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Hist. Geo Space Sci., 9, 924, 2018https://doi.org/10.5194/hgss-9-9-2018 Author(s) 2018. This work is distributed underthe Creative Commons Attribution 4.0 License.

The length of coastlines in Ptolemys Geography andin ancient periploi

Dmitry A. ShcheglovS.I. Vavilov Institute for the History of Science and Technology, St. Petersburg, Russian Federation

Correspondence: Dmitry A. Shcheglov ([email protected])

Received: 2 July 2017 Revised: 22 November 2017 Accepted: 2 December 2017 Published: 1 February 2018

Abstract. The lengths of the coastlines in Ptolemys Geography are compared with the corresponding valuestransmitted by other ancient sources, presumably based on some lost periploi (literally voyages around orcircumnavigations, a genre of ancient geographical literature describing coastal itineraries). The comparisonreveals a remarkable agreement between them, suggesting that Ptolemy relied much more heavily on these orsimilar periploi than it used to be thought. Additionally, a possible impact of Ptolemys erroneous estimate ofthe circumference of the Earth is investigated. It is argued that this error resulted in two interrelated distortionsof the coastal outlines in Ptolemys Geography. First, the northsouth stretches of the coast that were tied toparticular latitudes are shown compressed relative to the distances recorded in other sources in roughly the sameproportion to which Ptolemys circumference of the Earth is underestimated relative to the true value. Second,in several cases this compression is compensated by a proportional stretching of the adjacent eastwest coastalsegments. In particular, these findings suggest a simple explanation for the strange shape of the Caspian Sea inPtolemys Geography.

1 Introduction

Classics (or studies of Greco-Roman antiquity), which isthe field that the history of ancient geography and cartog-raphy belongs to, is a very old discipline. So, as time goesby, the chance to find something really new in this field, orto do something that nobody has ever done before, tendsto zero. Ptolemys Geography (ca. AD 150) is a happy ex-ception to this tendency. Although the Geography is oneof the most famous and often-studied works in the historyof cartography, its origins still remain an enigma. How-ever, in the last decade, after the publication of its new edi-tion by Stckelberger and Grahoff (2006), Ptolemys Ge-ography has seen an upsurge of scholarly interest. Numer-ous researchers have developed a wide array of differentmethodological approaches to studying its nature and gen-esis (e.g. Isaksen, 2011, 2013; Marx, 2011, 2016; He, 2016;Shcheglov, 2017; Grahoff et al., 2017; Arnaud, 2017; De-faux, 2017). One of the main approaches is a comparisonwith other ancient sources. Surprisingly, until this day no-body has ever tried to compare Ptolemys Geography withthe ample data on coastline length provided mostly by Agath-

emerus in his Geographical Sketch (the 1st century AD) andby Pliny the Elder in the geographical books of his NaturalHistory (AD 7779). The objective of the present study is tofill this gap. My contention is that this comparison can shedsome new light on Ptolemys modus operandi and the genesisof his Geography.

2 Periploi among the sources of PtolemysGeography

Ptolemys Geographical Guide, or simply the Geography,was essentially a description of the world map in terms ofspherical coordinates (latitude and longitude in degrees) as-signed to each of the 6300 listed localities.1 However, it isclear that only some of these coordinates could have beenbased on astronomical observations (e.g. the latitudes of the

1Consequently, the term Ptolemys Geography may be usedsynonymously with Ptolemys map when referring to a map re-constructed from the coordinates recorded in the text. These coor-dinates are now available in an electronic database attached to theedition of the Geography by Stckelberger and Grahoff (2006).

Published by Copernicus Publications.

10 D. A. Shcheglov: The length of coastlines in Ptolemys Geography and in ancient periploi

major cities: Alexandria, Rhodes, Athens, Rome, Massalia,etc.). Ptolemys predecessors and possible sources describedgeographic space mostly in terms of distances measured incustomary units (Greek stades, Roman miles, etc.).2 It isreasonable to suppose, therefore, that, with few exceptions,Ptolemys coordinates were derived from distances convertedto angular units (Cuntz, 1923, p. 110; Knapp, 1996, p. 3035; Grahoff et al., 2017; Arnaud, 2017, pp. 3, 1420). Thismakes comparison of Ptolemys Geography with other sur-viving sources a promising way to investigate its organizationand genesis. Interestingly, there are a lot of studies compar-ing Ptolemys distance data with the Roman itineraries (ordescriptions of the land routes),3 but only a few attempts tocompare them with the Greek periploi.4

Periploi (sing. periplus) is a genre of ancient geographicalliterature describing coastlines in the form of a linear succes-sion of stopping points and intervening distances. Periploiare considered to be the standard basis of ancient descrip-tive geography (Purcell, 2012, p. 1107).5 Many ancient ge-ographers Artemidorus, Strabo, Pomponius Mela, Plinythe Elder (in Books IIIVI of his Natural History), Diony-sius Periegetes, etc. presented their works in the form ofperiploi, even though they actually did not confine their nar-ratives to the coasts. Ptolemy himself emphasizes (Geogr.1.18.6) that it is much easier to indicate the positions of thecoastal cities than of the inland ones. It is reasonable to sup-pose, therefore, that in many respects it was periploi that pro-vided the foundation for his map of the world.

Only a few periploi survived from antiquity and onlyfour of them provide detailed information on distances: threePeriploi of the Pontus Euxinus (Black Sea) and the Stadias-mus of the Great Sea (Mediterranean).6 These sources, how-

2The length of the stade is a vexed issue. The majority of an-cient sources use the ratio of 1 Roman mile (for which the standardnotation is m.p. or mille passuum) to 8 Greek stades. This ratio isused throughout the present paper. Since the Roman mile measuresabout 1480 m, 1 stade is equal to ca. 185 m. For a detailed discus-sion with references to relevant literature, see Shcheglov (2016b,p. 694701).

