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was at the  cutting edge of geographical knowl-  N O T E S
                                                        edge.  Representations of the  world such as his
                                                        must  have catered to the  taste for mathematical  1.  Joan Kelly Gadol,  Leon  Battista Alberti:  Universal
                                                                                                              Early
                                                                                                                  Renaissance
                                                                                                           the
                                                                                                      Man
                                                                                                         of
                                                                                                                                       200-
                                                                                                                           (Chicago, 1969),
                                                        and cosmographical puzzles. There was a  fasci-  201, usefully summarizes the debate among  histo-
                                                        nation with the  notion  of measurement and   rians such as Lynn Thorndike, Pierre Duhem,  Leo
                                                        measuring instruments;  maps, globes, and     Olschki,  Ernst Cassirer, and Alexander Koyre.
                                                        armillary spheres became graphic symbols of  2.  David Woodward,  "Roger Bacon's Terrestrial  Coordi-
                                                                                                                       of
                                                                                                                         the Association of
                                                        scholarly learning. Later in the sixteenth cen-  nate System," in Annals 80(1)  1990,  109-122.
                                                                                                      American Geographers
                                                        tury,  manuals of surveying  practice and instru-  3.  Here is not the place to enter into this complex
                                                        mentation  became fashionable  for the educated  question  in detail, but  Ptolemy's third projection is
                                                        classes, long after  such mundane pursuits had  superficially  similar  to vanishing-point  perspective,
                                                        become part of common  life  in the  fifteenth  as Samuel  Y. Edgerton, Jr.,  "From  Mental  Matrix  to
                                                              13
                                                        century.  Likewise, the  survival of Rosselli's  Mappamundi  to Christian  Empire: The Heritage of
                                                                                                                      in the
                                                                                                                           Renaissance," in Art
                                                                                                      Ptolemaic Cartography
                                                        simple map may well reflect  an earlier broad  and  Cartography:  Six  Historical  Essays,  ed. David
                                                        and pervasive interest  in representations  of the  Woodward  (Chicago,  1987), 10-50, has  argued,
                                                        whole earth.                                  although  the plane on which the image is projected
                                                          In fifteenth-century Europe, therefore, a fun-  is not between  the viewer and the  object, as in Leon
                                                        damental change took place in geographical    Battista Alberti's  velum, but passes through  the
                                                        thinking.  The ideas for a measured, coherent,  object.  Svetlana Alpers is correct to claim that  "what
                                                                                                      is called a projection
                                                                                                                    in this cartographic
                                                                                                                                        is
                                                                                                                                  context
                                                        global map presented in Ptolemy's  Geography  never visualized by placing a plane between  the
                                                        were not  new, but they were received in a schol-  geographer  and the earth"  (see Alpers,  "The  Map-
                                                        arly climate that valued the universality and  ping Impulse in Dutch  Art,"  in Woodward  1987,  51-
                                                        interconnectedness of knowledge. Despite  the  96, especially p.  71),  but  there are plenty  of exam-
                                                        potential of the  Ptolemaic coordinate system,  it  ples of azimuthal projections in which this plane is
                                                                                                                                    through
                                                                                                                            or passing
                                                                                                      visualized as touching the earth
                                                        was not  always fully  understood at the practical  it.  There  is a danger in pressing the  similarity of
                                                        level and was certainly  viewed with  much  sus-  Ptolemy's projection to vanishing  point perspective
                                                        picion by navigators hardened by experience.  and inferring a cause-and-effect relationship because
                                                        Even after Gerardus Mercator  showed  in  1569  other  azimuthal  projections, such as the  stereo-
                                                        that geographical coordinates and straight  com-  graphic, had already been  in common  use for astro-
                                                                                                                     Middle Ages without
                                                                                                                                    a similar
                                                                                                      labes throughout
                                                                                                                  the
                                                        pass courses could be reconciled in the  same  causal effect  (J. V. Field,  "Perspective  and the  Math-
                                                                                14
                                                        map, the  suspicion continued.  But cosmo-    ematicians:  Alberti  to Desargues," in  Mathematics
                                                        graphical scholars had by then  long admired and  from  Manuscript  to Print, 1300-1600, ed.  C.  Hay
                                                        accepted the  elegance of the  global system.  [Oxford,  1988]).
