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Geography and cartography in the medieval Islamic world

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Medieval Islamic geography and cartographyrefer to the study ofgeographyandcartographyin theMuslim worldduring theIslamic Golden Age(variously dated between the 8th century and 16th century). Muslim scholars made advances to the map-making traditions of earlier cultures,[1]particularly theHellenisticgeographersPtolemyandMarinus of Tyre,[2]: 193 combined with what explorers and merchants learned in their travels across theOld World(Afro-Eurasia).[1]Islamic geography had three major fields: exploration and navigation,physical geography,andcartographyandmathematical geography.[1]Islamic geography reached its apex withMuhammad al-Idrisiin the 12th century.

History

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8th and 9th century

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Islamic geography began in the 8th century, influenced by Hellenistic geography,[3]combined with what explorers and merchants learned in their travels across theOld World(Afro-Eurasia).[1]Muslim scholars engaged in extensive exploration and navigation during the 9th-12th centuries, including journeys across theMuslim world,in addition to regions such as China,Southeast AsiaandSouthern Africa.[1]Various Islamic scholars contributed to the development of geography and cartography, with the most notable includingAl-Khwārizmī,Abū Zayd al-Balkhī(founder of the "Balkhi school" ),Al-Masudi,Abu Rayhan BiruniandMuhammad al-Idrisi.

Islamic geography was patronized by theAbbasidcaliphsofBaghdad.An important influence in the development of cartography was the patronage of the Abbasid caliphal-Ma'mun,who reigned from 813 to 833. He commissioned several geographers to perform anarc measurement,determining the distance on Earth that corresponds to one degree of latitude along ameridian(al-Ma'mun's arc measurement). Thus his patronage resulted in the refinement of the definition of theArabic mile(mīlin Arabic) in comparison to thestadionused in the Hellenistic world. These efforts also enabled Muslims to calculate thecircumference of the Earth.Al-Mamun also commanded the production of a large map of the world, which has not survived,[4]: 61–63 though it is known that its map projection type was based onMarinus of Tyrerather thanPtolemy.[2]: 193 

Islamic cartographers inherited Ptolemy'sAlmagestandGeographyin the 9th century. These works stimulated an interest in geography (particularly gazetteers) but were not slavishly followed.[5]Instead, Arabian and Persian cartography followedAl-Khwārizmīin adopting a rectangular projection, shifting Ptolemy'sPrime Meridianseveral degrees eastward, and modifying many of Ptolemy's geographical coordinates.

Having received Greek writings directly and without Latin intermediation, Arabian and Persian geographers made no use ofT-O maps.[5]

In the 9th century, thePersian mathematicianand geographer,Habash al-Hasib al-Marwazi,employedspherical trigonometryandmap projectionmethods in order to convertpolar coordinatesto a different coordinate system centred on a specific point on the sphere, in this theQibla,the direction toMecca.[6]Abū Rayhān Bīrūnī(973–1048) later developed ideas which are seen as an anticipation of the polar coordinate system.[7]Around 1025, he describes a polar equi-azimuthal equidistant projectionof thecelestial sphere.[8]: 153 However, this type of projection had been used in ancient Egyptian star-maps and was not to be fully developed until the 15 and 16th centuries.[9]

Khordadbeh–Jayhani tradition

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The works ofIbn Khordadbeh(c.870) andJayhani(c.910s) were at the basis of a new Perso-Arab tradition in Persia and Central Asia.[10]The exact relationship between the books of Khordadbeh and Jayhani is unknown, because the two books had the same title, have often been mixed up, and Jayhani's book has been lost, so that it can only be approximately reconstructed from the works of other authors (mostly from the eastern parts of the Islamic world[11]) who seem to have reused some of its contents.[10][12]According toVasily Bartold,Jayhani based his book primarily on the data he had collected himself, but also reused Khordadbeh's work to a considerable extent.[10]Unlike the Balkhi school, geographers of the Khordadbeh–Jayhani tradition sought to describe the whole world as they knew it, including the lands, societies and cultures of non-Muslims.[13]Asvizierof theSamanid Empire,Jayhani's diplomatic correspondence allowed him to collect much valuable information from people in faraway lands.[14]Nevertheless,Al-Masudicriticised Jayhani for overemphasising geological features of landscapes, stars and geometry, taxation systems, trade roads and stations allegedly few people used, while ignoring major population centres, provinces and military roads and forces.[15]