3Cuntz (1923), Spaul (1958, p. 57), Seabra Lopes (19951997), Knapp (1996), Meuret (1998), Gmez Fraile (2005), UrueaAlonso (2014a, b).

4Mittenhuber (2012) compares Ptolemys Hispania (i.e. theIberian Peninsula) with the distance data from the so-called Artemi-dorus papyrus, while Marx (2016) compares Ptolemys Atlanticcoast of Africa with the distance data from Plinys Natural History.

5On periploi as one of the basic forms of geographical descrip-tion in antiquity, see Janni (1984).

6Two Periploi of the Pontus Euxinus (Black Sea) composedby Menippus of Pergamon (the end of the 1st century BC) andFlavius Arrian (the beginning of 2nd century AD) served as thesources for the third and fuller Periplus known under the name ofPseudo-Arrian (3rd century AD). The standard edition of these threeperiploi is Diller (1952, p. 103146). The anonymous Stadiasmus ofthe Great Sea (1st century AD; for this dating, see Uggeri, 1996) de-scribes the coasts of Africa from Alexandria to Carthage and of Asia

ever, deserve a more thorough examination elsewhere. Fortu-nately, thanks mainly to the Geographical Sketch by a certainAgathemerus (Diller, 1975) and to Books IIIVI of PlinysNatural History (Jan and Mayhoff, 1892), as well as to someother sources, we have a set of values for the total coast-line lengths of the major regions as recorded by the mostfamous ancient geographers: Eratosthenes (the 3rd quarterof the 3rd century BC),7 Artemidorus of Ephesus (ca. 104100 BC),8 Marcus Vipsanius Agrippa (ca. 12 BC),9 Isidoreof Charax (around the turn of the 1st centuries BC and AD),and some others. These values evidently derive from somelost periploi.

This data set covers the largest part of the then-knownworld (Figs. 2 and 3). First of all, Artemidorus, Isidore, andAgrippa give the lengths of the coastlines of the Inner Sea(Mediterranean, Black, and Azov seas) as a whole and asdivided between the three continents: Europe from the Pil-lars of Hercules (or Calpe, i.e. Gibraltar) to the mouth of theTanais (Don), Asia from the Tanais to the Canobic (west-ernmost) mouth of the Nile, and Libya (Africa) from thismouth to Tingis (Tangier). The same geographers and someother authors give the perimeters of the major peninsulas (thePyrenean, the Italian, the Arabian), seas or gulfs (the PersianGulf and the so-called second and third gulfs of Europei.e. roughly speaking, the Adriatic, Ionic, and Aegean seasand the Red, Black, Azov, and Caspian seas), and the largestislands. The fact that different authors reproduce almost thesame or similar set of values suggests that these data wereregarded as a special category to be included in a geographi-cal treatise. For the sake of completeness, we will add to thisset several values of the total coastline lengths reported bythe surviving detailed periploi: Pseudo-Arrians Periplusand the Stadiasmus, as well as by Strabos Geography (ca.AD 23), our main source on its subject matter (Radt, 20032011).

from Aradus to Miletus including the adjacent islands of Cyprus andCrete. The most reliable edition is still Mller (1855, p. 427563);a new edition is being prepared by Pascal Arnaud. These periploimay be called detailed in the sense that, unlike other survivingperiploi, they divide the route into hundreds of course legs with themedian length of ca. 90 stades or 1617 km. On the ancient methodsof maritime distance estimation, see Arnaud (1993).

7Eratosthenes was probably the most famous ancient geographerbefore Ptolemy. His geographical treatise has survived only in frag-ments; for the editions, see Berger (1880) and Roller (2010).

8Schiano (2010).9Marcus Vipsanius Agrippa (6312 BC) was the right arm of the

emperor Augustus. According to Plinys testimony (Natural His-tory 3.17), he left behind an unfinished geographical work which, asmost scholars believe, served as the basis for a world map displayedin the Porticus Vipsania in the centre of Rome (before AD 14). Themap was accompanied by explanatory notes with an account of di-mensions and boundaries of 24 regions of the world. These noteshave come down to us only in fragments; the standard edition isKlotz (1931).

Hist. Geo Space Sci., 9, 924, 2018 www.hist-geo-space-sci.net/9/9/2018/

D. A. Shcheglov: The length of coastlines in Ptolemys Geography and in ancient periploi 11

The objective of this paper is to compare this data set withthe lengths of the corresponding coastlines in Ptolemys Ge-ography. But before attempting the comparison there are sev-eral methodological issues we need to discuss.

3 Method of comparison

How can we measure the lengths of the coastlines inPtolemys work? My contention is that the simplest and mostnatural way would be to take Ptolemys Geography as what itessentially is, namely as a catalogue of spherical coordinates.The distance between two points specified by these coordi-nates is an arc of the great circle that can be calculated usingthe rules of spherical trigonometry.10 Accordingly, I proposeto calculate the length of the coastlines in Ptolemys Geogra-phy as the sum of individual arcs joining coastal points mul-tiplied by the length of a degree of the great circle which hedefines as 500 stades (Geogr. 1.7.1, 11.2).

It is important to emphasize that actually next to nothing isknown about how Ptolemy worked with his sources and howhe converted their distance data into coordinates (Grahoffet al., 2017, p. 2, 67; Defaux, 2017, p. 12, 255). It is hardto imagine that he would have calculated the coordinates foreach of the 6000 points listed in his Geography. It would bemore reasonable to assume that calculations may have beenperformed only for the most important points, whereas allothers were localized by means of simpler methods, for ex-ample, Pythagoras theorem and/or a simple ruler; cf. simi-larly Spaul (1958, p. 57) and Grahoff et al. (2017, p. 1, 16,25).

