Dou bl y Percei ved Shape of the Ad ri ati c Sea Basi n on Earl y M od ern G eog raphi cal M aps and N au ti cal Charts

. The implementation of graticules on geographic maps and nautical charts, initially developed in the Hellenistic period, was a rediscovered novelty to Western European cartographers of the early modern period. The research sought to computationally examine the accuracy of spherical coordinates’ data extracted from selected geographical maps and nautical charts. Research results suggest that the cartographers who made geographic maps relied significantly on Claudius Ptolemy’s data on locations but managed to make certain accuracy improvements. The nautical charts with graticules showed significantly greater longitudinal accuracy, which suggests that they were created by using other data sources as their graphical templates; most likely the portolan charts that were already in existence at the time.


Related Cartometric Research
Although the cartometric analysis was initially introduced in the late nineteenth century by Hermann Wagner (Wagner 1896(Wagner (1969: 480), studies related to the history of cartography involving its application have begun to become more frequent in recent decades due to the development and increased availability ofGIS software tools. The examples ofextensive cartometric approach to nautical charts include doctoral studies made by Scott Allen Loomer (Loomer 1987) Joaquim Gaspar (Gaspar 2010), Roel Nicolai (Nicolai 2014) and Tome Marelić (Marelić 2020). Cartometric analyses of old geographical maps were, for example, performed by Tomáš Bayer with associates (Bayer et al. 2010), Marina Triplat Horvat (Triplat Horvat 2014) and Marina Viličić (Viličić 2019). A sole existing example of a cartometric approach to Vincenzo Maria Coronelli's geographical maps (whose map of the Adriatic Sea, created in 1688, was selected for this research) is a study performed by Caterina Balletti and Caterina Gottardi. They claim that, according to their methodology, a definitive conclusion about which map projection could be assigned to his maps of Central Europe cannot be drawn (Baletti and Gottardi 2015: 31−33). Sophisticated analyses of Claudius Ptolemy's coordinates were performed by Evangelos Livieratos with associates (Livieratos 2006;Livieratos et al. 2007Livieratos et al. , 2008, Christian Marx (Marx 2011;2012;2016), and Irina Tupikova (Tupikova 2014). Livieratos performed research in which he computationally compared the accuracy of geometric layouts represented on the old maps with the quantitative data extracted from their graticules. His conclusion is that two ptolemaic maps 2 of Crete he examined (one from the fourteenth, and one from the seventeenth century) geometrically correspond well to Ptolemy's coordinates datasets he used for the research (Livieratos 2006: 58−59).