Balkhi school

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The Balkhī school of terrestrial mapping, originated byAbu Zayd al-Balkhi(fromBalkh) in early 10-thcenturyBaghdad,and significantly developed byIstakhri,[11]had a conservative and religious character: it was only interested in describingmamlakat al-Islām( "Islamic lands" ), which the school divided into 20 or moreiqlīms( "climes" or provinces).[13]Balkhi and his followers reoriented geographic knowledge in order to bring it in line with certain concepts found in theQuran,emphasised the central importance ofMeccaandArabia,and ignored the non-Islamic world.[13]This distinguished them from earlier geographers such asIbn KhordadbehandAl-Masudi,who described the whole world as they knew it.[13] The geographers of this school, such asIstakhri,al-MuqaddasiandIbn Hawqal,wrote extensively of the peoples, products, and customs of areas in the Muslim world, with little interest in the non-Muslim realms,[4]and produced worldatlases,each one featuring aworld mapand twenty regional maps.[2]: 194 

Regional cartography

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Map ofFarsfrom theKitab al-Masalik wa'l-Mamalik(Book of postal routes and kingdoms) ofal-Istakhri

Islamic regional cartography is usually categorized into three groups: that produced by the "Balkhī school",the type devised byMuhammad al-Idrisi,and the type that are uniquely found in theBook of curiosities.[4]

The maps by the Balkhī schools were defined by political, not longitudinal boundaries and covered only the Muslim world. In these maps the distances between various "stops" (cities or rivers) were equalized. The only shapes used in designs were verticals, horizontals, 90-degree angles, and arcs of circles; unnecessary geographical details were eliminated. This approach is similar to that used insubwaymaps, most notable used in the "London UndergroundTube Map"in 1931 byHarry Beck.[4]: 85–87 

Al-Idrīsī defined his maps differently. He considered the extent of the known world to be 160° and had to symbolize 50 dogs in longitude and divided the region into ten parts, each 16° wide. In terms of latitude, he portioned the known world into seven 'climes', determined by the length of the longest day. In his maps, many dominant geographical features can be found.[4]

Book on the appearance of the Earth

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Muhammad ibn Mūsā al-Khwārizmī'sKitāb ṣūrat al-Arḍ( "Book on the appearance of the Earth" ) was completed in 833. It is a revised and completed version ofPtolemy'sGeography,consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.[16]

Al-Khwārizmī,Al-Ma'mun's most famous geographer, corrected Ptolemy's gross overestimate for the length of theMediterranean Sea[2]: 188 (from theCanary Islandsto the eastern shores of the Mediterranean); Ptolemy overestimated it at 63 degrees oflongitude,while al-Khwarizmi almost correctly estimated it at nearly 50 degrees of longitude. Al-Ma'mun's geographers "also depicted theAtlanticandIndian Oceansasopen bodies of water,not land-lockedseasas Ptolemy had done. "[17]Al-Khwarizmi thus set thePrime Meridianof theOld Worldat the eastern shore of the Mediterranean, 10–13 degrees to the east ofAlexandria(the prime meridian previously set by Ptolemy) and 70 degrees to the west ofBaghdad.Most medieval Muslim geographers continued to use al-Khwarizmi's prime meridian.[2]: 188 Other prime meridians used were set byAbū Muhammad al-Hasan al-HamdānīandHabash al-Hasib al-MarwaziatUjjain,a centre ofIndian astronomy,and by another anonymous writer atBasra.[2]: 189 

Al-Biruni

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Diagram illustrating a method proposed and used byAl-Birunito estimate the radius and circumference of the Earth in the 11th century.

Abu Rayhan al-Biruni(973–1048) devised a novel method of determining the Earth's radius by means of the observation of the height of a mountain. He carried it out atNandanainPind Dadan Khan(present-day Pakistan).[18]He used trigonometry to calculate the radius of the Earth using measurements of the height of a hill and measurement of the dip in the horizon from the top of that hill. His calculated radius for the Earth of 3928.77 miles was 2% higher than the actual mean radius of 3847.80 miles.[19]His estimate was given as 12,803,337cubits,so the accuracy of his estimate compared to the modern value depends on what conversion is used for cubits. The exact length of a cubit is not clear; with an 18 inch cubit his estimate would be 3,600 miles, whereas with a 22 inch cubit his estimate would be 4,200 miles.[20]One significant problem with this approach is that Al-Biruni was not aware ofatmospheric refractionand made no allowance for it. He used a dip angle of 34 arc minutes in his calculations, but refraction can typically alter the measured dip angle by about 1/6, making his calculation only accurate to within about 20% of the true value.[21]