Ptolemys coordinates are specified with precision up to5. This, however, must not mislead us about the accuracyof his data. The precision of Ptolemys coordinates corre-lates clearly with the density of the points on his map: itsrarest parts at the periphery (such as Asian Scythia or InnerLibya) have the highest percentage of coordinates in wholedegrees, but as we approach the Mediterranean, the fractionsof a degree become increasingly more frequent and smaller.In other words, Ptolemys coordinates can be precise not somuch because his sources were accurate, but rather in or-der to fit many points in a confined space. Statistical anal-ysis of the frequency of different fractions of a degree usedin Ptolemys coordinates shows that he tended to round allvalues to the largest possible fractions.11 It means that, fig-

10The distance between points A and B situated on a sphere canbe calculated by the formula cosSAB = cos1AB sin(90A) sin(90B)+cos(90A)cos(90B), where SAB is the dis-tance between points A and B expressed in degrees of the great cir-cle, 1AB is the longitudinal interval between them, A and Bare their latitudes. Certainly, Ptolemy did not have trigonometricformulas in their modern form, but the theorems of Menelaus thathe used to solve similar problems in the Almagest were an ancientequivalent of them (Neugebauer, 1975, p. 2130).

11The frequency of different fractions of a degree in Ptolemyscatalogue of coordinates conforms to a normal distribution: the co-

uratively speaking, Ptolemys map had low resolution: itcould reproduce general outlines of large objects, but wasquite inaccurate in details. For this reason, when comparingPtolemys data with the distances reported by other sources,it makes sense to consider only those applying to relativelylong intervals. It also needs to be born in mind that, owingto the peculiarities of the map, close matches can hardly beexpected from this comparison.

The text of Ptolemys Geography has been handed downto us in two recensions: 4 and (Fig. 1).12 Both of themdescend from antiquity, but none of the extant manuscriptsdates earlier than the late 13th century. The 4 recension isconsidered to be earlier and more authentic, but it is repre-sented by the sole manuscript Vaticanus Graecus 191 (ca.AD 1295) which omits all coordinates for the eastern half ofthe map (i.e. for the whole Asia, except for Asia Minor, Ar-menia, and Asiatic Sarmatia) and contains quite a few scribalerrors. The recension is apparently secondary to 4, but itincludes the majority of the manuscripts.13 In view of thesecircumstances, when comparing Ptolemys data with the dis-tances recorded in other sources, both recensions should betaken into account, but 4 should be regarded as more reli-able.

4 Comparison of the coastline lengths in PtolemysGeography and in other sources

Let us turn to the sources. All data needed for comparisonare given in Table 1, which constitutes the core of this pa-per, and are illustrated by Figs. 27. Table 1 compares thecoastline lengths derived from Ptolemys coordinates (in 4and ) with the corresponding distances given in the othersources, presumably based on periploi.14 Also, the tableshows how much Ptolemys values deviate from those of the

ordinates in integer degrees, without fractions, are the most fre-quent, those with 1/2 are less frequent, those with 1/3 or 2/3

are still less, those with 1/4 or 3/4 and 1/6 or 5/6 are still lessagain, and those with 1/12, 5/12, 7/12 or 11/12 are the rarest;see Wurm (1931, p. 2527), Marx (2011, p. 3036), Isaksen (2011,p. 262264, 2013, p. 4850).

12For a detailed discussion of the manuscript (MSS) tradition,see e.g. Schnabel (1938), Stckelberger and Grahoff (2006, p. 3034), Burri (2013, p. 6393), for a good synopsis, see Defaux (2017,p. 6781).

13See e.g. Cuntz (1923, p. 1516), Schnabel (1938, p. 44, 5557),Burri (2013, p. 540542). Polaschek (1965, cols. 717, 742744) andBerggren, Jones (2000), p. 4345 argued that the recension repre-sents a post-Ptolemaic Byzantine revision, whereas codex VaticanusGraecus 191 is the only piece of Ptolemys genuine text. However,I see no sufficient grounds for such a radical position; see similarlyDefaux (2017, p. 8081).

14All Ptolemys coordinates are taken from the electronicdatabase attached to the newest edition of the Geography (Stck-elberger and Grahoff, 2006) and are appended to the present paperas Excel files in the Supplement.

www.hist-geo-space-sci.net/9/9/2018/ Hist. Geo Space Sci., 9, 924, 2018


Figure 1. The outlines of the Mediterranean Sea according to the4 and recensions of Ptolemys Geography (Italy, the Balkans,and the Aegean Sea are taken as an example). This and all theother maps in the paper are drawn using the projection attributed byPtolemy to Marinus of Tyre (Geogr. 1.20.35), whom he introducesas his immediate predecessor and the primary source of information(Geogr. 1.6.1). In modern terms, it is an equidistant cylindrical pro-jection, in which the ratio between equal latitudinal and longitudinalintervals is represented as 5 : 4.

other sources, and how much deviates from 4, both interms of stades and in terms of percentage.

What conclusions can be drawn from this comparison?First of all, our sample clearly falls into two parts: shorter andlonger distances. Islands and other small features (such asPeloponnesus or no. 18 in Table 1, the Great Syrtis or nos. 7and 17, etc.) or relatively short coastal stretches exhibit littlesimilarity between Ptolemys data and the periploi data (theonly exceptions are Sicily nos. 15 and 16, Crete no. 8, andIllyria nos. 1 and 9; Figs. 3 and 7) This result accords withthe fact that Ptolemys map had a low resolution and was inprinciple incapable of representing small features accurately.

