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ABSTRACT
The earliest known historical clue to what might be a primitive nautical chart is in a medieval manuscript of c.1200, the Liber de existencia riveriarum et forma maris nostri mediterranei, which describes the Mediterranean Sea. The body of the manuscript consists of an account of the Mediterranean and Black seas and the Atlantic coasts of Europe and northern Africa organized in 45 regional sections, each introduced by a short text setting out the orientation and size of the region, followed by a portolan-like listing of contiguous coastal localities with the distances between them. These are complemented by additional tracks across the open sea (pelagic tracks) for which both distances and directions are provided. Two distinct types of directions can be distinguished: those not affected by magnetic declination, which indicates that they were probably determined by astronomical methods, and those affected by systematic errors that could only have originated in observations made with a marine compass. It is suggested that some of the pelagic courses in the Liber were compiled from an existing chart or sketch based on astronomical directions, which may have been used as a general reference for the work. The implication is that the genesis and technical evolution of the medieval portolan chart were more complex than has hitherto been thought by map historians, who have based their analyses on the few extant exemplars from the end of the thirteenth and beginning of the fourteenth centuries, all based on compass directions.
Le Liber de existencia riveriarum (vers 1200) et la naissance de la cartographie nautique
L’indice historique le plus ancien de ce qui pourrait être une carte nautique primitive se trouve dans un manuscrit daté d’environ 1200, le Liber de existencia riveriarum et forma maris nostri mediterranei, qui décrit la mer Méditerranée. Le corps du manuscrit consiste en une description de la mer Méditerranée, de la mer Noire et des côtes européennes de l’océan Atlantique, organisée en 45 sections, chacune introduite par un bref texte qui décrit l’orientation et la taille de la région, suivi d’une liste de paires de localités côtières, avec les distances entre elles, à la manière d’un portulan. D’autres paires de lieux concernent des parcours en pleine mer (parcours pélagiques), pour lesquels sont fournis à la fois les distances et les directions. Deux catégories différentes de directions peuvent être distinguées: celles qui ne sont pas affectées par la déclinaison magnétique, ce qui indique qu’elles ont probablement été déterminées par des méthodes astronomiques, et celles qui sont affectées par des erreurs systématiques, qui ne peuvent trouver leur origine que dans des observations faites à la boussole. Il est suggéré que certaines des routes de pleine mer dans le Liber furent compilées à partir d’une carte existante, qui aurait pu être utilisée comme source générale pour l’ouvrage. Ceci implique que la genèse et l’évolution technique de la carte-portulan médiévale fut un processus plus complexe que ne l’ont pensé jusqu’à présent les historiens de la cartographie, qui avaient fondé leurs analyses sur les quelques exemplaires existants de la fin du XIIIe et du début du XIVe siècle, tous construits d’après les directions de la boussole.
Das Liber de existencia riveriarum (um 1200) und die Geburt der Seekartographie
Der früheste bekannte historische Hinweis auf ein Dokument, das man als einfache Seekarte ansprechen könnte, befindet sich in einem, das Mittelmeer beschreibenden Manuskript aus der Zeit um 1200, dem Liber de existencia riveriarum et forma maris nostri mediterranei. Den Hauptteil des Manuskripts bildet die Beschreibung des Mittelmeeres, des Schwarzen Meeres sowie der europäischen Atlantikküste in 45 regional differenzierten Sektionen. Diese bestehen jeweils aus einem kurzen Text, in dem die Orientierung und die Größe der Region behandelt werden und einer Liste von entlang der Küsten gelegenen Ortspaaren mit der Angabe ihres Abstandes ähnlich den Portolanen. Weitere Listen kombinieren paarweise Örtlichkeiten, die durch offenes Meer getrennt sind, mit der Angabe von Richtung und Entfernung zwischen diesen. Zwei unterschiedliche Typen von Richtungsangaben können festgestellt werden: solche, die nicht durch die magnetische Deklination beeinflusst werden, was darauf hinweist, dass sie vermutlich mit Hilfe von astronomischen Methoden bestimmt wurden und solche, die systematische Fehler erkennen lassen, die nur durch die Verwendung eines Schiffskompasses verursacht worden sein können. Es ist davon auszugehen, dass einige der Routen über offenes Meer im Liber aus einer existierenden Seekarte übernommen wurden, die eventuell als grundlegende Quelle für das Werk diente. Die Folge ist, dass Entstehung und technische Entwicklung der mittelalterlichen Portolankarten auf einem wesentlich komplexeren Prozess basieren, als das bisher von Kartenhistorikern angenommen wurde, deren Analysen vor allem die wenigen Exemplare vom Ende des 13. und des beginnenden 14. Jahrhunderts in den Blick nahmen, die alle auf der Verwendung von Kompasskursen aufbauen.