In hisCodex Masudicus(1037), Al-Biruni theorized the existence of a landmass along the vast ocean betweenAsiaandEurope,or what is today known as theAmericas.He argued for its existence on the basis of his accurate estimations of theEarth's circumferenceandAfro-Eurasia's size, which he found spanned only two-fifths of the Earth's circumference, reasoning that the geological processes that gave rise toEurasiamust surely have given rise to lands in the vast ocean between Asia and Europe. He also theorized that at least some of the unknown landmass would lie within the known latitudes which humans could inhabit, and therefore would be inhabited.[22]

Tabula Rogeriana

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Main article:Tabula Rogeriana

The Arab geographerMuhammad al-Idrisiproduced his medieval atlas,Tabula RogerianaorThe Recreation for Him Who Wishes to Travel Through the Countries,in 1154. He incorporated the knowledge ofAfrica,theIndian Oceanand theFar Eastgathered byArab merchantsand explorers with the information inherited from the classical geographers to create the most accurate map of the world in pre-modern times.[23]With funding fromRoger II of Sicily(1097–1154), al-Idrisi drew on the knowledge collected at the University ofCordobaand paid draftsmen to make journeys and map their routes. The book describes the Earth as a sphere with a circumference of 22,900 miles (36,900 km) but maps it in 70 rectangular sections. Notable features include the correct dual sources of the Nile, the coast of Ghana and mentions of Norway. Climate zones were a chief organizational principle. A second and shortened copy from 1192 calledGarden of Joysis known by scholars as theLittle Idrisi.[24]

On the work of al-Idrisi, S. P. Scott commented:[23]

The compilation of Edrisi marks an era in thehistory of science.Not only is its historical information most interesting and valuable, but its descriptions of many parts of the earth are still authoritative. For three centuries geographers copied his maps without alteration. The relative position of the lakes which form the Nile, as delineated in his work, does not differ greatly from that established by Baker and Stanley more than seven hundred years afterwards, and their number is the same. The mechanical genius of the author was not inferior to his erudition. The celestial and terrestrialplanisphereof silver which he constructed for his royal patron was nearly six feet in diameter, and weighed four hundred and fifty pounds; upon the one side the zodiac and the constellations, upon the other—divided for convenience into segments—the bodies of land and water, with the respective situations of the various countries, were engraved.

— S. P. Scott, History of the Moorish Empire in Europe

Al-Idrisi's atlas, originally called theNuzhatin Arabic, served as a major tool for Italian, Dutch and French mapmakers from the 16th century to the 18th century.[25]

Piri Reis map

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Main article:Piri Reis map

ThePiri Reis mapis aworld mapcompiled in 1513 by theOttomanadmiral and cartographerPiri Reis.Approximately one third of the map survives; it shows the western coasts ofEuropeandNorth Africaand the coast ofBrazilwith reasonable accuracy. Various Atlantic islands, including theAzoresandCanary Islands,are depicted, as is the mythical island ofAntilliaand possiblyJapan.

Others

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Suhrāb, a late 10th-century Muslim geographer, accompanied a book of geographicalcoordinateswith instructions for making a rectangular world map, withequirectangular projectionor cylindrical equidistant projection.[4]The earliest surviving rectangular coordinate map is dated to the 13th century and is attributed to Hamdallah al-Mustaqfi al-Qazwini,who based it on the work of Suhrāb. Theorthogonalparallel lines were separated by one degree intervals, and the map was limited toSouthwest AsiaandCentral Asia.The earliest surviving world maps based on a rectangular coordinate grid are attributed to al-Mustawfi in the 14th or 15th century (who used invervals of ten degrees for the lines), and toHafiz-i Abru(died 1430).[2]: 200–01 

In the 11th century, the Karakhanid Turkic scholarMahmud al-Kashgariwas the first to draw a unique Islamicworld map,[26]where he illuminated the cities and places of theTurkic peoplesofCentralandInner Asia.He showed the lakeIssyk-Kul(in nowadaysKyrgyzstan) as the centre of the world.

Ibn Battuta(1304–1368?) wrote "Rihlah" (Travels) based on three decades of journeys, covering more than 120,000 km through northern Africa, southern Europe, and much of Asia.