However, for longer distances, with a threshold being ap-proximately at 10 000 stades, the pattern changes radically. Itis instructive to remember that, with only a few exceptions,these coastlines are very long and have very complex geom-etry. In these circumstances, one can hardly expect any sim-ilarity between Ptolemys figures and the periploi figures atall. Nevertheless, the correspondences between them are sonumerous and so close (Fig. 4) and their geographical cover-age is so wide (Figs. 2 and 3) that this can reasonably be re-garded as something more than just a series of coincidences.

Figure 4 shows that in most cases the differences betweenPtolemys data and the periploi-based sources fall between+4 and 1 %.15 How can we interpret these values? Is ita lot or not? Previous researchers who compared Ptolemysdata with the distances recorded in other sources regarded

15Of course, it is possible to find many contradictions betweenPtolemys data and distances reported by other sources, but thereis no reason to expect them to match always and everywhere. Forexample, Pliny gives evidently incredible and fictional values forthe coastlines of Germania (4.98 = Agrippa F 21; see Riese, 1878,p. 5) and Gaul (4.105 = Agrippa F 23 Riese = F 40 Klotz): 20 000and 14 000 stades, respectively.

the 510 % difference between them as small enough to sug-gest a common origin (Cuntz, 1923, p. 120122, 144145;Uruea Alonso, 2014a, p. 164, 169170; Marx, 2016, p. 3334). But for a more robust assessment, it would be infor-mative to compare the differences between Ptolemy and theother sources with the differences between the two recen-sions of Ptolemys own work (see Table 1 and Figs. 5, 6). Aconvenient benchmark for this comparison is provided by themeasurements of the Inner Sea (Mediterranean and Blackseas without the Azov Sea).16 In the 4 recension, its perime-ter measures 133 792 stades, which is 2.8 % longer than ac-cording to Artemidorus (130 120, no. 50 in Table 1), but init is 1.8 % longer (136 231) than in4. Remarkably, in a num-ber of cases the differences between4 and are appreciablylarger than those between 4 and the other sources: Europefrom Calpe to the Tanais (no. 48 in Table 1), Hispania (33),Italy (29), the second gulf of Europe (26), and the Red Sea(28). If we still believe that 4 and are, despite all the dis-agreements between them, two versions of the same work bythe same author, the similarity between Ptolemys 4 valuesand those reported by the other sources cannot be dismissedas a coincidence.

It makes sense to take a closer look at the outliers. Firstof all, however obvious it may seem, it is worth noting that,when ancient sources give different estimates for the samecoastline, Ptolemys data cannot agree with all of them. Forinstance, when Ptolemys data match one of the two knownvalues for the perimeter of Arabia (no. 45: 38 120 stades),they must naturally disagree with the other (no. 44: 32 000).The same is true for the Great Syrtis (nos. 7 and 17), theMaeotis (22, 25), Hispania (33, 38), the Pontus Euxinus (3537, 39), Africa (4043), and the Mediterranean without thePontus (49, 50). Taking this into account, only two out-liers stand out: the Red Sea coast of Arabia (no. 27) andthe Mediterranean coast of Africa (nos. 4043). The esti-mated 14 000 stades for the Arabian coast, repeated by Er-atosthenes, Artemidorus, and Agrippa, goes back as far asto Alexanders commander Anaxikrates and was regarded astoo much (

) already by Strabo (16.4.4 C768).But it seems that the best way to explain a drastic reduction ofthis coast by 22 % in Ptolemys Geography would be to linkit to his adoption of an erroneous value for the circumferenceof the Earth (see below Sect. 5). The case of Africa seems tobe more complicated: Ptolemys distance is 5 % shorter thanthe Stadiasmus value for the coast between Alexandria andUtica (no. 30), but it is 5.66 % longer than the largest valuerecorded by Pliny (no. 43) for the coast between Canobusand Tingis. Yet, it is remarkable that Pliny calls this valuethe average of all the various accounts (6.208: ut media ex

16It is important to emphasize that Artemidorus, followed by themajority of other ancient authors, estimated the circumference ofthe Maeotis (Azov Sea) at 9000 stades, whereas Ptolemy may haveadopted an alternative estimate of 11 248 stades attested by Pliny4.78.



Tabl

e1.

Com

pari

son

ofth

eco

astli

nele

ngth

sin

Ptol

emy

sG

eogr

aphy

and

inth

eot

hers

ourc

es.

No.

Coa

stlin

eof

Peri

ploi

-bas

edso

urce

sPt

olem

yD

evia

tion

ofPt

olem

ys

dist

ance

valu

esfr

omD

iffer

ence

betw

een

the

valu

esgi

ven

byth

eot

hers

ourc

es4

and

Anc

ient

geog

raph

erSo

urce

Dis

tanc

e(D

)D

ista

nce

4

inst

ades

in%

inst

ades

in%

inst

ades

in%

4

(4D

)(4

D)/

(D

)(

D)/

(4

)(

4)/

D

100

D

100

4

100

1Il

lyri

afr

omth

eD

rinu

m(D

rilo

n)A

grip

paF

13R

iese=

F16

Klo

tz14

0013

5013

88

50

3.6

12

0.

938

2.8

toth

eA

croc

erau

nia

=Pl

in.3

.150

2C

orsi

ca(p

erim

eter

)Pl

iny

3.81

2600

4060

4283

1460

56.2

1683

64.7

223

5.5

3C

ypru

s(p

erim

eter

)Is

idor

ePl

in.5

.129

3000

4204

1204

40.1

4C

ypru

s(p

erim

eter

)St

adia

smus

Mar

isM

agni

315

3250

4204

954

29.4

5C

aspi

anSe

afr

omth

eC

asus

Agr

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F31

Rie

se=

F53

Klo

tz34

0037

2637

2832

69.

