Introduction (translated imperfectly from the book by Kleineberg, Marx, Knobloch and Lelgemann) Ptolemy and the geography of Germania The most important works of ancient literature that give us a picture of ancient Germania are the Germania of Tacitus (around AD 55 to around 120) and the Geographike Hyphegesis of Klaudios Ptolemaios (around 100 to around 170), hereinafter referred to as Geography. While the Roman historian Tacitus concentrated on ethnographic description of the Germanic tribes, the focus of the portrayal by the Greek scholar Ptolemy is cartography. He wrote his Geography in the middle of the second century in Alexandria. This city, founded by Alexander the Great on an estuary of the Nile, was not only a spiritual center of the Greco-Roman world, where Ptolemy had the most important library of antiquity at his disposal (Canfora 2002), but also a trading metropolis where information about all the then known countries of the world, over the oikumene, flowed together. In his geographical work, Ptolemy first describes the theoretical basis for a true-to-scale cartographic representation of the oikumene. In the main part of Geography he then gives the geographic coordinates of more than 6300 locations and topographic points, such as estuaries, foothills, or mountains. A special feature of this catalogue of places is that Ptolemy uses a uniform, global coordinate system that corresponds to today's geographic coordinate system from a prime meridian. Latitudes are counted from the equator, the prime meridian is, as later in the Ferro system, placed at the Canary Islands, the westernmost end of the world known at the time. Degrees are given in the form of the so-called Milesian system, in which the letters of the Greek alphabet are used as numerals. The minute values are shown as fractions of degrees. Since, with the exception of the value 2/3, only fractions with 1 are used as numerators, some values appear as the addition of simple fractions, e.g. 1/2 + 1/4 = 3/4. The smallest fraction of a degree given by Ptolemy in the local catalogue is 1/12; this corresponds to 5'. Since Ptolemy also gives a value of 180,000 stadia for the circumference of the earth (GH VII, 5, 12) and he uses a circle division of 360°, 1° at the equator corresponds to 500 stadia. Ptolemy divides the cartographic representation of the entire oikumene into an overview map and 26 individual maps: ten maps for Europe, four for Africa, and twelve for Asia. Within this structure, the 6300 places mentioned, to which the names of peoples and landscapes appear without coordinates, are distributed over 84 countries or regions, the boundaries of which are described in each case. In the second book of Geography there is Ptolemy’s representation of Germania, i.e. of the settlement area of Germanic tribes that did not belong to the Roman Empire. He calls this area Germania Megale ("Greater Germania", reproduced below in the Latin form Germania Magna). According to Ptolemy, it is bordered by the Rhine in the west, the North Sea and the Baltic Sea in the north, the Danube in the south, and the Vistula and the Western Carpathians in the east. The area of Germania at that time included not only parts of today's Germany, but also parts of Denmark, Poland, Austria, Czechia, and Slovakia. Conversely, today's Germany also includes areas that Ptolemy found in the description of the Roman provinces Raetia and Germania Inferior and Superior, whereby he treated these two Germanic provinces in the description of Gallia Belgica. Noricum, which borders on Raetia to the east and Germania Magna to the south-east, is in present-day Austria. Ptolemy shows us the state of Central Europe in the early Roman Empire. The particularities in the representation of the individual areas are discussed in the present work in the corresponding sections. Not only the Germanic area is dealt with here, but also the adjacent territory of the Roman Empire. Identifying the ancient places Problems with location identification "But only if we succeed in gaining more clarity here, where we can proceed on safe ground, about the sources of Ptolemy, his method in determining the positions and the value of the tradition available to us, it will perhaps still be possible, also to find the key for his portrayal of Germania Magna, which is so immensely important for the prehistory of our fatherland, but still defies research like an enchanted castle." This is how Karl Zangemeister wrote in 1892 and indeed Ptolemy’s representation of Germania Magna must have seemed to him like an“ enchanted castle ”. Because on the one hand Ptolemy gives us the most comprehensive topographical description of Germania of antiquity, on the other hand it was hardly possible to reliably locate even some of the places he mentioned. An expression of this is the abundance of investigations that were carried out with undiminished intensity even after Zangemeister's statement mentioned above, and the large number of often significantly different identification proposals that resulted from this. The three questions named by Zangemeister turned out to be fundamental problems for the identification of the ancient places in Germania Magna: the text transmission, the sources used by Ptolemy, and his method of determining the geographic coordinates. The text transmission The "original copy" of the Geography from the time of Ptolemy no longer exists. The text available today is wholly or partially transmitted through 53 (previously known) Greek manuscripts, the