El Liber de existencia riveriarum (c.1200) y el nacimiento de la cartografía náutica
El primer indicio histórico conocido de lo que pudo ser una primitiva carta náutica se encuentra en un manuscrito medieval de c.1200, el Liber de existencia riveriarum et forma maris nostri mediterranei, que describe el mar Mediterráneo. El conjunto del manuscrito consiste en una descripción de los mares Mediterráneo y Negro y las costas europeas del Atlántico, organizado en 45 secciones regionales, cada una introducida por un texto corto describiendo la orientación y tamaño de la región, seguido por una especie de portulano que lista parejas de localidades costeras con la distancia entre ellas. Otras parejas de lugares relatan las vías a través del mar abierto (vías pelágicas) para las cuales se proporcionan distancias y direcciones. Se pueden distinguir dos tipos distintos de direcciones: aquellas no afectadas por la declinación magnética que indican que probablemente han sido determinadas por métodos astronómicos, y las que han sido afectadas por errores sistemáticos que sólo podrían haberse originado en observaciones hechas con la brújula. Se ha sugerido que algunas de estas rutas pelágicas en el Liber fueron compilados de una carta original que puede haberse usado como referencia general para el trabajo. La implicación es que la génesis y la evolución técnica de la carta portulana medieval fue un proceso más complejo de lo que hasta ahora habían pensado los historiadores de la cartografía que habían fundado sus análisis en unos pocos ejemplares del final del siglo XIII y comienzos del XIV, todos basados en las direcciones de la brújula.
Acknowledgements
I warmly thank Domingos Lucas Dias, Ricardo Nobre, Mary Pedley and Wouter Bracke for their invaluable expert help in the translation and interpretation of the prologue of the Liber de existencia riueriarum, without which this enterprise would not have been possible. I also thank Patrick Gautier Dalché, Ramon Pujades and Tony Campbell for their kind reading of a preliminary version of this article and for providing suggestions of improvement; failure to consult them would have been negligent on my part. The fact that we do not always agree is part of scholarship.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 714033-MEDEA-CHART/ERC-2016-STG).
Notes
1. Adolf Erik Nordenskjöld, Periplus: An Essay on the Early History of Charts and Sailing-Directions (Stockholm, P.A., Norstedt, 1897).
2. Tony Campbell, ‘Portolan charts from the late thirteenth century to 1500’, in The History of Cartography, vol. 1: Cartography in Prehistoric, Ancient, and Medieval Europe and the Mediterranean (Chicago, University of Chicago Press, 1987), 371–463; Ramón Pujades i Bataller, Les cartes portolanes: la representació medieval d’una mar solcada (Barcelona, Institut Cartogràfic de Catalunya, 2007). Tony Campbell continues to complement his 1987 chapter with a series of online-studies headed A Critical Re-examination of Portolan Charts with a Reassessment of Their Replication and Seaboard Function. These contain corrections to and updates of the original chapter, with essays on specific aspects such as the cartographical innovations introduced in the earliest charts, the dating of the Carte Pisane, and the study of conventional shapes and colours in the representation of islands and estuaries: http://www.maphistory.info/portolan.html (last consulted August 2018).
3. Campbell, ‘Portolan charts from the late thirteenth century to 1500’ (see note 2), 380.
4. Ibid., 385.
5. Ibid., 384.
6. Pujades, Les cartes portolanes (see note 2,), 514.
7. Ibid., 514–15; 517–18. My opinion, however, is that maps drawn to scale already existed before the earliest portolan charts were constructed (for example, those in the 12th-century Tabula Rogeriana and, to a lesser extent, in the 11th-century Book of Curiosities), which demonstrate that this particular innovation was not strictly necessary in the genesis of the portolan chart.
