Publication Date
2009
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In terms of graphic syntax, the following are the main features of Ptolemaic cartography:
- Ptolemaic cartography show the change toward the conception of space as an abstract geometric transformation;
- The Ptolemaic terrestrial coordinate system assumes an isotropic, uniform surface on which abstract positions are plotted;
- The Ptolemaic terrestrial coordinate system implies the interest for the third dimension and in methods to create the illusion of the third dimension and shows a tentative movement toward more conventionalised coding in map simbology; with regards to the space-time issue, which was one of the main feature of mappaemundi, Ptolemaic cartography increasingly ensures that elements represented on a map should be cosynchronous, leading to a separation of time and space, of geography from history;
- The Ptolemaic terrestrial coordinate system implies the separation of written descriptions from graphic signs;
- Ptolemaic maps, meaning maps based upon map projections, satisfied the desires of scholars and patrons for a system of representing the world that would maintain scale or 'just proportion';
- Ptolemaic maps provide an alternative framework for the whole earth that, differently from mappaemundi, could render an 'apparent' three-dimensional picture of the spherical earth bounding a uniform space in which objects were cosynchronous;
- Ptolemaic maps provided an apparently abstract, disembodied or objective picture of the world conform to a linear style - later on, magnified by the semiotics of printing - that created the 'illusion' of precision.
In most instances, it could be safely argued that the Ptolemaic Geography gave origin to a methodologically coherent way of geometric representation of space that excluded pictorial elements from the representations of the world.
Ptolemy's Projections
The Geography deals above all with the question of cartographical representation, which literally consists of "drawing maps of the oikumene on a flat surface". Ptolemy's opening sentence clearly states: "Cartographical representations are pictorial imitations of the entire known world, together with the things that are, broadly speaking, connected with it" (Geography, I.1).
For Ptolemy, the purpose of explaining and defining mapmaking methods was to achieve as close a resemblance as possible to the 'picture of the globe', i.e. the image perceived by a spectator while gazing at a spherical representation of the Earth, while avoiding the difficulties involved in the use of a real globe. In the Almagest and in the Geography Ptolemy explained that this could be achieved by following certain geometrical and empirical methods, which subsequent historiography has dubbed 'map projections'.
In chapters 23 and 24 of Book I and in chapter 6 of Book VII of the Geography (Books II-VIII contain a long list of almost eight thousand toponyms that span the entire known inhabited world, with their respective latitudes and longitudes), Ptolemy explained how to prepare maps according to four geometric methods: a technique using straight and perpendicular parallels and meridians, which had already been employed by Marinus of Tyre and was recommended by Ptolemy for regional maps, for which the Earth's curve could be considered to be irrelevant (Geography 1.24.1); a technique with straight and converging meridians and curved parallels (Geography 1.24.3); a technique with curved and converging meridians and curved parallels (Geography I.24.9); and finally a special kind of projection in which the oikumene was visualised on a globe represented within an armillary sphere, viewed from a distance that allowed the beholder to take in the entire hemisphere in a single gaze (Geography VIII.6-7). Book I.24 is illustrated with four diagrams that explain the various phases of the geometrical construction of the first and second projections, which are generally present in almost all the codices of the composite tradition of the Geography, both in Greek as well as in Latin.
The First Ptolemaic Projection (Geography I.24.3)
The simplest method, which is generally called the "first Ptolemaic projection" in the historiography pertaining to this subject, has straight meridians that converge on a theoretical point, placed to the North at a distance that is equivalent to 34º with respect to the dimensions of the grid. The parallels are concentric arcs drawn around this geometrical centre. Since the meridians are represented as straight lines, it is relatively easy to situate points corresponding to places whose latitude and longitudes are known. Ptolemy suggested using this method for maps of large parts of the Earth's surface, especially for intermediate latitudes.
The Second Ptolemaic Projection (Geography I.24.9)
Ptolemy introduced the second method for the specific purpose of heightening the similarity between the perception of the beholder and the vision of a real globe (Geography, I.22). With the "second projection", which consisted of curved meridians and parallels, Ptolemy sought to give the meridians the appearance they would have had on a sphere when seen by a viewer looking directly at the centre of the globe (Geography, I.24.9). As has been mentioned, this second method, used for a planisphere in a late 13th century Greek codex of the Geography (Istanbul, Topkapi Müzesi Serai, ms. 57), was first adopted by Nicolaus Germanus and Piero del Massaio in their Florentine codices dating from about 1457-60. The world map drawn by Nicolaus Germanus subsequently served as the model for the planispheres of the editions of the Geography printed at Ulm in 1482 and 1486.