oldest of which were created around 1300 (Burri, pp. 10-20). For more than a millennium, the text transmission has eluded our direct knowledge. (The Rylands papyrus No. 522 from the beginning of the 3rd century is an exception, see Stückelberger / Mittenhuber / Koch, pp. 142-144.) The preserved Greek manuscripts can now be divided into two text variants, the so-called Ω recension and the so-called Ξ recension. The first splits into two subgroups; the latter is only represented by one manuscript (Stüuckelber-Ger / Mittenhüber p. 21 25). In these two recensions, the coordinates differ from each other in well over a thousand cases, so that not inconsiderable differences can arise when locating an ancient place; For example, the place Bicurgtum in Germania Magna has a latitude of 51°15'according to the Ωrecension, and 49° according to the Ξ recension. These deviations may be caused by typographical errors or by modifications of the coordinates, which may have already been made by Ptolemy or by later editors. Last but not least, Ptolemy himself took into account the possibility of later corrections when creating his catalog of places by leaving space accordingly in his tables (GH II. 1. 3). As a rule, however, in cases of deviating coordinates, the mathematical-geodetic analysis methods described in Section 1.2.2 could determine the presumably correct values. In other cases, it turned out that places are roughly incorrectly localized according to the ancient coordinates and none of the traditional interpretations offers a suitable value. On the one hand, Ptolemy may have already found incorrect information about these places. on the other hand, it is possible. that he himself made mistakes in locating them. Of course, numerous possibilities of spelling mistakes on the part of the copyists can also be assumed here, such as mistakes in the transcription from uppercase to lowercase, wrong interpretation of illegible written numbers, slipping in the line, mixing up whole numbers and fractions, forgetting fractions, hearing errors when dictating, etc. As opposed to lexical, orthographic or grammatical errors in a coherent text are, however, more difficult to recognize when writing coordinates. especially since copyists usually do not have the appropriate specialist knowledge to check the correctness of the coordinates. If the assumption arose that the coordinates of a place were corrupted by a typing error, nominal values were calculated based on the distortion analysis of the ancient data, by means of which conjectures could be suggested. As with the coordinates, there may also be discrepancies between the manuscripts or groups of manuscripts or typographical errors in the ancient place names. In addition, there is a fluctuating orthography, e.g. due to iotacism. If these are names that are also covered by other sources, a correction is usually possible. For example, the correct forms Belgike and Vindobona can easily be determined for the obviously incorrectly transmitted names Beltike or Iuliobona. This is especially true for location information within the Roman Empire. With place names that belong to areas outside the Roman Empire, it is often not possible to decide on the correct reading (for place names see section 1.2.4). Here, spelling mistakes are all the more likely. when, for example, Germanic place names are words of a language that was alien to the copyists in Alexandria and later in Byzantium. The sources used by Ptolemy For identification of the places mentioned by Ptolemaios it is important to ask where he could have got information about them from. Ptolemaios reports that his representation of the oikumene is also based on his own view (GH V 11, 5, l), but his own travel activity may not have been too extensive. It is also very likely that he did not visit Germania, Gaul and the Roman provinces on the Danube himself, so that his description of these areas is not based on his own local knowledge, but exclusively on external sources. The basis of the entire Geography is the work of Marinos of Tyre, a geographer of the 1st / 2nd centuries, of whom we owe our knowledge, apart from a few references by the Arab geographer al- Mas’üdi (died 956), only to Ptolemy. In the first book of Geography he honours the scientific achievement of Marinos on the one hand, and on the other hand also takes a critical look at him. Marinos not only collected an enormous amount of geographical information, in which he "looked at almost all reports of his predecessors with care" (GH I, 6, 1), but he also compiled numerous texts, including, for example, lists of places of the same geographical latitude or the same geographical longitude (GH I. 18, 4). Of particular importance is the draft of a world map made by Marinos and revised several times. Ptolemy compared, however, as he himself says (GH I, 17.2), the information of Marinos also with more recent, i.e. documents created after his work. Unfortunately, Ptolemy gives no information about these materials in his local catalogue. With the help of some hints that he himself gives in the first book of Geography, as well as other ancient evidence, however, different types of sources can be found, and how he might have used them: • Itineraries: These are street directories that indicate stages and distances from country roads (cf. Olshausen, p. 87 90). The most important preserved itineraries, which, however, date from the post- Ptolemaic period, are the Antonine Itinerary provinciarum Augusti (early 3rd century) and