8. Pujades, Les cartes portolanes (see note 2), 512–15.
9. Jonathan Lanman, On the Origin of Portolan Charts (The Hermon Dunlap Smith Center for the History of Cartography, Occasional Publication No. 2, 1987). Lanman used the navigational information on courses and distances between adjacent ports along the shores of the Mediterranean in Lo Compasso de Navegare (1296) and in the Parma-Magliabechhi Portolano (15th century) to reproduce its coastlines. He then compared the results with the corresponding outlines on a modern map and with two portolan charts, the Carte Pisane (c.1280) and the Matteo Prunes chart of 1559.
10. In my view, Lamnan’s results would have benefited from better information on the spatial distribution of magnetic declination in the region (unavailable at the time) and by referring to the routes between distant places. The use of the short distance tracks only—those between adjacent coastal places—in the reconstruction of a chart is historically unconvincing. It is my conviction that the earliest nautical sketches of the Mediterranean were made using pelagic tracks, that is, tracks connecting places across large stretches of open water.
11. Scott Allen Loomer, ‘A Cartometric Analysis of Portolan Charts: A Search for Methodology’ (unpublished doctoral dissertation, Madison, University of Wisconsin, 1987).
12. It must be stressed that Loomer emphatically stated that in his view the medieval cartographers did not consciously adopt any formal map projection. What he said was that the construction method may have preserved characteristics of the underlying data which could be inferred from the properties of the best fitting projection. See Loomer, ‘A Cartometric Analysis of Portolan Charts’ (note 11), 107.
13. For the description of a recent model for estimating magnetic declination in ancient times, see M. Korte, F. Donadini and C. G. Constable, ‘Geomagnetic field for 0–3 ka: 2. A new series of time-varying global models’, G3—Geochemistry, Geophysics, Geosystems 10:6 (2009, online); M. Korte and C.G. Constable, ‘Continuous geomagnetic field models for the past 7 millennia: 2. CALS7K’, G3—Geochemistry, Geophysics, Geosystems 6:1 (2005, online).
14. The average tilt of the charts remained approximately constant to the end of the 16th century despite the changing secular variation of magnetic declination. See Joaquim Alves Gaspar, ‘Dead reckoning and magnetic declination: unveiling the mystery of portolan charts’, e-Perimetron 3:4 (2008): 191–203.
15. For a general description of the methods of cartometric analysis and numerical modelling alluded here, see Joaquim Alves Gaspar, ‘From the Portolan Chart of the Mediterranean to the Latitude Chart of the Atlantic: Cartometric Analysis and Modeling’ (unpublished doctoral dissertation, Lisboa, Universidade Nova de Lisboa, 2010), 45–84; idem, ‘Using empirical map projections for modeling early nautical charts’, in Advances in Cartography and GIScience, vol. 2: Selection from ICC 2011, ed. A. Ruas (Paris, Lecture Notes in Geoinformation and Cartography 6; Berlin and Heidelberg, Springer Verlag, 2011), 227–47.
16. Gaspar, ‘Dead reckoning and magnetic declination’ (see note 14).
17. This method of construction continued to be employed in nautical cartography up to the middle of the 18th century, when the longitude problem was solved, and the Mercator projection was fully adopted for navigation. An early textbook discussing the geometry and construction of portolan charts is Pedro Nunes, Tratado en defensam da carta de marear [Treatise in defence of the nautical chart], in Pedro Nunes, Obras, vol. 1: Tratado da Sphera (1537; Lisboa, Academia das Ciências de Lisboa & Fundação Calouste Gulbenkian, 2002), 120–84, at 134–35.
18. The large confidence interval results from the uncertainty of the calibration curve used in the dating process. The most probable date of c.1245 is merely the median of the probability curve, which is asymmetrical. See Catherine Hofmann, ‘Is the Carta Pisana still the oldest known marine chart? The results of laboratory analysis and radiocarbon dating’ (unpublished paper presented at the International Workshop for the Origin and Evolution of Portolan Charts, Lisbon, 6–7 June 2016). For a discussion of the dating of the Carte Pisane see Ramon Pujades. ‘The Pisana Chart: really a primitive portolan chart made in the 13th century?’, Cartes et géomatique 216 (June 2013): 17–32; and Tony Campbell, ‘Dating the Carte Pisane’, cartographic innovations by the early portolan chart makers’, http://www.maphistory.info/PortolanChartInnovations.html#pisane (consulted in August 2018). A more detailed study by Campbell, based on the analysis of toponymy, hydrography and drafting conventions, is ‘Does the Carte Pisane need to be redated?’ http://www.maphistory.info/CartePisaneMenu.html.