The Third Ptolemaic Projection (Geography VII.6)
In the final part of the Geography, Ptolemy describes another method through which 'the hemisphere in which the inhabited world is placed could be represented on a flat surface, with the hemisphere itself being surrounded by an armillary sphere.' (Geography, VII.6). The aim of this third method was to achieve a representation corresponding to the visual impression of the terrestrial globe within the armillary sphere, in such a way that the oikoumene could be clearly seen and depicted on the surface of Earth visible through the astronomical circles of the armillary sphere, the equator and the tropics. Ptolemy conceived the viewer as being situated outside these astronomical circles at such a distance that the ring representing the celestial summer tropic would just clear the parallel of Thule on the globe, and the ring representing the celestial equator would just clear the most southerly parallel of the inhabited world (Anti-Meroe). The geometrical construction of the image of the ringed globe consists of two distinct parts: a first part dealing with the determination of points through which the equator, the tropics and the ecliptic are to be drawn; a second part defining the way in which the graticule for the map of the oikoumenē remains visible between the rings. According to Berggren and Jones, two authoritative translators of the Greek text of the Geography, the first part of the algorithm for the design of the third projection would be the only documented example of the use of a graphic procedure that can be traced back to the linear perspective in classical antiquity.
For the drawing of the parallels of latitude portrayed on the terrestrial globe Ptolemy's method makes use of projected rays from the point representing the eye in a manner that only superficially resembles the linear perspective used for the rings. The resulting grid resembles Ptolemy's second projection in using circular arcs to represent all meridians except the central one, which is a straight line.
In conclusion, it is important to stress that of the eight books of the Geography, the section concerning the explanation of the methods for drawing the geographical grid, upon which the maps of the entire known inhabited world are drawn, was undoubtedly the most influential part of this work in terms of the future development of cartography.
Bibliography:
VALERIO, V., Cognizioni proiettive e prospettiva lineare nell'opera di Tolomeo e nella cultura tardo-ellenistica, Firenze, Olschki, 1998. J.L. Berggren - A. Jones (eds.), Ptolemy's Geography. An Annotated Translation of the Theoretical Chapters, Princeton, Princeton University Press, 2000. SNYDER, J.P., "Map Projections in the Renaissance," in Cartography in the European Renaissance, edited by David Woodward, vol. 3 of The History of Cartography, Chicago, University of Chicago Press, 2008, pp. 365-381. WOODWARD, D., "Cartography in the Renaissance: Continuity and Change," in Cartography in the European Renaissance, edited by David Woodward, vol. 3 of The History of Cartography, Chicago, University of Chicago Press, 2008, pp. 3-24.
Auhor: Angelo Cattaneo
- Ptolemaic cartography show the change toward the conception of space as an abstract geometric transformation;
- The Ptolemaic terrestrial coordinate system assumes an isotropic, uniform surface on which abstract positions are plotted;
- The Ptolemaic terrestrial coordinate system implies the interest for the third dimension and in methods to create the illusion of the third dimension and shows a tentative movement toward more conventionalised coding in map simbology; with regards to the space-time issue, which was one of the main feature of mappaemundi, Ptolemaic cartography increasingly ensures that elements represented on a map should be cosynchronous, leading to a separation of time and space, of geography from history;
- The Ptolemaic terrestrial coordinate system implies the separation of written descriptions from graphic signs;
- Ptolemaic maps, meaning maps based upon map projections, satisfied the desires of scholars and patrons for a system of representing the world that would maintain scale or 'just proportion';
- Ptolemaic maps provide an alternative framework for the whole earth that, differently from mappaemundi, could render an 'apparent' three-dimensional picture of the spherical earth bounding a uniform space in which objects were cosynchronous;
- Ptolemaic maps provided an apparently abstract, disembodied or objective picture of the world conform to a linear style - later on, magnified by the semiotics of printing - that created the 'illusion' of precision.
In most instances, it could be safely argued that the Ptolemaic Geography gave origin to a methodologically coherent way of geometric representation of space that excluded pictorial elements from the representations of the world.
Ptolemy's Projections
The Geography deals above all with the question of cartographical representation, which literally consists of "drawing maps of the oikumene on a flat surface". Ptolemy's opening sentence clearly states: "Cartographical representations are pictorial imitations of the entire known world, together with the things that are, broadly speaking, connected with it" (Geography, I.1).
For Ptolemy, the purpose of explaining and defining mapmaking methods was to achieve as close a resemblance as possible to the 'picture of the globe', i.e. the image perceived by a spectator while gazing at a spherical representation of the Earth, while avoiding the difficulties involved in the use of a real globe. In the Almagest and in the Geography Ptolemy explained that this could be achieved by following certain geometrical and empirical methods, which subsequent historiography has dubbed 'map projections'.