the Tabula Peutingeriana, which was created in the Middle Ages but is based on an ancient model; this represents an example of an itinerary in map form. (An overview of preserved ancient itineraries can be found in Löhberg. p. 3 5.) • Periploi (Singular Periplus): These are descriptions of sea routes with information on the coastline, distances, landmarks such as estuaries or foothills, and other nautical information. Periploi were important for Ptolemy when depicting the coasts (cf. GH I. 18, 6; on the periploi see Gungerich, Meyer, Olshausen, p. 81 87). • Individual maps: Ptolemy explicitly mentions that he used individual maps (GH I, 19, 1) to correct errors in the representation of Marinos. • Travel reports: In connection with his theoretical explanations on the cartographic representation of the oikumene (Book I), Ptolemy himself cites several reports of military and trade expeditions on land and at sea. • Astronomical and geographical specialist literature: this was available to Ptolemy in the library of Alexandria. The works of Eratosthenes (approx. 276-194 BC) and Hipparchus (approx. 160-125 BC) were of particular importance. Hipparchus is mentioned twice in Ptolemy's Geography (GH I, 4, 2 and I, 7, 4), Eratosthenes is mentioned in the Almagest (I, 12 p. 68 Heiberg) (for Eratosthenes see Lelgemann 2010). For the Roman provinces, in particular, the geographic information provided by the military and the administration formed the basis of geographic information. In addition to (military) maps and itineraries, Ptolemy also used materials like the dimensuratio provinciarum, a description of the location of the provinces, or the Notitia dignitatum, an administrative manual. Examples of both preserved from late antiquity give us an idea. The chorographia of M. Vipsanius Agrippa (64 or 63-12 BC) was also important, which included a list of distances, the so-called Commentari, and a pictorial representation of the oikumene, which was exhibited in a school hall in Rome. The topographical knowledge of Germania Magna can also be traced back to a not inconsiderable extent to the explorations of the Roman army, the results of which were recorded in the form of war reports and certainly also on maps. In addition, the reports from traders will have provided information, for example about the settlement areas of the individual tribes (for information sources for Germania Magna, see Section 2.1.2). Unfortunately, none of the sources used by Ptolemy has survived, so that a comparison with the Ptolemy information is not possible. This applies not only to Germania Magna, but to the entire Geography. The loss of the maps mentioned is particularly painful, although there are references to them in ancient literature (see Stuckelberger, p. 132f.). An exception is the so-called 'Artemidor papyrus' from the 1st century, which, in addition to a description of the coast of the Iberian Peninsula by the Greek geographer Artemidoros (1st century BC), contains an – albeit unfinished – map sketch (for the Artemidoros papyrus, see Canfora 2008 and Settis). Although Ptolemy tried to use the latest possible materials (GH I, 67, 2), in view of the immense scope of the task that he set himself, namely the mapping of the entire then known earth, it was almost impossible to receive up-to-date information for all treated areas, especially since this was certainly more available in Rome than in the capital of the province of Aegyptus. Ptolemy and also Marinos often relied on sources that at that time could already be several decades, in some cases several centuries old. This explains, for example, the lack of important locations or localizations of tribes that contradict the information provided by other sources; places or military bases that had already been abandoned in the middle of the second century may also be recorded by Ptolemy. Ptolemy’s procedure for determining geographical coordinates In the introduction to Geography Ptolemy writes that the aim of his work is a proportionally accurate representation of the oikumene. While he now describes in detail the methods of a planimetric representation of the oikumene while maintaining the proportions on the spherical surface of the earth, the methods by which he obtained the coordinate information recorded in the local catalog remain largely in the dark. The main difficulty was that most of the materials from which Ptolemy could infer geographical information were not designed for scientific purposes but for practical needs, i.e. they mainly served as orientation in military and civil road and ship traffic. Thus they contained descriptions of land and sea routes, but no geographic coordinates in the form of longitude and latitude. In most cases, Ptolemy had to determine these coordinates for his local catalogue. The representation of traffic routes, on the other hand, plays no role for him. To determine the coordinates, as Ptolemy explains, it is first of all important to use data obtained through reliable observations as a themelioz ("cornerstone") to which the data from other sources are then adapted (GH I, 4, 2). The so-called poleis episémoi (“important cities”), which are not only listed in the eighth book of “Geography”, but also in the Prochetrot kanones (“hand tables”), could have served as such themelioi. These tables form a collection of tables with mostly astronomical information, which, however, is only preserved in an arrangement by Theon of Alexandria (4th century). However, the coordinates of these approximately 