the¡¡courage¡¡of¡¡Columbus¡¡would¡¡have¡¡balked¡¡at¡¡the¡¡greater¡¡distance£»¡¡and¡¡since¡¡the¡¡protests¡¡of¡¡the¡¡sailors£»¡¡which¡¡nearly¡¡thwarted¡¡his¡¡efforts£»¡¡were¡¡made¡¡long¡¡before¡¡the¡¡distance¡¡as¡¡estimated¡¡by¡¡Ptolemy¡¡had¡¡been¡¡covered£»¡¡nevertheless¡¡it¡¡is¡¡interesting¡¡to¡¡recall¡¡that¡¡the¡¡great¡¡geographical¡¡doctrines£»¡¡upon¡¡which¡¡Columbus¡¡must¡¡chiefly¡¡have¡¡based¡¡his¡¡arguments£»¡¡had¡¡been¡¡before¡¡the¡¡world¡¡in¡¡an¡¡authoritative¡¡form¡¡practically¡¡unheeded¡¡for¡¡more¡¡than¡¡twelve¡¡hundred¡¡years£»¡¡awaiting¡¡a¡¡champion¡¡with¡¡courage¡¡enough¡¡to¡¡put¡¡them¡¡to¡¡the¡¡test¡£
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