632

89.

62

0to

the

Cyr

usa

=Pl

in.6

.39

6C

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sTi

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then

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Stra

b.14

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C68

2;34

2042

0478

422

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Plin

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29

7G

reat

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ape

Cep

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17.3

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C83

539

3035

4435

48

386

9.

8

382

9.

74

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Cap

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2641

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4.

745

611

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716

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from

the

Ars

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Agr

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F13

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se=

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4042

1244

31

28

0.7

191

4.5

219

5.2

the

Dri

num

(Dri

lon)

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10Si

cily

(per

imet

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Posi

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249

Ede

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4400

4714

4968

314

7.1

568

12.9

254

5.4

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1C

266

11Pe

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0364

3665

9119

3342

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8846

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62.

412

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inia

(per

imet

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Plin

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8445

2050

5459

5353

411

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3331

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017

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Cre

te(p

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4537

3909

4556

62

8

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190.

464

716

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Cre

te(p

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4.58

4712

3909

4556

80

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156

3.

364

716

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Sici

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4740

4714

4968

26

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622

84.

825

45.

416

Sici

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paF

7R

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F13

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Plin

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649

4447

1449

68

230

4.

724

0.5

254

5.4

17G

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isfr

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Era

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hene

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0035

4435

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18Pe

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5627

6436

6591

809

14.4

964

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156

2.4

19It

aly,

the

sout

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Plin

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49,5

1,56

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6226

73.

711

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875

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62,7

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Art

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3267

5670

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1176

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1486

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16

63

20.2

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2.6

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Stra

b.2.

5.23

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0011

430

1124

924

3027

2249

25

182

1.

6w

ithou

tthe

stra

it)7.

4.5

C31

0;Pl

in.4

.78;

6.20

7;A

rria

n,Pe

ripl

us30

;Ps.

-Arr

ian,

Peri

plus

72(4

3).1

21(9

2)

Dis

tanc

esov

er10

000

stad

es

23Pe

rsia

nG

ulff

rom

Har

moz

onto

the

Era

tost

hene

sF

94=

Stra

b.16

.3.2

1000

010

368

368

3.7

east

ern

mou

thof

the

Tigr

isC

766

24Pe

rsia

nG

ulff

rom

Cap

eM

akes

(Asa

bon)

Era

tost

hene

sF

94=

Stra

b.16

.3.2

1000

010

412

412

4.1

toth

eea

ster

nm

outh

ofth

eTi

gris

C76

725

Lak

eM

aeot

is(p

erim

eter

Plin

y4.

7811

248

1143

0d11

249

182

1.6

10

18

2

1.6

with

outt

hest

rait)

26S

econ

dgu

lf

ofE

urop

efr

omV

arro

(?)o

rPl

in.3

.97,

150

1360

013

814

1460

721

41.

610

077.

479

35.

7L

acin

ium

toth

eA

croc

erau

niae

Agr

ippa

(?)

27R

edSe

aco

ast

Era

tost

hene

s,E

rat.

F95=

Stra

b.16

.4.4

C76

8;14

000

1088

2

3118

22

.3of

Ara

bia

Art

emid

orus

,A

gath

em.3

.14;

Agr

ippa

F34

Rie

seA

grip

pa=

Plin

.6.1

6428

Red

Sea

from

Her

oonp

olis

toD

eire

Art

emid

orus

Aga

them

.3.1

315

500

1551

916

074

190.

157

43.

755

53.

6



Table1.C

ontinued.

No.

Coastline

ofPeriploi-based

sourcesPtolem

yD

eviationofPtolem

ysdistance

valuesfrom

Difference

between

thevalues

givenby

theothersources

4and

Ancientgeographer

SourceD

istance(D

)D

istance4

instades

in%

instades

in%

instades

in%

4

(4D

)(4

D

)/(

D

)(

D

)/(

4

)(

4

)/D

100D

1004

100

29Italy

between

them

outhsof

Pliny3.44

16392

16763

18111

3712.3

171910.5

13488

theV

arusand

theA

rsia30

Africa

fromA

lexandriato

Utica

Stadiasmus

thesum

ofallsections17

30416

44716

911

857

5

393

2.3464

2.8M

arisM

agniofthe

route31

PersianG

ulf(perimeter)

Eratosthenes,

Agathem

.3.1213;Erat.F

9320

00020

780780

3.9A

rtemidorus

Roller=

Plin.6.10832

Caspian

Sea(perim

eter) gA

rtemidorus

Agathem

.3.1213Plin.6.37

;20

00020

35020

390350

1.7390

241

0.233

Hispania

(perimeter) h

Pliny(V

arro?) i

4.11820

80020

61021

246

190

0.9446

2.1635

3.134

Asia

fromC

anobusto

Chalcedon j

Timosthenes

Plin.5.4721

10421

97722

092873

4.1988

4.7115

0.535

PontusE

uxinus(perim

eterE

ratosthenesF

116R

oller=

Plin.5.47;23

06823

55123

832483

2.1764

3.3282

1.2w

ithoutthestraits) k

F115

Roller=

Plin.6.336

PontusE

uxinus(perim

eterStrabo

thesum

ofallsections23

29023

85824

123568

2.4833

3.6265

1.1including

thestraits)

oftheroute

37Pontus

Euxinus

(perimeterincluding

thestraits)