360 poleis episémoi may only have been partially determined by astronomical measurements (for the measurement methods of antiquity, see Lelgemann 2010, p. 179ff.). For cities outside the Roman Empire they are even unlikely. Furthermore, Ptolemy assumes that the information on places often visited come much closer to reality than the information on places visited more rarely (GH II, 1, 2) because of their continuous and usually consistent transmission. Although Ptolemy gave priority to data obtained through astronomical observation over information from other sources, such data were only available to him for a few places in the oikumene. Apart from the mentioned individual maps and the lists of places of the same geographical latitude or the same geographical length, which Marinos of Tire created (cf. 1.2.1.2), most of the sources evaluated by Ptolemy contained route information obtained by terrestrial methods, from which Ptolemy first had to derive geographic longitude and latitude values using mathematical and certainly also drawing processes. Several difficulties may have arisen: • Different units of measurement: • Distance information was not only available in stadia, but also in the form of day travels that had to be converted into stadia. • Different stage dimensions were used in the sources. — Roman sources give distances in miles, in Celtic Gaul the leuga was also used, materials on distant areas can be based on other units of measure such as the Indian Yojana (cf. Herrmann, p. 74). • Determination of position using distance information: — Although distances between the places are mentioned in itineraries, they do not contain any directions or statements about the mutual position of the places to one another. — In itineraries, the distances between locations are recorded along the course of the road, not as straight-line distances. • Accuracy and reliability: - The accuracy of the information can vary in the sources used due to different methods of spatial recording. —The sources can contain contradicting or incorrect information about a place. — The sources used may already contain typographical errors. The consequence of this are systematic and gross errors in the coordinates of the Ptolemaic catalog of places, which make it difficult to identify the ancient places. Despite the problems described with regard to the Ptolemaic location information, it is possible to locate a large part of the ancient places. However, this requires an interdisciplinary approach, because on the one hand the occurring distortions of the ancient coordinates must be investigated, for which modern mathematical-geodetic methods were used for the first time in the present work (see Section 1.2.2), on the other hand it is important to compare the results of this analysis with as much additional information as possible on the history and archaeology, but also on the topography of the area concerned. There are also considerations of place names. In principle, the statement made by Reismann-Grone (p. 41) with regard to the identification of the Ptolemaic places applies: "After several misinterpretations, it seemed right to proceed as in politics, namely to see things as simply as possible, to deal with each question individually without fixed ideas.” This means that each area has its own set of problems and therefore requires a corresponding approach. Nevertheless, the investigations carried out so far show that Ptolemy's location information is often remarkably accurate. 1.2.2 Geodetic rectification of Ptolemaic coordinates 1.2.2.1 The Ptolemaic coordinates If one compares the Ptolemaic coordinates of a place with its coordinates in the modern geographic reference system, it can be seen that these in general show great differences. With the length specifications this is, among other things, due to the different zero meridians of the Ptolemaic and modern reference systems. But even after taking this known length difference into account, large differences still remain. The cause of the coordinate differences are various errors in the Ptolemaic coordinates. In the Ptolemaic coordinates, the smallest fraction of a degree 1/12° = 5'occurs. The analysis of the frequency of occurrence of the individual minute values (5', 10', 15', ...) showed that not all coordinate values actually have a resolution of 5'; other, coarser resolutions >10' also occur. For the regions dealt with here, there are hardly any coordinates with a resolution of 5', which reduces their accuracy. However, the resolution of the coordinate values does not reflect their real accuracy. The true errors of the Ptolemaic coordinates can be much larger than the resolution suggests. This is due to systematic and gross errors in the coordinates. After they have been taken into account or removed, residual errors of a random nature remain, the size of which is closely related to the resolution. The systematic errors in the coordinates are evidently shifts and dimensional falsifications. One can only speculate about their exact causes. In addition to the underestimation of the circumference of the earth by Ptolemy, which caused the lengths to be scaled with a factor of >1, it can be assumed that Ptolemy unknowingly ignored the differences between ancient stadion definitions. While the scaled distortions appear to be large, i.e. appear similar in country size, there are smaller groups of places that are shifted from one another. The cause of the shifts can be reference locations from which the position of the