In chapters 23 and 24 of Book I and in chapter 6 of Book VII of the Geography (Books II-VIII contain a long list of almost eight thousand toponyms that span the entire known inhabited world, with their respective latitudes and longitudes), Ptolemy explained how to prepare maps according to four geometric methods: a technique using straight and perpendicular parallels and meridians, which had already been employed by Marinus of Tyre and was recommended by Ptolemy for regional maps, for which the Earth's curve could be considered to be irrelevant (Geography 1.24.1); a technique with straight and converging meridians and curved parallels (Geography 1.24.3); a technique with curved and converging meridians and curved parallels (Geography I.24.9); and finally a special kind of projection in which the oikumene was visualised on a globe represented within an armillary sphere, viewed from a distance that allowed the beholder to take in the entire hemisphere in a single gaze (Geography VIII.6-7). Book I.24 is illustrated with four diagrams that explain the various phases of the geometrical construction of the first and second projections, which are generally present in almost all the codices of the composite tradition of the Geography, both in Greek as well as in Latin.
The First Ptolemaic Projection (Geography I.24.3)
The simplest method, which is generally called the "first Ptolemaic projection" in the historiography pertaining to this subject, has straight meridians that converge on a theoretical point, placed to the North at a distance that is equivalent to 34º with respect to the dimensions of the grid. The parallels are concentric arcs drawn around this geometrical centre. Since the meridians are represented as straight lines, it is relatively easy to situate points corresponding to places whose latitude and longitudes are known. Ptolemy suggested using this method for maps of large parts of the Earth's surface, especially for intermediate latitudes.
The Second Ptolemaic Projection (Geography I.24.9)
Ptolemy introduced the second method for the specific purpose of heightening the similarity between the perception of the beholder and the vision of a real globe (Geography, I.22). With the "second projection", which consisted of curved meridians and parallels, Ptolemy sought to give the meridians the appearance they would have had on a sphere when seen by a viewer looking directly at the centre of the globe (Geography, I.24.9). As has been mentioned, this second method, used for a planisphere in a late 13th century Greek codex of the Geography (Istanbul, Topkapi Müzesi Serai, ms. 57), was first adopted by Nicolaus Germanus and Piero del Massaio in their Florentine codices dating from about 1457-60. The world map drawn by Nicolaus Germanus subsequently served as the model for the planispheres of the editions of the Geography printed at Ulm in 1482 and 1486.
The Third Ptolemaic Projection (Geography VII.6)
In the final part of the Geography, Ptolemy describes another method through which 'the hemisphere in which the inhabited world is placed could be represented on a flat surface, with the hemisphere itself being surrounded by an armillary sphere.' (Geography, VII.6). The aim of this third method was to achieve a representation corresponding to the visual impression of the terrestrial globe within the armillary sphere, in such a way that the oikoumene could be clearly seen and depicted on the surface of Earth visible through the astronomical circles of the armillary sphere, the equator and the tropics. Ptolemy conceived the viewer as being situated outside these astronomical circles at such a distance that the ring representing the celestial summer tropic would just clear the parallel of Thule on the globe, and the ring representing the celestial equator would just clear the most southerly parallel of the inhabited world (Anti-Meroe). The geometrical construction of the image of the ringed globe consists of two distinct parts: a first part dealing with the determination of points through which the equator, the tropics and the ecliptic are to be drawn; a second part defining the way in which the graticule for the map of the oikoumenē remains visible between the rings. According to Berggren and Jones, two authoritative translators of the Greek text of the Geography, the first part of the algorithm for the design of the third projection would be the only documented example of the use of a graphic procedure that can be traced back to the linear perspective in classical antiquity.
For the drawing of the parallels of latitude portrayed on the terrestrial globe Ptolemy's method makes use of projected rays from the point representing the eye in a manner that only superficially resembles the linear perspective used for the rings. The resulting grid resembles Ptolemy's second projection in using circular arcs to represent all meridians except the central one, which is a straight line.
In conclusion, it is important to stress that of the eight books of the Geography, the section concerning the explanation of the methods for drawing the geographical grid, upon which the maps of the entire known inhabited world are drawn, was undoubtedly the most influential part of this work in terms of the future development of cartography.
Bibliography:
VALERIO, V., Cognizioni proiettive e prospettiva lineare nell'opera di Tolomeo e nella cultura tardo-ellenistica, Firenze, Olschki, 1998. J.L. Berggren - A. Jones (eds.), Ptolemy's Geography. An Annotated Translation of the Theoretical Chapters, Princeton, Princeton University Press, 2000. SNYDER, J.P., "Map Projections in the Renaissance," in Cartography in the European Renaissance, edited by David Woodward, vol. 3 of The History of Cartography, Chicago, University of Chicago Press, 2008, pp. 365-381. WOODWARD, D., "Cartography in the Renaissance: Continuity and Change," in Cartography in the European Renaissance, edited by David Woodward, vol. 3 of The History of Cartography, Chicago, University of Chicago Press, 2008, pp. 3-24.
Auhor: Angelo Cattaneo