Artem

idorusPlin.4.77

23352

23858

24123

5062.2

7713.3

2651.1

38H

ispania(perim

eter)Pliny

(Agrippa

?)4.118

=A

grippaF

39K

lotz23

392 l20

61021

246

2782

11.9

2146

9.2635

3.139

PontusE

uxinus(perim

eterPeriplus

Pontithe

sumofallthe

course23

457,5 m23

85824

123400

1.7665

2.8265

1.1including

thestraits)

Euxini

legsofthe

route40

Africa

fromTingis

toC

anobus nA

rtemidorus

Agathem

.3.10;Plin.5.4029

25232

10531

6442853

9.82392

8.2

461

1.441

Africa

fromTingis

toC

anobusIsidore

Plin.5.4029

57632

10531

6442529

8.62068

7

461

1.442

Africa

fromTingis

toC

anobusA

rtemidorus

(?)M

arcianusH

ercl.1.530

280 o32

10531

6441825

61364

4.5

461

1.443

Africa

fromTingis

toC

anobusPliny

6.20830

38432

10531

6441721

5.71260

4.1

461

1.444

Arabia

fromE

lanato

Charax

IubaPlin.6.155

32000

37895

589518.4

45A

rabiafrom

Elana

toC

haraxPliny

(Isidore?)

6.15638

120 p37

895

225

0.646

Asia

fromC

anobusto

theTanais r

Artem

idorus,IsidoreA

gathem.3.10;Plin.5.47

40111

41239

41057

11282.8

9462.4

182

0.4

47E

uropaw

ithoutthePontus

(fromC

alpeto

Byzantium

) sA

rtemidorus

Plin.4.77,5.47,6.20656

41255

92458

368

488

0.91956

3.52444

4.448

Europe

fromC

alpeto

theTanais

Artem

idorus,IsidoreA

gathem.3.10;Plin.4.121

69709

71643

74770

19342.8

50617.3

31264.4

49M

editerraneanSea

withoutthe

Maeotis

Agrippa

F36

Riese=

Plin.6.207124

072 t133

792136

2319720

7.812

1599.8

24391.8

50M

editerraneanSea

withoutthe

Maeotis

Artem

idorusPlin.6.207

130120

133792

136231

36722.8

61114.7

24391.8

51M

editerraneanSea

includingthe

Maeotis

Artem

idorusA

gathem.3.10

139072

144792

147471

57204.1

83996

26791.9

aF

31R

iese=

Plin.6.39:oramom

nema

Caso

praealtisrupibus

accessum

gareper

CC

CC

XX

Vp.auctor

estAgrippa.Ptolem

yscoordinates

forthem

outhofthe

Casius

are8230long.,46

lat.and

84

long.,4215lat.forthe

mouth

oftheC

yrus.b

Contrary

tothe

generaltendency,thereare

goodreasons

tothink

thatforSicily,recension4

isless

reliablethan

,because

in4

Cape

Pelorus(one

ofthethree

principalcapesofSicily)is

omitted,and

Segesta(the

westernm

ostpoint)isshifted

considerablyfurtherto

theeast,w

hereasin

thelatteris

quitereasonably

placedon

thesam

em

eridianw

ithO

stia.c

SincePtolem

ylocates

theisland

ofGades

toofarfrom

thecoast,itw

ouldbe

more

correcttom

easurethis

distancefrom

thetem

pleofH

eraon

thecoast(see

theSupplem

ent).d

Codex

Vaticanus

Graecus

191contains

two

clearerrors.First,Paniardisis

displacedfarto

theeast(to

5330lat.,69

40long.instead

of5330,6730in

)relative

tothe

restofthecoast.Second,Parthenion

andM

yrmekion

onthe

European

coastoftheC

imm

erianB

osporus(m

odernK

erchStrait)are

placedsouth

ofAchillessanctuary

onits

Asian

side(at48

15lat.and

4810lat.,respectively).In

,how

ever,theyare

placedatthe

same

latitude(at48

30lat.,the

latitudeofthe

Borysthenes),w

hichis

more

logicalbecauseParthenion

andM

yrmekion

areknow

nto

besituated

oppositeto

Achillessanctuary

inthe

narrowestpartofthe

strait(Strabo11.2.8

C494).E

xceptforthesetw

odifferences,

4m

atchesw

ith

almostexactly.

eN

aturalHistory

3.97:ALacinio

promunturio

secundusE

uropaesinus

incipit,magno

ambitu

flexusetA

croceraunioE

pirifinitusprom

unturio,aquo

abestLXX

V;3.150:universum

autemsinum

ItaliaeetIllyriciam

bituX

VII.T

helatterquotation

follows

imm

ediatelyafterthe

fragmentofA

grippaaboutthe

coastofIllyria

(F13

Riese=

F16

Klotz;no.1

inthis

table),which

allows

Riese

andK

lotzto

ascribeitalso

toA

grippa(F

13R

iese=

F47

Klotz).D

etlefsen(1886,243

p.,247248)hasreasonably

notedthatthis

quotationis

alsoconnected

with

Plinyspassages

abouttheso-called

secondand

thirdgulfs

ofEurope

(3.97;4.1)w

hichhe

ascribesto

Varro,although

theym

ayw

ellbeattributed

toA

grippaas

well.

fIn

anum

berofcases,theinconsistencies

inthe

4data

havebeen

corrected:thepositions

ofCape

Circei,Tarracina,Privernum

,andH

idruntumare

givenaccording

to

;cf.alsoC

untz(1923,inserted

map),Polaschek

(1965,cols.726727,730731,insertedm

ap).The

coordinatesofTarentum

(4130long.,40

lat.)are

takenfrom

theso-called

Canon

ofthenotew

orthycities

(6.1;StckelbergerandM

ittenhuber,2009,p.162);theoutlines

oftheG

ulfofTarantoare

givenaccording

tothe

reconstructionproposed

byPolaschek

(1965,cols.720721,730731,map),even

thoughitdoes

notsolveallcontradictions

inPtolem

ysdata.