                                                        Navigational practice was ultimately to catch up  4.  Gadol  1969,  143-211, especially 157-195.  in
                                                                                                    5.
                                                                                                                   "Medieval Mappaemundi,"
                                                                                                          Woodward,
                                                                                                      David
                                                        with the  great hypothesis of looking at the  History  of  Cartography:  Cartography  in Prehistoric,
                                                        world in global terms.                        Ancient, and Medieval  Europe  and the  Mediterra-
                                                          The record presented by the  maps shows an  nean, eds. J. B. Harley  and  David Woodward  (Chi-
                                                        emergence from  the medieval center/periphery  cago, 1987), 286-370, especially  316.
                                                        frame  of mind,  in which places in the  world  6.  Tony  Campbell,  "Portolan Charts  from the  Late
                                                                                                                      1500," in Harley
                                                                                                                    to
                                                                                                              Century
             rather modest map made around  1508  by Fran-  were accorded widely different  levels of impor-  Thirteenth  371-463, especially  386.  and  Wood-
                                                                                                      ward
                                                                                                          1987,
             cesco Rosselli (cat.  133) —graduated with  360°  tance. As the  ideas in Ptolemy's  Geography  7.  Paul D. A.  Harvey,  "Local and Regional  Cartography
             longitude and  180° latitude —is the earliest  took hold, the more abstract notion developed  in Medieval Europe," in Harley  and Woodward  1987,
             extant  map of the world in the pure sense of  that space could be referenced to a  geometrical  464-501, especially  474.
             "map"  and  "world/ 7  It takes on special signifi-  net  of lines of longitude and latitude and could  8.  Gadol  1969,  201.
                                                                                                                       Voyages
             cance as being drawn on an oval projection into  thus everywhere  be accorded the  same  impor-  9.  Richard Hakluyt,  Divers the  Islands Touching  the ed. Dis-
                                                                                                                              Adjacent,
                                                                                                      covery
                                                                                                           of America and
             which every point on earth could theoretically  tance.  The idea of a finite  globe was implicit in  John Winter  Jones (London, 1850), 50.
             be plotted and on which every potential  route  Ptolemy's Geography,  but the projections he  10.  From Columbus'  copy of Cardinal Piccolomini's  His-
             for  exploration could be shown.  If ever there  proposed could not explicitly show it.  In  the  toria  rerum  ubique  gestarum, now in the Biblioteca
             was a geographical idea of elegant simplicity  course of the  fifteenth  century, the  map  frame  Colombina,  Seville.
                                                                                                                         and Terrestrial
             since the realization that  the earth was a sphere,  expanded little by little and at times literally  11.  Jozef  Babicz,  "The  Celestial  from  1477,  and  Globes of
                                                                                                      the Vatican Library, Dating
                                                                                                                                     Their
             this was it.                               burst to accommodate a discovery, such as the  Maker Donnus  Nicolaus Germanus  (c. 1420-c.
               Rosselli's coordinate world map was accompa-  rounding of the  Cape of Good Hope in  Martel-  1490)," Der Globusfreund  35-37 (1987),  155-168.
             nied by a navigation chart on a rhumb-line  lus' maps. A map projection such as Rosselli's,  12.  Johannes Keuning,  "The  History of Geographical
             structure;  the pairing of these two fundamen-  intended to  solve the puzzle of showing  the  Map Projections  until 1600," Imago  mundi 12
             tally different  map structures symbolizes a  globe on  a flat  piece of paper, apparently had  to  (1955),  1-24.
                                                                                                   13.
             mathematical puzzle of how properly  to  repre-  wait until the  early years  of the sixteenth  cen-  14.  Gadol 1969,  171.  the  Mediterranean  Portu-
                                                                                                      W. G. L. Randies, "From
             sent the  spherical world on a plane. Rosselli was  tury.  Such an image of the  whole earth allowed  lan Chart to the  Marine  World  Chart  of the Great
             a commercial printmaker  in  Florence —one of  the  idea of a finite world  over which  systematic  Discoveries: The Crisis in Cartography  in the  Six-
             the  first to be independently successful —and  dominance was possible, and provided a power-  teenth  Century,"  Imago  mundi 40 (1988),  115-118.
             although  he was working in one of the  most  ful  framework for political expansion  and
             active humanist centers, it is unlikely that  he  control.
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