19. The Cortona chart is in the Biblioteca dell’Accademia Etrusca in Cortona, Italy. Its usual dating, to the first decades of the fourteenth century, was recently challenged by Jacques Mille, who considers that it may predate the Carte Pisane: see Jacques Mille, The French Mediterranean Coasts on Portolan Charts (self-published and presented at the International Workshop on the Origin and Evolution of Portolan Charts, Lisbon, 6–7 June 2016), 25–28. The Avignon chart, of which a fragment was rediscovered in 2002, depicts the western Mediterranean with part of the European Atlantic coasts including the east coast of Britain. Jacques Mille and Paul Fermon consider that the chart was likely to have been completed c.1300; see Jacques Mille and Paul Fermon, Une carte portulan récemment découverte. Peut-être une des plus anciennes conservées? La carte d’Avignon, published online by the Brussels Map Circle: http://www.bimcc.org/history-of-cartography/avignon-chart (last consulted August 2018); Jacques Mille and Paul Fermon, ‘A recently discovered portolan chart. Maybe one of the oldest extant? The Avignon chart’, Maps in History (Brussels, Brussels Map Circle) 59 (September 2017): 19–25. The Lucca fragment, discovered in 2000 and now in the Archivio di Stato of Lucca, Italy, was studied by Philipp Billion, who suggested a date of before 1327: Philipp Billion, ‘A newly discovered chart fragment from the Lucca archives, Italy’, Imago Mundi, 63:1 (2011): 1–21.
20. The term ‘formative period’ is Tony Campbell’s: see http://www.maphistory.info/CartePisaneTEXT.html#methodology.
21. This possibility is reinforced by the fact, mentioned above, that the average tilt of the extant charts remained more or less constant until the end of the 16th century, indicating that it had not been adjusted since the first prototype charts were produced. The earliest known mention of the use of magnetic compasses in the Mediterranean is in the two texts compiled c.1190 by the English monk Alexander Neckam: De Naturis Rerum and De Utensilibus. See Thomas Wright, ed., De naturis rerum libri duo (London, Longman, Green, Longman, Roberts, and Green, 1863); ‘The Treatise De Utensilibus of Alexander Neckam’, ed. Thomas Wright, in A Volume of Vocabularies (London, 1857), 96–120.
22. The Liber de existência riveriarum et forma maris nostri mediterranei is London, British Library, Cotton MS Domitian A XIII, fols. 114r–129v.
23. Roberto Almagià, Monumenta Cartographica Vaticana, vol. 1: Planisferi, Carte Nautiche e Affini Dal Sec. XIV al XVII Esistenti Nella Biblioteca Vaticana (Città del Vaticano, Biblioteca Apostolica Vaticana, 1944), 133 ff; Patrick Gautier Dalché, Carte marine et portulan au XIIe Siècle. Le Liber de Existencia Riveriarum et Forma Maris Nostri Mediterranei (Pise, circa 1200) (Rome, Palais Farnèse: École Française de Rome, 1995).
24. Gautier Dalché, Carte marine et portulan (note 23), 7–16.
25. Pujades, Les cartes portolanes (note 2), 519, n.76. Gautier Dalché later acknowledged Pujades’s remark in ‘Les cartes marines: origines, caractères, usages. À propos de deux ouvrage récents’, Geographia Antiqua 20–21 (2012): 215–27, at 217.
26. The whole prologue was transcribed by Gautier Dalché, Carte marine et portulan (note 23), 115–16, who later introduced some minor amendments: Gautier Dalché, ‘Les cartes marines: origines, caractères, usages’ (note 25), 219). A partial transcription of the prologue was made by Pujades, Les cartes portolanes (see note 2), 512–13.
27. To make the unpunctuated original text easier to follow, Gautier Dalché inserted some punctuation into his transcript, which has not always been adopted in the version given here.
