Latitude and Longitude in the
Middle ages or…
what can you learn from a table of
numbers and names about the
world of the 12th Century?
Prof. John Huth
Circa 200 AD
• Ptolemy:
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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
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)
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
Gerard of Cremona – 1114-1187 translator from Arabic to Latin
Snippet of values in Marseilles Tables
(From John Kirtland Wright, 1928)
Outer Ranges of Marseilles Tables Locations
Determining latitude: the sun throughout the year
Path of sun
in sky
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)
θ
Latitude is given by θ at shortest length of
shadow during the equinox
Accuracy ≈ 1 degree
The problem with longitude
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”
Most precise determination of longitude in 12th century:
Timing of sunset to lunar eclipse (Roger of Hereford)
Eclipse tables used by Columbus
Lat/long separations in Toledo tables versus modern
City difference
Long. descr
Lat . descr
Mecca-Damascus
3.6 deg.
0.15 deg
Mecca-Baghdad
8.3 deg
0.57 deg
DamascusBaghdad
11.0 deg
0.42 deg
Longitude less precise!
Travel difficult between
these cities (large desert)
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?
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.
Locations on an equirectangular plot
Latitude difference = -0.25 ± 0.27 degrees
 Consistent with equator as zero
Longitude difference = 23.0 ± 1.3 degrees
 Consistent with ????
Latitude standard deviation = 1.4 degrees
 Consistent with typical shadow stick method
Longitude standard deviation = 6.5 degrees
 Consistent with dead reckoning
What on Earth is at 23 degrees W Long.?
But but but…
Cape Verde Is.
discovered by
Portuguese in
1460.
Inconsistent with
Canary Is.
(16 deg. W)
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.
Roger Bacon: placed the Prime Meridian – furthest
extent of terra firma - 28 degrees W. of Toledo,
inconsistent with Canary Islands
Systematic effects?
Diameter of the Earth?
Some correlation
for cities around
Mediterranean
12.00
10.00
Deviation from 21.57
However,
consistent w/ flat
Long diff
8.00
6.00
4.00
2.00
-10.00
Would require
a 20%
underestimate
of Earth’s diam.
(far more precision
in Muslim world)
0.00
0.00
-2.00
Long diff
10.00
20.00
-4.00
-6.00
-8.00
Modern longitude
30.00
40.00
50.00
Summary
• Table of latitude/longitude illustrates extent of
Earth known in 12th 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