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Latitude and Longitude in the Middle ages or… what can you learn from a table of numbers and names about the world of the 12 th Century? Prof. John Huth

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Circa 200 AD Ptolemy: Inhabited world (occumene) documented Segregated latitude regions into climes Tables of latitude and longitude of major cities Prime meridian = Fortunate Isles (Canaries) Astrology Astronomy (geocentric universe) Works inherited by Arabs – Copied by scribes, added to over the years

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Equator and pole define 0 and 90 degrees of latitude. Prime meridian ( 0 degrees) of longitude is arbitrary Modern: Greenwich, Ancient: Canary Islands (Fortunate Is)

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Primary motivations for latitude and longitude Horoscopes need birth information Lat., long date, and time of birth Face Mecca to pray (Qibla) along great circle route

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Gerard of Cremona – translator from Arabic to Latin

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Snippet of values in Marseilles Tables (From John Kirtland Wright, 1928)

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Outer Ranges of Marseilles Tables Locations

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Determining latitude: the sun throughout the year Path of sun in sky

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θ Latitude is given by θ at shortest length of shadow during the equinox Latitude is given by θ at shortest length of shadow during the equinox The shadow of a stick traces out the path of a line over the course of the day at the equinox (other days are hyperbolae) The shadow of a stick traces out the path of a line over the course of the day at the equinox (other days are hyperbolae) Accuracy 1 degree

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The problem with longitude

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Finding longitude Dead reckoning (deduced reckoning) – Travel times/distances between locations – Need radius of earth – Accurate at 10-20% level Clocks using a common time (eg. Greenwich mean time) – Nothing stable enough in middle ages Astronomical events as clock

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Most precise determination of longitude in 12 th century: Timing of sunset to lunar eclipse (Roger of Hereford)

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Eclipse tables used by Columbus

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City differenceLong. descrLat. descr Mecca-Damascus3.6 deg.0.15 deg Mecca-Baghdad8.3 deg0.57 deg Damascus- Baghdad 11.0 deg0.42 deg Lat/long separations in Toledo tables versus modern Longitude less precise! Travel difficult between these cities (large desert) Travel difficult between these cities (large desert)

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Fitting Toledo/Marseilles Tables Goals: – Establish typical precision of latitude – Establish typical precision of longitude – Compare zero degrees for equator to table – Find best fit to Prime Meridian Canary Islands?

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Data selection Establish correspondence with place names – Not so easy, many names have no modern correlates (Missera? Aranida?) Throw out islands – Too large for a precise target Throw out locations where dead reckoning was likely used for latitude (Gana, Urbs a Nuba) Throw out entries that looked like transcription errors.

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Locations on an equirectangular plot

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Latitude difference = ± 0.27 degrees Consistent with equator as zero Latitude difference = ± 0.27 degrees Consistent with equator as zero Longitude difference = 23.0 ± 1.3 degrees Consistent with ???? Longitude difference = 23.0 ± 1.3 degrees Consistent with ???? Latitude standard deviation = 1.4 degrees Consistent with typical shadow stick method Latitude standard deviation = 1.4 degrees Consistent with typical shadow stick method Longitude standard deviation = 6.5 degrees Consistent with dead reckoning Longitude standard deviation = 6.5 degrees Consistent with dead reckoning

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What on Earth is at 23 degrees W Long.? But but but… Cape Verde Is. discovered by Portuguese in Inconsistent with Canary Is. (16 deg. W) But but but… Cape Verde Is. discovered by Portuguese in Inconsistent with Canary Is. (16 deg. W)

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Contemporary sources Yaqut al-Hamani: the Fortunate Islands lie 200 farsakhs west of the coast of the lands of the Maghrib 600 miles consistent with Cape Verde, not Canary Is. Yaqut al-Hamani: the Fortunate Islands lie 200 farsakhs west of the coast of the lands of the Maghrib 600 miles consistent with Cape Verde, not Canary Is. Roger Bacon: placed the Prime Meridian – furthest extent of terra firma - 28 degrees W. of Toledo, inconsistent with Canary Islands Roger Bacon: placed the Prime Meridian – furthest extent of terra firma - 28 degrees W. of Toledo, inconsistent with Canary Islands

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Systematic effects?

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Diameter of the Earth? Some correlation for cities around Mediterranean Some correlation for cities around Mediterranean However, consistent w/ flat However, consistent w/ flat Would require a 20% underestimate of Earths diam. (far more precision in Muslim world) Would require a 20% underestimate of Earths diam. (far more precision in Muslim world)

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Summary Table of latitude/longitude illustrates extent of Earth known in 12 th century to the West and Muslims Latitude measurements consistent with shadow – stick method Longitude measurements consistent with dead reckoning Location of Prime Meridian at 23 degrees suggests that Muslims knew of Cape Verde Islands – more work would be needed to advance this

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