28. The letters following M, in the manuscript, have been erased.
29. Quem, in Gautier Dalché’s later transcription (‘Les cartes marines’ (see note 25), 219). The original script appears to have been amended, either from quam to quem or from quem to quam. I have accepted the feminine quam, in which case it can refer only to forma.
30. Should read numeris.
31. Should read eorum.
32. In Gautier Dalché’s view, the reading should be longitudinem et latitudinem (Carte marine et portulan (see note 23), 116).
33. Here illorum (of those) should refer to locorum (places), above. Gautier Dalché takes it to refer to gradientibus (Carte marine et portulan (see note 23), 81). See note 46 below.
34. Should read narracione.
35. Should read composicione.
36. Should read recordacione.
37. Unknown word. Gautier Dalché, Cartes marine et portulan (note 23), 116, proposes curiosius instead.
38. See Gautier Dalché, Carte marine et portulan (note 23), Pujades, Les cartes portolanes (note 2), 512–13; Gautier Dalché, ‘Les cartes marines’ (note 25), 217–20; and John Pryor, ‘The preface of the Liber de existencia riveriarum’, in Roel Nicolai, The Enigma of the Origin of Portolan Charts. A Geodetic Analysis of the Hypothesis of a Medieval Origin (Leiden, Brill, 2016), Appendix H: 517–19.
39. Gautier Dalché has also made the point on several occasions that some descriptions are couched as if the author were reading a map. See Gautier Dalché, Carte marine et portulan (note 23), 23–38.
40. It would seem that Gautier Dalché has subsequently consolidated his ideas and revised his reading of the Latin syntax at the start of the prologue, making it identical to Pujades’s. The original French translation, in Gautier Dalché, ‘Les cartes marines’ (note 25, 219), reads: Notre mer Méditerranée … nous proposons de la mettre par écrit à partir de la forma de cette mer et de ses côtes, selon la façon dont ces lieux sont situés dans le monde habité dans les parties des vents. Afin d’assembler [ce monde habité] en une petite cartula de mappemonde, nous avions composé ce petit ouvrage du nombre des milles et de la distance qui sépare ces lieux, en reproduisant leurs noms de l’époque moderne; dans certains (cas), j’ai inséré des choses antiques et leur cause, selon la reference des livres, pour que ceux qui connaissent les livres comprennent plus facilement.
41. Pujades’ translation (Les cartes portolanes (see note 2), 513) reads as follows: ‘We propose to write about our Mediterranean Sea, about the form of the sea itself and its shores, in accordance with how its places are located in terms of the winds on the globe of the earth. In order to represent it on a mappamundi chart, I drew up this brief text on the number of miles that separate its places, giving their modern names; in some places I also gave their ancient names according to the books (the Bible) so that those familiar with the Scriptures might recognize them more easily’.
42. The proposed partial translation by John Pryor is the following: ‘We propose this sea … to be rendered in writing from the shape of this sea and of its coasts, according as their locations lie in the orbit of the lands in the directions of the winds; for arranging which [the orbis] on a chart of a mappa mundi we had composed this little work on the number of miles of distance of their places, copying their names in modern times. In certain of which I inserted the ancient [names] and the establishment of them according to books so that those who know books may understand more easily’. From which he considered that ‘The author wrote the book first and then compiled a map (or perhaps intended to compile a map)’. See Pryor, ‘The preface of the Liber de existencia riveriarum’ (note 38), 517–19.
43. I have been at pains to avoid as far as is possible being influenced by any preconceived ideas about the genesis of nautical cartography. This was not always easy, given the necessity of putting the work into the context of what is known about the subject. In the long process that culminated with the present English version, I arrived at the conclusion that, despite its overall lack of clarity and the presence of a few errors, the original text must have been prepared by someone with a good knowledge of Latin. That was not Gautier Dalché’s opinion in 1995 (Gautier Dalché, Carte marine et portulan (note 23), 87)), which he retracted in 2012 (Gautier Dalché, Les cartes marines (note 25), 219), saying: Mon jugement selon lequel le style est caractérisé par la maladresse est peut-être à abandonner … le Latin du prologue, marqué par une grande artificialité stylistique, paraît hypersavant, ce qui peut être aussi bien le propre d’un personnage qui manie la langue de façon experte (et maniérée) ou de quelqu’un qui souhaite montrer avec une évidence particulière une maitrise d’une culture qu’il ne domine pas totalement avec le naturel requis. Je ne saurais décider. As in other medieval and modern works, we noted a marked contrast between the complex and somewhat contorted style of the prologue and the simplicity of expression in the rest of the work. The square brackets in the translation are conventional and were added for clarity.