surrounding locations was determined (by measurement or by calculation). If the mutual position of the reference locations was only inaccurately or incorrectly determined, the errors were transferred to the local groups concerned in the form of shifts. The systematic errors can be described with a mathematical function. After the sizes of the systematic errors of individual local groups have been determined, this enables rectified coordinates to be calculated in the modern reference system (transformation) for previously unidentified locations and thus their identification. The data from itineraries and surveys used by Ptolemy as measured variables or variables derived from them inevitably have random errors. Accidental falsifications also occurred during the preparation and compilation of the data by Ptolemy. The size of the random errors is described by the standard deviation, assumed to be approx. 5° for the most precise coordinates (Lelgemann et al.). There are also gross errors in Ptolemaic coordinates. They may already have existed in the data used by Ptolemy, or have been inserted by Ptolemy himself, or have been created in copies of the local catalogue of Geography. The major errors need to be uncovered during the distortion analysis. However, this is only possible for larger gross errors, smaller gross errors cannot be distinguished from random errors. Due to the interaction of the various coordinate errors, it can happen that the mutual position of two places indicated by Ptolemy is absurd (e.g. far too great a distance, topological errors such as west instead of east). Examples are Rhenus fluvius (middle estuary of the Rhine according to Ptolemy) and Asciburgium, with their identifications Oude Rijn and Moers-Asberg. The differences between the Ptolemaic coordinates (Λ, Φ) and the modern coordinates (λ, φ) of both places are: Asciburg Rhenus difference Λ 27°30' 27°00' 0°30' λ 6°39' 4°34' 2°05' Φ 52°30' 53°10' -0°40' φ 51°26' 52°08' -0°42 ' Accordingly, the mutual position of the places in the Ptolemaic system is strongly falsified in length (error approx. 1½°). A spelling mistake cannot be assumed here, since both places with their coordinates match their nearest neighboring places (only minor, random coordinate errors). The two places or local groups are obviously systematically shifted in length from one another. 1.2.2.2 Geodetic rectification The computational, geodetic analysis of coordinate information in the Geography catalog of locations aims to: • locate local groups of the same distortion systematics (transformation units) and to determine the type and size of the distortions (distortion parameters); • uncover inconsistent locations, i.e. misidentifications and gross ancient coordinate errors or spelling mistakes in the manuscripts; • determine modern coordinates for Ptolemaic places by means of an equalizing transformation and thus to identify them; • make statements about the accuracy of the Ptolemaic data. In some cases, several ancient coordinates have been handed down for a location (see Section 1.2.1.1). Likewise, several uncertain modern identifications can exist for an ancient location. Both are taken into account by the evaluation process, i.e. the probably correct values or identifications are determined. When searching for local groups with the same systematic distortion, an adjustment calculation is used (method of least squares). It is usually used when more observations than necessary to determine the parameters of a functional relationship are available. Overdetermination has the advantage that statements and hypothesis tests etc about the accuracy of the observations can be done. Such statistical tests, in turn, enable the search for local groups for each of which a specific distortion model including its parameters is valid. In the Gauss-Markov model used here, the Ptolemaic coordinates represent the observed, error-prone quantities. Since the modern coordinates have significantly smaller uncertainties than the Ptolemaic, these can be viewed here as error-free. The unknown quantities sought are the transformation parameters. The transformation approach for the transfer of the modern to the Ptolemaic coordinates is

Λi + vΛi = mλλi + Λ0

Φi +vφi = mφφi + Φ0 with the modern longitude λi and latitude φi, the Ptolemaic longitude Λi and latitude Φi, the scale parameters mλ and mφ, the translations Λ0 and Φ0 and the random residual errors (improvements) vΛi and vφi. The systematic distortions of the Ptolemaic location information are modeled with the scale parameters and translations. In practice, the model proves to be accurate enough, i.e. the resulting residual errors usually have no systematic residuals and their amounts are consistent with the resolution or the size of the uncertainty of the Ptolemaic coordinates. The procedural steps of the geodetic analysis of the Ptolemaic coordinates are as follows: Since only combinatorial methods are promising in the present task, the practicability of such methods is strongly dependent on the amount of data, an area of investigation is divided into local groups in advance, in which the search for transformation units is initially carried out separately. Such a start division can be generated on the basis of the residual image that results after a first transformation with approximate values for the distortion parameters. In the residual image, areas of homogeneous T distortion at similar residual vectors (vλ vφ) become clear (determined by means of (1.1)). Since the start division may separate places that belong together, further follow-up examinations are required after the search for transformation units in the start areas (3 and 4). 