Muslim astronomersand geographers were aware ofmagnetic declinationby the 15th century, when the Egyptian astronomer'Abd al-'Aziz al-Wafa'i(d. 1469/1471) measured it as 7 degrees fromCairo.[27]

Instruments

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Astrolabe from 9th century North Africa

Muslim scholars invented and refined a number of scientific instruments in mathematical geography and cartography. These included theastrolabe,quadrant,gnomon,celestial sphere,sundial,andcompass.[1]

Astrolabe

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Astrolabeswere adopted and further developed in themedieval Islamic world,whereMuslim astronomersintroduced angular scales to the design,[28]adding circles indicatingazimuthson thehorizon.[29]It was widely used throughout the Muslim world, chiefly as an aid to navigation and as a way of finding theQibla,the direction ofMecca.Eighth-centurymathematicianMuhammad al-Fazariis the first person credited with building the astrolabe in the Islamic world.[30]

The mathematical background was established by Muslim astronomerAlbateniusin his treatiseKitab az-Zij(c. 920 AD), which was translated into Latin byPlato Tiburtinus(De Motu Stellarum). The earliest surviving astrolabe is datedAH315 (927–28 AD). In the Islamic world, astrolabes were used to find the times of sunrise and the rising of fixed stars, to help schedule morning prayers (salat). In the 10th century,al-Sufifirst described over 1,000 different uses of an astrolabe, in areas as diverse asastronomy,astrology,navigation,surveying,timekeeping, prayer,Salat,Qibla,etc.[31][32]

Compass

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See also:History of the compass
Al-Ashraf's diagram of the compass and Qibla. From MS Cairo TR 105, copied in Yemen, 1293.[33]

The earliest reference to acompassin theMuslim worldoccurs in aPersiantalebook from 1232,[34][35]where a compass is used for navigation during a trip in theRed Seaor thePersian Gulf.[36]The fish-shaped iron leaf described indicates that this early Chinese design has spread outside of China.[37]The earliestArabicreference to a compass, in the form of magnetic needle in a bowl of water, comes from a work by Baylak al-Qibjāqī, written in 1282 while in Cairo.[34][38]Al-Qibjāqī described a needle-and-bowl compass used for navigation on a voyage he took from Syria to Alexandria in 1242.[34]Since the author describes having witnessed the use of a compass on a ship trip some forty years earlier, some scholars are inclined to antedate its first appearance in theArab worldaccordingly.[34]Al-Qibjāqī also reports that sailors in the Indian Ocean used iron fish instead of needles.[39]

Late in the 13th century, theYemeniSultan andastronomeral-Malik al-Ashrafdescribed the use of the compass as a "Qiblaindicator "to find the direction toMecca.[40]In a treatise aboutastrolabesandsundials,al-Ashraf includes several paragraphs on the construction of a compass bowl (ṭāsa). He then uses the compass to determine the north point, themeridian(khaṭṭ niṣf al-nahār), and the Qibla. This is the first mention of a compass in a medieval Islamic scientific text and its earliest known use as a Qibla indicator, although al-Ashraf did not claim to be the first to use it for this purpose.[33][41]

In 1300, an Arabic treatise written by theEgyptianastronomer andmuezzinIbn Simʿūn describes a dry compass used for determining qibla. Like Peregrinus' compass, however, Ibn Simʿūn's compass did not feature a compass card.[33]In the 14th century, theSyrianastronomer and timekeeperIbn al-Shatir(1304–1375) invented atimekeepingdevice incorporating both a universalsundialand a magnetic compass. He invented it for the purpose of finding the times ofprayers.[42]Arab navigatorsalso introduced the 32-pointcompass roseduring this time.[43]In 1399, an Egyptian reports two different kinds of magnetic compass. One instrument is a “fish” made of willow wood or pumpkin, into which a magnetic needle is inserted and sealed with tar or wax to prevent the penetration of water. The other instrument is a dry compass.[39]

In the 15th century, the description given byIbn Majidwhile aligning the compass with the pole star indicates that he was aware ofmagnetic declination.An explicit value for the declination is given by ʿIzz al-Dīn al-Wafāʾī (fl. 1450s in Cairo).[36]

Premodern Arabic sources refer to the compass using the termṭāsa(lit. "bowl" ) for the floating compass, orālat al-qiblah( "qibla instrument" ) for a device used for orienting towards Mecca.[36]

Friedrich Hirthsuggested that Arab and Persian traders, who learned about the polarity of the magnetic needle from the Chinese, applied the compass for navigation before the Chinese did.[44]However, Needham described this theory as "erroneous" and "it originates because of a mistranslation" of the termchia-lingfound inZhu Yu's bookPingchow Table Talks.[45]