44. The common meaning of existencia (existence, manifestation) makes scant sense in the present context. More appropriate words would be ‘appearance’ or ‘disposition’.
45. That is, their origin. See Gautier Dalché, Carte marine et portulan (note 23), 20.
46. According to Gautier Dalché and Pujades, gradientibus is likely to refer to the mariner’s nautical guides (portolans), an interpretation I do not accept, especially in the light of the advice I have received from other Latinists. In my view, gradientibus illorum (from the travellers of those) refers to eorum locorum [of those places], above. If it referred to partes riueriarum [the parts of the coastlines] then illorum should be amended to illarum. Thus, our proposed translation ‘and [from] the travellers of those [places]’ not only respects the form of the manuscript but also makes sense.
47. The Latin word manus (usually meaning ‘hand’) may also mean ‘handwriting’. The expression manus operis suggests the interpretation that the cleric’s criticism might have been directed at both the content and the quality of the calligraphy of the texts describing the Mediterranean.
48. Following the indication of Gautier Dalché, Carte marine et portulan (see note 37), I have replaced the unknown word aurious with curiosius.
49. According to Gautier Dalché, such opusculum preceded the final work and comprised a text and a chart (forma). See Gautier Dalché, ‘Les cartes marines’ (note 25), 219–20.
50. Gautier Dalché, Carte marine et portulan (see note 23), 23–37, 103–6; Pujades, Les cartes portolanes (see note 2), 513.
51. In the Compasso de Navegare, each interval of 45 degrees can be subdivided in 16 parts. This portolano is dated 1296 but is usually considered to be a copy of an older original, probably of c.1250. See Gautier Dalché, Carte marine et portulan (note 23), 75. The Compasso de Navegare is Berlin, Staatsbibliothek Preuss, Kulturbesitz, MS Hamilton 396.
52. Gautier Dalché, Carte marine et portulan (see note 23), 19.
53. Al-Idrisi’s book Nuzhat al-mushtāq fi’khtirāq al-āfāq, also known as Tabula Rogeriana or Book of Roger, was commissioned by the King of Sicily, Roger II. It comprises a written description of the world, in Arabic, divided into seven climates, each one subdivided into ten sections. The text is accompanied by seventy sectional maps that can be assembled into a world map. Ten manuscript copies are extant, eight containing maps. See S. Maqbul Ahmad, ‘Cartography of al-Sharīf al-Idrīsī’, in The History of Cartography, vol. 2, book 1: Cartography in the Traditional Islamic and South Asian Societies, ed. J. B. Harley and David Woodward (Chicago, University of Chicago Press, 1992), 156–74. For an up to date analysis of al Idrisi’s geographical writings and maps and Roger II’s involvement in the translation of Arab scientific and other works, see Tarek Kahlaoui, Creating the Mediterranean: Maps and the Islamic Imagination (Leiden: Brill, 2018). On the circulation of Arab manuscripts in western Europe from the tenth century onwards, see Charles Burnett, The Introduction of Arabic Learning into Europe (The Panizzi Lecture for 1996; London, The British Library, 1997). Current thinking supports the suggestion made in this article that Arab representation of the Mediterranean might have been seen by Europeans from the tenth century onwards, giving them the idea of a detailed map of the whole area, as in al-Idrisi’s map of the Mediterranean.
54. According to the transcription of Gautier Dalché, Carte marine et portulan (note 23), 111–15.
55. It would have been inappropriate to use the differences in degrees in the analysis given the fact that the original directions are expressed in intervals of 22½ degrees.
56. See E. G. R. Taylor, The Haven-Finding Art: A History of Navigation from Odysseus to Captain Cook (London, Hollis & Carter, 1958), 35–64; Fernando Pimenta, ‘Astronomy and navigation’, in Handbook of Archaeoastronomy and Ethnoastronomy, ed. C. L. N. Ruggles (New York, Springer, 2017), 43–65. For a comprehensive survey of the prehistoric evidence, see Barry Cunliffe, On the Ocean: The Mediterranean and the Atlantic from Prehistory to AD 1500 (Oxford, Oxford University Press, 2017).