g4

givescoordinates

onlyforthe

north-western

coastoftheC

aspianSea,therefore

alltherestare

takenfrom

.

hT

heprovinces

ofSpaintaken

alltogether,measured

fromthe

two

promontories

ofthePyrenees

alongthe

sealine,are

estimated

tocoverby

thecircum

ferenceofthe

whole

coast2924m

iles,orbyothers

2600m

ilestrans.by

H.R

ackhamin

theL

oebC

lassicalLibrary

(omnes

autemH

ispaniaea

duobusP

yrenaeiprom

unturiisper

maria

totiusorae

circuituX

XV

IIIIX

XIIIIcolligere

existimantur,ab

aliisX

XV

I).Itmeans

fromC

apeO

iasonto

theTem

pleofA

phroditein

Ptolemys

Geography.

iForarguments,see

Detlefsen

(1877,p.24)andK

lotz(1931,p.441442).

j4

omits

thecoordinates

forthecoastfrom

Anthedon

(6450long.,31

40lat.)to

theborderofC

ilicia(69long.,36

20lat.),so

theyare

takenfrom

.

kPliny

(4.77)listsotherestim

atesofthe

circumference

ofthePontus:2150

m.p.=

17200

stadesaccording

toV

arroand

theold

authoritiesgenerally

(fereveteres),2500

m.p.=

20000

stadesin

Cornelius

Nepo,2540

m.p.=

20320

stadesin

Agrippa,and

2425m

.p.=

19400

stadesin

Mucianus.Polybius

(History

4.39.1)estimated

itat22000

stades.Neitherofthese

valuesagrees

with

Ptolemys

data.lK

lotz(1931,p.441442)em

endsPlinys

figureto

XX

VIIIX

XIII(2823

m.p.=

22584

stades).m

How

ever,thesum

totalstatedin

thePeriplus

(121[92])is23,587.Foran

explanationofsom

eofthe

numericalerrors

underlyingthis

discrepancy,seeD

iller(1952,p.104).n

Rem

arkably,thesum

ofalldistancesgiven

byStrabo

forthecoastofL

ibyaam

ountsto

alittle

more

than28

000stades:5000

fromC

apeC

otesto

Cape

Metagonium

(17.3.6C

827),thence6000

toC

apeTretum

(17.3.9C

829),2500to

Carthage

(17.3.13C

832),more

than5000

toC

apeC

ephalae(in

astraightline

acrossthe

LesserSyrtis)and

thence3930

alongthe

GreatSyrtis

(17.3.18C

835),1000from

Berenice

toA

pollonia(17.3.20

C837),2200

toC

atabathmus

(17.3.22C

838),900to

Paraetoniumand

1300to

Alexandria

(17.1.14C

798),120to

Canobus

(17.1.17C

801).With

fewexceptions,these

distancesdisagree

with

Ptolemys

data,suggestingthatStrabo

andPtolem

ydrew

ondifferentsources.

oM

ller(1855,p.520).Itistem

ptingto

emend

Marcianusfigure

(30280)to

(30380)w

hichw

ouldbe

inaccord

with

Pliny6.208.

pcircuitus

Arabiae

aC

haraceLaeana

colligereproditur

XLV

IILXV

p.Some

secondaryM

SSread

thisfigure

asX

LVL

XV=

36520

stadesorX

LVIIIL

XV=

38920

stades.r4

omits

thecoordinates

forthecoastfrom

Anthedon

(6450long.,31

40lat.)to

theborderofC

ilicia(69long.,36

20lat.),so

theyare

takenfrom

.

sA

rtemidoruslength

ofthecoastofE

uropecan

bederived

fromthe

othervaluesrecorded

byPliny

forthecircum

ferenceofthe

Mediterranean

Seaw

ithouttheM

aeotis(no.50

inTable

1),theperim

eterofthePontus

(no.37),thecoastofA

frica(no.40),and

thecoastofA

siafrom

Canobus

toC

halcedonaccording

toTim

osthenes(no.34).

tThe

deviationofthis

valuefrom

thatofArtem

idorusis

mostprobably

dueto

thefactthatA

grippasestim

ateofthe

circumference

ofthePontus

was

about6000stades

shorterthanaccording

toA

rtemidorus

(Plin.4.77).Klotz

(1931,p.458459),however,argues

thatthisfigure

couldnothave

come

fromA

grippa.



Figure 2. Differences between the coastline lengths as derived from Ptolemys coordinates and as given by Artemidorus (including those thathe has inherited from Timosthenes and Eratosthenes: nos. 20, 2224, 2728, 32, 40, 4647 in Table 1). The percentages refer to the deviationof Ptolemys values from those of Artemidorus. The outlines are drawn according to the 4 recension supplemented with coordinates from for the areas of Asia that are missing in 4.

Figure 3. Differences between the coastline lengths as derived from Ptolemys coordinates and as given by other periploi-based sources(nos. 2, 56, 8, 12, 1619, 21, 25, 28, 33, 39, 4344 in Table 1). The percentages refer to the deviation of Ptolemys values from those ofother sources. The outlines are drawn according to the 4 recension supplemented with coordinates from for the areas of Asia that aremissing in 4.

omni varietate prodentium sumatur computatio), which im-plies that he knew even larger estimates.