Notable geographers

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Khordadbeh–Jayhani tradition geographers

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Balkhi school geographers

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  • Abu Zayd al-Balkhi(850–934):Suwar al-aqālīm( "Images of the Climes" )[11]oral-Amthila wa-suwar al-ard( "Similitudes and Images of the Earth" ), written in 920 or after[11]

Others

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See also

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References

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Citations

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  1. ^abcdefBuang, Amriah (2014). "Geography in the Islamic World".Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures.Springer. pp. 1–5.doi:10.1007/978-94-007-3934-5_8611-2.ISBN978-94-007-3934-5.A prominent feature of the achievement of Muslim scholars in mathematical geography and cartography was the invention of scientific instruments of measurement. Among these were the astrolab (astrolabe), the ruba (quadrant), the gnomon, the celestial sphere, the sundial, and the compass.
  2. ^abcdefgKennedy, Edward S. (1996). "Mathematical Geography". In Rashed, Roshdi; Morelon, Régis (eds.).Encyclopedia of the History of Arabic Science.Vol. 3. Routledge. pp. 185–201.ISBN978-0-415-12410-2.
  3. ^Gerald R. Tibbetts,The Beginnings of a Cartographic Tradition,in: John Brian Harley, David Woodward:Cartography in the Traditional Islamic and South Asian Societies,Chicago, 1992, pp. 90–107 (97-100),ISBN0-226-31635-1
  4. ^abcdefEdson and Savage-Smith (2004)[full citation needed]
  5. ^abEdson & Savage-Smith 2004,pp. 61–63.
  6. ^Koetsier, T.; Bergmans, L. (2005).Mathematics and the Divine.Elsevier.p.169.ISBN978-0-444-50328-2.
  7. ^O'Connor, John J.;Robertson, Edmund F.,"Abu Arrayhan Muhammad ibn Ahmad al-Biruni",MacTutor History of Mathematics Archive,University of St Andrews
  8. ^King, David A. (1996). "Astronomy and Islamic society: Qibla, gnomics and timekeeping". In Rashed, Roshdi (ed.).Encyclopedia of the History of Arabic Science.Vol. 1. London, UK and New York, USA:Routledge.pp. 128–184.
  9. ^Rankin, Bill (2006)."Projection Reference".Radical Cartography.
  10. ^abcdefBosworth & Asimov 2003,p. 217–218.
  11. ^abcdBosworth & Asimov 2003,p. 218.
  12. ^Minorsky 1937,p. xvi–xvii.
  13. ^abcdefghijklBosworth & Asimov 2003,p. 219.
  14. ^abcdeMinorsky 1937,p. xvii.
  15. ^Minorsky 1937,p. xviii.
  16. ^O'Connor, John J.;Robertson, Edmund F.,"Cartography",MacTutor History of Mathematics Archive,University of St Andrews
  17. ^Covington, Richard (2007)."Nation, identity and the fascination with forensic science in Sherlock Holmes and CSI".Saudi Aramco World, May–June 2007.10(3): 17–21.doi:10.1177/1367877907080149.S2CID145173935.Archived fromthe originalon 2008-05-12.Retrieved2008-07-06.
  18. ^Pingree 2010b.
  19. ^Sparavigna, Amelia (2013)."The Science of Al-Biruni".International Journal of Sciences.2(12): 52–60.arXiv:1312.7288.doi:10.18483/ijSci.364.S2CID119230163.
  20. ^Douglas (1973, p.211)
  21. ^Huth, John Edward (2013).The Lost Art of Finding Our Way.Harvard University Press. pp. 216–217.ISBN9780674072824.
  22. ^Starr, S. Frederick(12 December 2013)."So, Who Did Discover America? | History Today".historytoday.Retrieved2018-07-06.
  23. ^abScott, S. P. (1904).History of the Moorish Empire in Europe.Harvard University Press. pp. 461–2.
  24. ^"Slide #219: World Maps of al-Idrisi".Henry Davis Consulting.Archived fromthe originalon 2006-06-26.Retrieved2019-09-08.