Scope and Methodology
The aim of the research is to determine the geometrical properties of the Adriatic Sea basin's coastline renderings on selected graticule-equipped geographical maps and nautical charts produced in the early modern age (before the era of systematic geodetic and hydrographic surveys), according to their longitudinal and latitudinal data. The main research sample consists of three geographical maps and three nautical charts (Table 1). 3 Giacomo Gastaldi's Italiae Novissima Descriptio map (1570) is one of the earliest more detailed, and presumably more accurate early modern maps on which the Adriatic Sea and its surrounding areas are displayed. The dashes in its map frame, representing the degrees of longitude, appear to be slightly tilted and mirrored towards its central meridian, and those which represent the degrees of latitude are equally spaced, which indicates that it was intentionally made in a "Ptolemy's first projection". Pierre Duval's Golfe de Venise map (1664) resembles the aesthetics ofcontemporary nautical charts to a certain extent, by containing a 16-point wind rose at its centre, a compass rose painted in its south-eastern part, and its spatial data focused on the coastline rendering (Figure 1), which suggests that he might have been influenced by nautical charts available at his disposal. However, even at the level ofmere observation, it is noticeable that a map could not be used for navigational purposes. The first reason is its significant longitudinal "stretch", which implies the usage of Ptolemy's longitudinally inaccurate data on locations (Marx 2011: 36;2012: 100). The second reason is the geometry of its graticule -the LON/LAT ( / ) ratio of its equal-degree intervals is about 0.8, meaning that it was intentionally made in normal equidistant cylindrical projection 0 =36°, which is not conformal. 4 A similar graphical appearance ofthe Adriatic Sea, and an identical LON/LAT ratio of 0.8, exist on Vincenzo Maria Coronelli's Golfo 2 Late medieval and early modern attempts to reconstruct the (lost) cartographic content of Geographike Hyphegesis.
di Venezia map (1688). It also contains a wind rose, but its body of geographical data is (besides being substantially more detailed in comparison with Duval's map) evenly distributed across its entire spatial extent (Figure 3). His map also contains several place names written in duplicates, with Hellenistic Greek names written near their Italian counterparts, 6 which implies that he, at least partly, relied on Ptolemy's geographical data.
A sample of printed nautical charts -which were produced approximately during the same period as the selected maps and contain graticules as well -includes Fig. 1 Residual vectors (red) of identical points (yellow) for Pierre Duval's 1 664 map, georeferenced by using the coordinates extracted from the map and with the application of its proprietary E-W shift (∆ 0 ). The thick black line represents its vectorized coastline, while the thick semi-transparent red line represents its vectorized coastline generated upon its geometrical best-fit.  (1737). Those three charts were already cartometrically examined to a certain extent (Marelić 2023b), but the accuracy of their spherical coordinates was not discussed in the wider context which also includes some other contemporary cartographic sources with graticules.
čitavom polju karte (slika 3). Coronellijeva karta sadrži i manji broj dvostruko navedenih toponima, tako da su helenistička imena napisana pored lokaliteta koji su imenovani i na talijanskom jeziku, 6 što upućuje na to da se pri izradi karte koristio Ptolemejevim geografskim podatcima. Uzorak pomorskih karata -koje su izrađene u približno sličnom razdoblju kao i odabrane geografske karte te također sadrže kartografsku mrežu -uključuju prikaz Jadranskog mora na tri lista koji je izradio Robert Dudley i koji je objavljen u knjizi Dell'arcano del mare (1646), kartu Golfe de Venise (1700), koju je izradio Slika 3. Vektori reziduala (crveno) identičnih točaka (žuto) na karti Vincenza Marie Coronellija iz 1 688., georeferencirane upotrebom koordinata preuzetih s karte uz primjenu odgovarajućeg longitudinalnog pomaka (∆ ). Široka crna linija predstavlja vektoriziranu obalnu crtu, dok široka poluprozirna ljubičasta linija označava vektoriziranu obalnu crtu pri dodatnom georeferenciranju na temelju optimalnog geometrijskog podudaranja. Izvor karte: Nacionalna sveučilišna knjižnica u Zagrebu, zbirka karata i atlasa, S-JZ-XVII-56. Izvor pozadinskih shp datoteka: marineregions.org (Claus i dr. 201 7). Euclidean geometry and requires a map projection to be assigned to the reference dataset 7 in advance, three map projections were selected for the task: normal equidistant cylindrical projection 0 =36°(CYL36), normal equidistant conic projection 0 =36°(CON36) and Mercator projection 0 =36°(MERC36). The former two were selected due to the selected maps' apparent resemblance with the Hellenistic cartographical approach, while the Mercator projection was selected because it appears to be the geometrical basis oflate medieval and early modern manuscript (portolan) charts, as well as the majority of early modern printed nautical charts (Loomer 1987: 144−146;Nicolai 2014: 253, 387, Marelić 2022: 98−99, 2023b. The georeferencing of maps and charts was performed in two separate ways. The first, and merit-wise more significant for the research, is by using their proprietary LON and LAT values (manually extracted and plotted as GIS point-datasets) as "pseudo-reference points" and comparing them to their corresponding LON and LAT reference values on a WGS84 ellipsoid. The second way, in which the selected locations on charts and maps are used as identical points is purely geometric in nature and was conducted in order to determine the bestfit of their coastline renderings, regardless of the coordinates' values assigned to them. 8 Since both scenarios yield their results in Euclidean geometry of (reference) map surface in scale 1:1 (determined by the parameters of its selected map projection), the displacements (residuals) ofidentical points need to be spherically corrected in addition in order to nullify their map projection-induced distortions, and their angular displacements ( The accuracy ofspherical coordinates observed on maps and charts, and extracted as point datasets, was examined in three different analyses. The first analysis is the comparison of their proprietary longitudinal and latitudinal extents for the Adriatic Sea basin area to its corresponding extent on WGS84. The second analysis is an assessment ofthe accuracy ofthe map coordinates compared to a point-dataset extracted from the transcript of Ptolemy's Geographike Hyphegesis (Stevenson 1991). To achieve this, 39 locations that showed higher identification reliability ( Figure  5) 10 were pinpointed on maps (34 locations on GAS_1570, 32 on DUV_1664, and 38 on COR_1688 map), and extracted as point-datasets attributed with their proprietary LON and LAT values. The third analysis is the estimation of the accuracy of the coordinates extracted from maps and charts by comparing them to their reference counterparts, as well as to the "pseudo-coordinates" of their LSE-generated geometrical best-fit, obtained in parallel. In addition, certain possibilities for calculating map scale factors for longitude-wise poorly accurate map(s) are presented.