2. The search for transformation units is done combinatorially. The locations of a starting area are combined with one another until a maximum consistent location group is found. The consistency check is carried out using statistical tests. A transformation unit thus determined is removed from the data and the search is repeated among the other locations until a consistent group is no longer found. Since there are several uncertain identification proposals for quite a few locations, the procedure was geared towards including such alternatives in the combinatorial search in order to determine the possible or the most likely identification among the possible. 3. After the determination of transformation units in the starting areas, there will generally still be locations that are not assigned to any transformation unit. Possible causes are: • systematic errors (locations are consistent in another transformation unit); • errors in the Ptolemaic coordinates (e.g. incorrect coordinate variant used, spelling mistake); • errors in modern coordinates (due to incorrect identification); • Errors in the stochastic model (uncertainty of the Ptolemaic coordinate greater than assumed). The first two causes are checked, i.e. it is determined for the previously unassigned locations whether they are consistent in a transformation unit in their neighbourhood with one of their identifications and ancient coordinate variants. For this purpose, the possible combinations of modern identification and ancient point variants for each location are individually switched into the transformation units in question and an adjustment is carried out. If the point groups remain consistent, the best assignment is carried out (measure is the size of the test statistic used) and the procedure for the remaining unassigned points is continued. 4. If the differences between the transformation parameters of neighbouring transformation units in terms of location are not statistically significant (statistical test), they can be summarized. The search for maximum groups that can be summarized is also combinatorial. That possible combination is carried out which brings together the greatest number of locations, and the search for further combinations is continued among the remaining transformation units. 5. The results are checked for plausibility. This applies above all to the location and form of the transformation units. In the event of strong positional overlaps, rebalancing and statistical tests are used to check for the causative locations whether the assignment to another transformation unit is possible. If, after the procedure has been carried out, locations remain without a possible assignment to a transformation unit, it must first be decided whether changes in the stochastic model are possible for them (larger standard deviations). If such changes can no longer be justified, modern identification must be reconsidered. By means of transformation, modern coordinates (λ, φ) can be determined from the Ptolemaic coordinates (Λ, Φ):

λi = mΛΛi + λ0

φi = mφΦi + φ0

Here mΛ and mφ are the scale parameters and λ0 and φ0 are the translation parameters of the equalizing function. The rectification parameters are obtained by inverting the determined distortion parameters: mΛ = 1 / mλ mΦ = 1 / mφ

λ0 = Λ0 / mλ φ0 = Φ0 / mλ If new identifications can be found by means of transformation, the evaluation process (steps 2-5) must be repeated. If the transformation does not result in a plausible identification, a gross error in the Ptolemaic coordinates must be assumed. Assumptions about copying errors can be checked by changing the relevant coordinate accordingly, in that a new adjustment including statistical consistency tests has to be carried out for the relevant transformation unit. 1.2.3 Information from antiquity For the provinces of the Roman Empire, the Barrington Atlas initially serves as the basis for location identification. With its help, some of the places mentioned by Ptolemy can be located, although, as the investigation of the corresponding chapters in Geography has shown, in the individual Roman provinces there are sometimes not inconsiderable differences with regard to the proportion of places reliably identified. In some cases, the identifications given by the Barrington Atlas turn out to be insecure or incorrect, so that further investigations are necessary. In contrast, the Barrington Atlas hardly provides any information for the Germania Magna area. If a place cannot be located using the Barrington Atlas, the next step must be to check whether there are any references to it in other ancient sources. Since all the places were on traffic routes, the Itinerarium provinciarum Antonini Augusti and the Tabula Peutingeriana are of particular interest since they are road maps. The details of other ancient authors are included insofar as they contain information useful for location identification. Naturally, it is also true here that far more information can be found in the written sources for the places in the Roman Empire than for Germania Magna, because most of the place names mentioned by Ptolemy have only come down to him himself. Since Ptolemaic geography has long been the subject of intensive research, there are already numerous studies on individual regions. The identifications proposed by historians, geographers, philologists