  25. ^Glick, Thomas F.; Livesey, Steven; Wallis, Faith (2014).Medieval Science, Technology, and Medicine: An Encyclopedia.Routledge. p. 261.ISBN9781135459321.
  26. ^Hermann A. Die älteste türkische Weltkarte (1076 η. Ch.) // Imago Mundi: Jahrbuch der Alten Kartographie. — Berlin, 1935. — Bd.l. — S. 21—28.
  27. ^Barmore, Frank E. (April 1985), "Turkish Mosque Orientation and the Secular Variation of the Magnetic Declination",Journal of Near Eastern Studies,44(2),University of Chicago Press:81–98 [98],doi:10.1086/373112,S2CID161732080
  28. ^See p. 289 ofMartin, L. C. (1923), "Surveying and navigational instruments from the historical standpoint",Transactions of the Optical Society,24(5): 289–303,Bibcode:1923TrOS...24..289M,doi:10.1088/1475-4878/24/5/302,ISSN1475-4878.
  29. ^Berggren, J. Lennart (2007),"Mathematics in Medieval Islam",in Katz, Victor J. (ed.),The Mathematics of Egypt, Mesopotamia, China, India, and Islam: a Sourcebook,Princeton University Press,p. 519,ISBN978-0-691-11485-9
  30. ^Richard Nelson Frye:Golden Age of Persia.p. 163
  31. ^Dr. Emily Winterburn (National Maritime Museum),Using an Astrolabe,Foundation for Science Technology and Civilisation, 2005.
  32. ^Lachièz-Rey, Marc; Luminet, Jean-Pierre (2001).Celestial Treasury: From the Music of Spheres to the Conquest of Space.Trans. Joe Laredo. Cambridge, UK: Cambridge University Press. p. 74.ISBN978-0-521-80040-2.
  33. ^abcSchmidl, Petra G. (1996–97)."Two Early Arabic Sources On The Magnetic Compass".Journal of Arabic and Islamic Studies.1:81–132.doi:10.5617/jais.4547.http:// uib.no/jais/v001ht/01-081-132schmidl1.htm#_ftn4Archived2014-09-02 at theWayback Machine
  34. ^abcdKreutz, Barbara M. (1973) "Mediterranean Contributions to the Medieval Mariner's Compass",Technology and Culture,14(3: July), p. 367–383JSTOR3102323
  35. ^Jawāmeʿ al-ḥekāyāt wa-lawāmeʿ al-rewāyātby Muhammad al-ʿAwfī
  36. ^abcSchmidl, Petra G. (2014-05-08). "Compass". In Ibrahim Kalin (ed.).The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam.Oxford University Press. pp. 144–6.ISBN978-0-19-981257-8.
  37. ^Needham p. 12-13 "...that the floating fish-shaped iron leaf spread outside China as a technique, we know from the description of Muhammad al' Awfi just two hundred years later"
  38. ^Kitāb Kanz al-tujjār fī maʿrifat al-aḥjār
  39. ^ab"Early Arabic Sources on the Magnetic Compass"(PDF).Lancaster.ac.uk.Retrieved2016-08-02.
  40. ^Savage-Smith, Emilie (1988). "Gleanings from an Arabist's Workshop: Current Trends in the Study of Medieval Islamic Science and Medicine".Isis.79(2): 246–266 [263].doi:10.1086/354701.PMID3049439.S2CID33884974.
  41. ^Schmidl, Petra G. (2007)."Ashraf: al-Malik al-Ashraf (Mumahhid al-Dīn) ʿUmar ibn Yūsuf ibn ʿUmar ibn ʿAlī ibn Rasūl".In Thomas Hockey; et al. (eds.).The Biographical Encyclopedia of Astronomers.New York: Springer. pp. 66–7.ISBN9780387310220.(PDF version)
  42. ^(King 1983,pp. 547–8)
  43. ^Tibbetts, G. R. (1973). "Comparisons between Arab and Chinese Navigational Techniques".Bulletin of the School of Oriental and African Studies.36(1): 97–108 [105–6].doi:10.1017/s0041977x00098013.S2CID120284234.
  44. ^Hirth, Friedrich (1908).Ancient history of China to the end of the Chóu dynasty.New York, The Columbia university press. p.134.
  45. ^Needham, Joseph (1962).Science and Civilisation in China: Volume 4, Physics and Physical Technology, Part 1, Physics.Cambridge University Press. pp. 279–80.ISBN978-0-521-05802-5.
  46. ^abMinorsky 1937,p. xix.
  47. ^Bosworth & Asimov 2003,p. 218–219.
  48. ^Minorsky 1937,p. xviii–xix, 5.
  49. ^abMinorsky 1937,p. xviii–xix.

Sources

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