Differences in the Perceived Extent of the Adriatic Sea
The reference extent of the Adriatic Sea basin on WGS84 was measured between its longitudinal and latitudinal endpoints ( Table 2). The longitudinal extent error (d ) of the Adriatic Sea on maps (+2.1°, or +169.6 km on average) is significantly greater than that on charts (a fraction of a degree, or only −3.8 km on average). On the other hand, the latitudinal extent error (d ) on maps (being −0.1°, or −13.3 km on average), is smaller than that on charts (−0.3°, or −37.0 km on average). Its extent, according to Ptolemy's data, and measured between its proprietary endpoints; the mouth ofriver Drim -Ravenna (E-W extent), and Triestecape Leuca (N-S extent) 11 , is the most erroneous coordinates-dataset by far, especially longitude-wise.
Karte su georeferencirane na suvremenu kartu Sredozemlja (shp datoteka), preuzetu s marineregions.org. (Claus i dr. 2017 (1688) map. Ptolemy's dataset was (in order to perform the correction of its prime meridian) longitudinally (E-W) shifted by 0 =−25.2°, which corresponds to the longitude of Santa Antão; the westernmost island of the Cape Verde archipelago -an adjustment which was previously applied by Marx in his quantitative analysis of Ptolemy's coordinates for the Adriatic Sea basin (Marx 2012: 100). The same E-W shift (solely for the purpose of this analysis) was selected to longitude-wise adjust the coordinates of Ptolemy's locations identified and pinpointed on each ofthe three maps ( Figure 5). 12 In comparison with WGS84, Ptolemy's coordinates showed RMSE|dLON| accuracy of 1.7°(136.8 km), and RMSE|dLAT| accuracy of 0.6°(63.9 km). 13 In comparison with Ptolemy's dataset, the geometric centres of Ptolemy's locations on maps, computed and plotted as point-datasets, showed RMSE|dLON| of 1.7°(135.2 km), and RMSE|dLAT| of 0.8°(86.4 km), while in comparison with the reference WGS84 coordinates, their average results are RMSE|dLON| of 1.4°(111.2 km), and RMSE |dLAT| of 0.3°(35.3 km). Both the longitudinal and latitudinal accuracy of the map coordinates proved to be higher than those of Ptolemy. Also, map coordinates proved to be more similar to the reference data than to Ptolemy's data, which suggests that certain progress in the spatial perception of selected place-locations on the Adriatic Sea basin's coastline had occurred during the period of map production, or slightly earlier. Geometric centres of identical points on each of the three maps show that significant longitudinal corrections have been made for the northernmost part of the Adriatic Sea, while the southernmost subset of coordinates shows significant latitudinal corrections ( Figure 5).

Doubly Perceived Shape of the Adriatic Sea
The coordinates of selected 45 locations on each map and chart and plotted in GIS software as pointdatasets, were compared to their corresponding reference values on WGS84 (Figure 1-4, Figure 6) in order to compute their RMSE|dLON| and RMSE|dLAT| values [km]. In order to minimize their prime meridian misalignments, an individual optimal E-W shift ( 0 ) for each map and chart was computed as the average of biased displacements between the longitudes extracted from it and the longitudes of their corresponding reference points. 15 In addition, each map and chart was compared to "pseudo-coordinates" of its LSE-generated identical points, 16 which are the product of two-dimensional conformal scale-wise and orientation-wise ( LSE ) adjustment of each map and chart in order to achieve their geometric best-fit according to the shape ofthe Adriatic Sea basin as it is rendered on them (semi-transparent coastline renderings in Figure 1-4, section B in Table 3).
The purely geometrical approach to the georeferencing of selected maps and charts (section B in Table 3) yields somewhat intriguing results. The "pseudo-coordinates" (hypothetical, and geometry-wise ideal coordinates, derived directly from the shape of their Adriatic Sea rendering) at which the identical points on selected charts "land" after the completion oftheir geometric-georeferencing are longitude-wise significantly similar to their believed-to-be-true values (with a difference ofonly 7.5 kilometres on average). On the other hand, the comparison of coordinates extracted from maps to their "pseudo-coordinates" reveals their average longitudinal "offset" of56.3 kilometres (section C in Table 3). Also, the LSE-induced rotations of geometrically-georeferenced maps are significant; +7.2°for Duval's map (1664), and +7.4°for Coronelli's map (1688), in comparison with +0.9°and 0.1°, respectively, obtained by georeferencing them with regards to their proprietary coordinates' dataset ("pseudo-reference points"). The accuracy of coordinates on charts (in comparison with their reference WGS84 values) proved to be very similar to the accuracy of their "pseudo-coordinates" obtained from the geometrical best-fit of their coastlines, predominantly because oftheir considerably high longitudinal accuracy. This immense similarity of the results yielded from two separate and distinctively different methodological approaches explicitly demonstrates that both the perceived shape ofthe Adriatic Sea basin, as well as the values ofcoordinates assigned to selected locations are significantly more accurate 18 in comparison with the corresponding features on maps (compare thick black vectorized coastlines with semi-transparent colour-coded coastlines in Figure 1-4, and section A, and B in Figure 6).
When the renderings of the Adriatic Sea basin's coastline on selected maps are visually compared to its renderings on selected charts (displayed in the same map scale and aligned longitude-wise; Figure 6) it can be clearly observed that two rather different perceptions ofits appearance existed in two separate "cartographic realms" in parallel. Simply put; ifits actual shape, which shows rather a similar width along the majority of its geometric (NW-SE) axis, were imagined as a simplistic drawing ofa (tilted) rectangle, then its shape -as it was perceived by the cartographers who created geographic maps -could be imagined as a "banana" or a "cucumber". In a similar manner, its shape -as it was perceived by the authors ofnautical charts -could be imagined as a (tilted) "funnel" (that widens towards the NW) -a "geometric footprint" which already existed on portolan charts (Marelić 2022(Marelić : 95-96, 2023b).