57. Because of the curvature of the earth’s surface, a ship sailing away from the coast progressively loses sight of it, starting with the lowest lying land. Exactly at what distance a given feature (a specific mountain or other landmark) disappears below the horizon depends on its elevation above sea level and on the altitude of the observer. Effective visibility at sea is also dependent on the transparency of the air, which is affected by the weather. See Pimenta, ‘Astronomy and navigation’ (note 56), 52, after William Schüle, ‘Navegación primitiva y visibilidad de la tierra en el Mediterrâeno’, in LX Congresso Nacional de Arqueologia (Mérida, 1968), 449–62.
58. According to Gautier Dalché, there is no reason to believe that the history of a chart for navigation does not go back to well before the mid-13th century (Carte marine et portulan (see note 23), 105): loin de naître dans la deuxième moitié du XIIIe siècle, comme on l’admet d’habitude, cette cartographie non seulement existe un siècle auparavant, mais rien n’empêche qu’elle ait à cette date déjà vécu une longue existence.
59. Gautier Dalché, Carte marine et portulan (see note 23), Appendix III, 204–19. Gautier Dalché did not attempt any conclusion from the comparison.
60. A few routes include an overland section, which could suggest that the information had been copied from a chart rather than taken from a text. See Gautier Dalché, Carte marine et portulan (note 23), 80.
61. I have chosen to represent the errors in degrees on the map, rather than in points of 22½ degrees, to make the representation more expressive. Otherwise most of the values would be zero.
62. In fact, the absolute value of the errors in the whole data set is negatively correlated to the length of the tracks, that is, larger errors are associated with shorter distances. This feature, already noticed in the geographical summary, was also mentioned by Lanman when he analysed the distances compiled from the Compasso de Navegare. See Lanman, On the Origin of Portolan Charts (note 9), 11–14.
63. No such symmetry is found in the directions of the Compasso de Navegare compiled by Lanman, where the average errors range between −6.8 and −10.4 degrees depending on the region of the Mediterranean. This result is expected considering that the directions in the Compasso are affected by magnetic declination. See Lanman, On the Origin of Portolan Charts (note 9), 19.
64. Alexander Neckam, De Naturis Rerum (see note 21), 183; idem, ‘The Treatise of De Utensilibus’ (see note 21), 114. Translations were adapted from those by Thomas Wright, 1857. The mention of the needle pointing to the east, instead of to the north, is probably an error of the author or an early copyist.
65. John Orr, ed., Les Oeuvres de Guiot de Provins (Manchester, Imprimerie de l’Université, 1915), 20–30. The original reads: un art font que mentir ne puet par la vertu de la manate; une pierre laide et brunet ou li fers volentiers se joint ont, si esgardent lor droit point; puez c’une aguile l’ait touchié et en un festu I’ont afichié, en l’augue la mettent sens plus et li festuz la tient desus. Puis se forme la pointe tourney contre l’estoille, si sens doute que ja por rien n’i faucerait ne mareniers ne douterait … Contre l’estoille va la pointe por ce sont li marenier cointe de la droite voie tenir. C’est uns ars qui ne puet mentir. The English translation given in the text here is taken from Arnold Pierre, The Letter of Petrus Peregrinus on the Magnet, A.D. 1269 (New York, McGraw-Hill, 1904), 38–39.
66. Ibid., 25–31.
67. See Campbell, ‘Portolan charts from the late thirteenth century to 1500’ (note 2), 383. Concerning the possibility of preparing a chart using only the information in the text of the Liber, a visual inspection of its routes makes clear that such a task would have been impossible for obvious lack of data.
68. I have already demonstrated that the main geometrical features of portolan charts can be satisfactorily explained by assuming the use of navigational information (pelagic courses and distances between places) in their construction. See Gaspar, ‘Dead reckoning and magnetic declination’ (note 14); idem, ‘From the Portolan Chart of the Mediterranean to the Latitude Chart of the Atlantic’ (note 15), 73–84. Precisely which tracks were used to construct the earliest charts is not, and probably cannot be, known because the final geometry of a chart is only weakly dependent on the set of routes used in the construction, assuming that they covered the charted area uniformly.