and authors from other disciplines are therefore recorded as far as possible and are included in the bias analysis (see Section 1.2.2.2). On the one hand, identification suggestions can be confirmed, on the other hand misinterpretations can be pointed out. Of particular importance are archaeological finds, which, due to the lack of written sources and epigraphic evidence, offer important clues for the location of ancient places in Germania Magna. However, especially in areas with a wide range of finds, it is often not possible to associate a Ptolemaic place name with a specific site. Often it is currently only possible to specify the region in which the relevant location can be located using the transformed ancient coordinates. However, the results obtained are based on the current state of research. New archaeological finds and the recording of areas that have not been explored so far will expand our level of knowledge and shape the picture of Germania Magna even more precisely. 1.2.4 Place names In addition to the mathematical-geodetic methods for analyzing the ancient coordinates and diverse information from antiquity, the identification of ancient places is flanked by the examination of place names. An identification is problem-free with uninterrupted settlement and name continuity since antiquity, as is the case with many places in the area of the Roman Empire. In addition, other written certificates can often be used for comparison. Even in the case of places that have been abandoned as settlements or military sites, identification is sometimes possible using other sources such as the Itinerarium provinciarum Antonini Augusti or the Tabula Peutingeriana. However, similar names can also lead to misinterpretations, such as the equation of the Rhaetian place Vicus mentioned by Ptolemyus with Viviscus/Vevey or Claudivium in Norica with Iuvavum/Salzburg. The decisive factor here is whether there is a correspondence between the position of a place, as determined by the corrected ancient coordinates, and the identification proposal made on the basis of the similarity of names. The investigation of place names in the non-Roman areas is much more difficult. Most of the place names in Germania Magna occur nowhere else and are only handed down by Ptolemy, not by any other source. If these place names are also available in different readings, it is usually very difficult to decide which variant to use. Reconstruction of the original form is also made more difficult by the fact that the Germanic place names were first translated into Latin and then into Greek. In addition to spelling mistakes, phonetic changes are also to be expected. Steche remarks aptly (p. 8): “You have to be clear about this. that Germanic names for an ancient Roman or Greek were just as cheeky as we are today, for example, with Russian or Indian names.” Roman soldiers, surveyors and traders could write the place names only according to the sound, since written documents from the Germanic peoples did not exist. Foreign place names were latinized and possibly in some cases also adjusted to known and similar- sounding Roman names. Ptolemy, who was most likely ignorant of Germanic, finally reproduced the names in Greek. However, some indications make it clear that the geographical information about Germania goes back to the Romans. For example, in the Greek transcription of a place name the consonant sequence -νγ- or -νκ- instead of the -γγ- or -γκ- expected in Greek suggests that the place name in question is taken from a Latin source. The place names Lupfurdum and Tulifurdum mentioned by Ptolemy are of neuter sex, although the Germanic word furd (‘ford’) they contain is masculine (Bach, vol. Il / l, p. 23). Obviously, these forms are originally directional accusatives, as found in Roman itineraries. However, some clues for location can be obtained from the place names; a Germanic formation with the mentioned element -furdum indicates a river crossing. However, attempts to identify Ptolemaic places on the basis of simple similarities with today's places, such as Mesuium with Merseburg or Viritium with Wrietzen, should be treated with caution, because only a few modern German place names can be derived from the ancient ones. For example, out of “local patriotism”, attempts were made to equate one's hometown with a Ptolemaic place. In addition to the Germanic and Celtic place names or the toponyms with links to the so-called Balkan- Illyrian languages such as Leucaristus (Grunzweig, p. 309) there are also names whose origin is disputed. A comprehensive, albeit partially outdated, work on place names in Germania is the study by Rasch; Further information on the name etymology can be found in the corresponding entries in the Reallexikon der Germanischen Altertumskunde. Krahe provides a brief description of the significance of place names as a historical source. 