Map Scale of Longitude-Wise Poorly Accurate Geographical Maps
Due to significant longitudinal errors on early modern maps, it is reasonable to discuss the possible ways ofcomputing their map scale. Some methodological possibilities will be shown in the example of Coronelli's (1688) map, which, despite its detailed geographic content, state-ofthe-art aesthetics, and six scale-bars (each calibrated in its own unit of distance), shows significant longitudinal inaccuracy (Figure 3, Figure 6) and best geometric fit with normal equidistant cylindrical projection 0 =36°, whose standard parallel is located outside its spatial extent.
If, additionally, we take into account his errors ofthe Adriatic Sea's longitudinal extent of+2.36°(32.2% greater than its extent in reality), ofwhich he most likely was not aware, this means that the longitudinal scale factor (which has already been divided by 1.10) should be additionally divided by 1.32, which yields an "actual" longitudinal map scale along its mid-parallel of1:1,209,229 (1:1,210,000 as its rounded value). Ifwe assume that Coronelli had not tailored his scale bars in accordance with =36°as its latitude of true scale (because it is not its mid-latitude), then its longitudinal scale factor should be divided by 1.32 exclusively, which yields a rounded longitudinal scale along its mid-parallel of 1:1,354,337 (1:1,355,000 as its rounded value). His latitudinal extent error is negligible (only 0.0012°) and was thus not considered in any ofthese computations. Whatever particular value should be used to describe his map scale is arbitrary; these paragraphs serve mainly to emphasize the parameters which may affect its determination and as a methodology proposal on how to determine the map scale of (poorly accurate) old maps according to these criteria.

Conclusions
The implementation of graticules on maps and charts, although it actually was a rediscovery ofmethodology that was already developed in the Hellenistic period, was a novelty to Western European cartographers of the early modern age. Research results showed that at the time of reinvention of the "graticule-equipped cartography", two parallel paths ofcartographic renderings (of the Adriatic Sea basin) existed simultaneously. The cartographers who created the geographical maps relied significantly on the preserved geographic opus of Claudius Ptolemy, while those who were producing the nautical charts seemed to be mainly inspired by the geometry of portolan charts. Both of those two "spatial layout matrices" were already in existence at the time, and since these maps and charts were made before the era of systematic geodetic and hydrographic surveys, their authors were constrained with the inherited materials at their disposal, supplemented with trial-and-error attempts to "enhance the image ofthe world".
Although the examined maps showed considerable geometric improvements in comparison with Ptolemy's geographical data, the values of longitudes assigned to their locations were still significantly less accurate than those on nautical charts. The methodology ofthis research cannot detect or explain the cause-and-effect order of those improvements -perhaps their authors were comparing Ptolemy's longitudinally "extended" data with longitude-wise more "compact" extents displayed on portolan charts and sought to create their "optimal graphic blend". Whichever course of action had happened, additional research should be conducted in order to obtain more detailed clarifications on that matter. 20 According to Picard, Earth's equatorial circumference consists of 9,000 lieües de 25 au degré (Picard 1671: 23 23 The map scale on normal equidistant cylindrical projection is true along its standard parallel ( 0 ) and all meridians. In order to retain the rectangular shape of the map, i.e., the equal length of displayed parallels, those with latitudes greater that 0 are, thus, plotted increasingly "stretched" (on a smaller scale), while parallels with latitudes lower than 0 are plotted increasingly "compressed" (on a larger scale). (nagnuti) "lijevak" (koji se proširuje prema SZ) -"geometrijski otisak" kakav je otprije postojao na portulanskim kartama (Marelić 2022(Marelić : 95-96, 2023b).