1.3 The structure and content of the following papers The focus of this book is investigation of Germania Magna, as described in Ptolemy's Geography. In addition, the neighbouring Roman provinces of Raetia, Noricum, Germania Inferior and Germania Superior are treated. Since these two Germanic provinces are represented in Ptolemy's description of Gallia Belgica, this area as a whole was included in the present work. It therefore includes the following chapters from the second book of Geography: • Chapter 9 - Gallia Belgica • Chapter 11 - Germania Magna • Chapter 12 - Raetia et Vindelicia • Chapter 13 - Noricum. The essays on these chapters are divided into: • General (including map) • Coordinates and identifications of ancient places and landmarks • Comments on the identifications • Literature. As an additional treatise, this book includes a contribution to the location of the island of Thule. In what follows, the above subsections of the individual treatises on the chapters of Geography are explained in more detail. General In this section there is a general introduction that briefly describes the area concerned and points out the peculiarities and problems in the representation of Ptolemy. At the end of this section there is a map of the area. Coordinates and identifications of the ancient places and landmarks The places and topographical points of the treated area are listed in a table. Their order corresponds to the arrangement in Ptolemy's Geography. The new edition of Geography published in 2006 (cited as Basel-Edition 2006) was taken as the basis for the text. For investigation of the ancient coordinates, the editions of Müller and Cuntz were also consulted in order to take into account as many of the interpretations given there as possible, i.e. even those that were viewed by the editors of the text editions as inferior, because “sometimes the poorer manuscripts contain just the right thing” (Steche, p. 8). The table contains the following information: • consecutive number of the place • ancient place name and Ptolemaic longitude Λ and latitude Φ • modern place name and modern longitude λ and latitude φ • transformed Ptolemaic longitude λ̅ and latitude φ̅; they were transformed by means of

λ̅ = mΛΛi + λ0

φ̅ = mφΦi + φ0 with scales mΛ and mφ and the translations λ0 and φ0; the parameter values are listed in the appendix • difference between modern and transformed coordinates λ - λ̅ or φ - φ̅ • transformation unit (column TE); it indicates which locations are to be transformed uniformly with the same transformation parameters or have the same systematic distortions (scale, translation) • Category of identification security (column S): - s: sure - w: probably - u: unsure The following criteria were used as a basis for certainty of identification: - the coordinates; - research results in archaeology and study of antiquity; - topographical conditions, - possibility of deriving the modern place name from the ancient one. All places that can be clearly identified on the basis of settlement or name continuity or epigraphic evidence are deemed to be "sure". An identification is regarded as "likely" if the location by the coordinates agrees with reports of written sources and archaeological findings, if the transformed coordinates indicate a site of particular regional or supra-regional importance, or even if less significant archaeological evidence in connection with the transformed coordinates, the topographical conditions of the location, and possibly the possibility of deriving the modern place name from the ancient one confirm the proposed location of a Ptolemaic place. All places that can only be located using the transformed ancient coordinates, or for which, according to the current state of research, no precise delimitation of the location is possible, have been classified as "unsafe". This is also the case if identification was only carried out on the basis of assumed similarity of names. • Source of the ancient coordinates (column Q): - Ω = Ω-recension - Ξ = Ξ-recension - M = text of Müller - m = uncertain reading in the apparatus of Müller - N = text of Nobbe - A = alternative proposal due to a suspected typographical error The table lists all the places and topographical points mentioned by Ptolemy in the area concerned, i.e. locations for which there is no identification and which therefore do not appear on the map are also given. Notes on the identifications This section provides a brief commentary on the identifications specified. All places and topographical points that are reliably identified and whose ancient coordinates do not show any contradictions remain uncommented. In the case of frequent references to the work of Müller and Hansen, page numbers were generally omitted, as these are continuous comments in which the relevant passages can be easily found. Since Latin was not only the official language in the western provinces of the Roman Empire, all place names and names of topographical points in Gallia Belgica, Raetia and Noricum are given in Latin form below. Name variants are in brackets. The area of Germania Magna was outside the Roman Empire, but the topographical information about it reached Ptolemy through Roman mediation (see Section 2.1.2). That is why the place names in Germania Magna are uniformly listed in a Latinized form. The basis for this is the Latin translation of the Müller edition. Germanic forms have not been translated into German or reconstructed, an explanation of Latin geographical names can be found in the subject index at the end of this book. For places in Germania Magna, the Greek spelling of the place name is also given, as it appears in Ptolemy. (If no Greek spelling is given, the Latin and Greek form of the name are identical.) The location identifications determined in the course of our investigations are each printed in bold. Since the identification of the ancient places in the present work is based on the analysis of Ptolemaic coordinates, all information that was not provided with coordinates by Ptolemy, such as the settlement areas of the individual tribes in Germania Magna, is not taken into account.