Remarkably, Table 1 shows that the distances in4 are usu-ally shorter than in , but longer than in the other sources.This ratio can easily be explained by the so-called coast-line paradox: the well-known fact that a coastline lengthvaries depending on the level of detail of its geometry. Theperiploi described, of course, the coastal routes. However,these routes did not have to replicate all the minor, but numer-ous curves and bends of the coast. It is unsurprising, there-fore, that the coastline in Ptolemys Geography, when mea-sured with all its curves, proves to be a little longer than thedistances recorded in periploi, and , as the second recen-

sion, has usually a more detailed and, therefore, even longercoastline than 4 (Fig. 1).

5 The influence of Ptolemys erroneous estimate ofthe circumference of the Earth

Distance data derived from periploi were bound to come intoconflict with other Ptolemy sources, and particularly with hislatitude data. In this case, contradictions must have been es-pecially prominent because Ptolemy adopted an erroneousvalue for the Earths circumference, namely 180 000 stades,which was about 17 % less than the actual value, if he usedthe stade of 185 m length (Shcheglov, 2016b). Owing to this



Figure 4. Deviation of Ptolemys coastline length values from those given in the periploi-based sources for the distances over 10 000 stades(as expressed in the percentage terms). Ptolemys data are mostly taken from 4 and in a few cases from (nos. 2324, 27, 32, 4445).Nos. 31, 4951 are omitted since they are the sums of the other values.

Figure 5. Differences between the coastline lengths in 4 and in as expressed in terms of percentage of the 4 values (for the samecoastal stretches as shown on Fig. 2).

error, all northsouth distances which were tied to particu-lar latitudes must also have been reduced by approximatelythe same amount. This effect may be illustrated by the exam-ple of the Red Sea coast of the Arabian Peninsula (no. 27 inTable 1). In Ptolemys Geography, this coast is squeezed be-tween the latitude of its northern extremity (Elana, 2915)and that of Ocelis (12) near the Strait of Deire (Bab-el-Mandeb), the latter being based on astronomical observa-tions (Ptol. Geogr. 1.7.4). It is unsurprising, therefore, thatthis coast exhibits a 22 % reduction in length.

However, I would like to draw attention to another possibleand arguably more unusual side-effect of Ptolemys underes-timated circumference of the Earth. This effect is observedwhen a coastline in Ptolemys Geography falls into two dis-tinct parts: one oriented northsouth, the other eastwest. Ina number of such cases the same pattern is seen: while thenorthsouth part is shorter than the recorded periploi dis-tance, which is understandable, the eastwest part is propor-tionally longer, which requires explanation. It is reasonableto suppose that such a stretching of the eastwest parts wasintended to compensate for the shortening of the northsouthpart in order to maintain the total coastline length unchanged.If this explanation is valid, it can give us an important key tounderstanding Ptolemys modus operandi.

The effect of proportional shortening/stretching of theneighbouring segments of the coast can be illustrated mostclearly by three examples: Italy, the Caspian Sea, and the RedSea. In the case of Italy, the southern part of the peninsula issqueezed between the latitudes of the Strait of Messina (atRhegium) and Naples, whereas the part between Naples andOstia is proportionally stretched from east to west (Fig. 7).The Caspian Sea is probably compressed from north to southtogether with the circumference of the Earth, but proportion-ally stretched from east to west (Figs. 2 and 3). In the case ofthe Red Sea, the largest part of its African coast is orientedfrom north to south and squeezed between the latitudes ofits northern extremity and of Ptolemais Theron in the south,whereas its southern part, turning eastward to the Bab-el-Mandeb Strait, is proportionally stretched (Fig. 3). Below Iconsider these instances in detail.



Figure 6. Differences between the coastline lengths in 4 and in as expressed in terms of percentage of the 4 values (for the same coastalstretches as shown on Fig. 3).

Figure 7. Plinys points of the coast of Italy on Ptolemys map (4recension). The percentages refer to the deviation of Ptolemys val-ues for the coastline length from those given by Pliny (no. 29 inTable 1) and Agrippa (nos. 1 and 9).

5.1 Italy

Only a few ancient sources provide detailed information onindividual distances along the coast. Plinys description ofItaly is among them (Natural History 3.49, 51, 56, 62, 70,73, 95, 97, 99, 100, 111, 115, 127). Table 2 shows howPlinys values for the separate coastal stretches constitutingthe perimeter of Italy relate to Ptolemys data (see also Figs. 3and 7).

Ptolemys Italy may be divided into three parts (Fig. 7):(1) the northern part lying west of Ostia and Ancona, (2) themiddle part lying east of Ostia and Ancona and north ofNaples, and (3) the part lying to the south of Naples. Ta-ble 2 shows that for northern Italy Ptolemys distances ac-cord tolerably with Plinys figures.17 Ptolemys middle Italy

17Ptolemys coast from Ravenna to the mouth of the Formiomatches Plinys distances pretty well. The length of the coast fromthe Varus to Cape Circei is exaggerated by 8 % (or 42.5 m.p.) on

Figure 8. Plinys points of the coast of Italy on the modern map.

is distinctly stretched in the eastwest direction relative toPlinys distances, whereas southern Italy is almost equallycompressed. For example, Ptolemys coast from Circei toSurrentum is stretched by 78 m.p., whereas that from Saler-num to Rhegium is shortened by 83 m.p. Similar compres-sions and stretchings of these coastal sections are exhib-ited by Ptolemys map relative to the modern map (Table 2,Fig. 8).

The compression of southern Italy in the northsouth di-rection can be easily explained, first of all, by Ptolemys un-derestimated value for the Earths circumference. Ptolemyslatitudes for southern Italy are rather accurate: for example,the interval between his latitudes of Surrentum and Rhegium

average as compared to Plinys figures, which is quite a lot, but itcan still be explained by the fact that Ptolemys data almost alwaysexhibit a similar overestimation of distances relative to the periploidata (Table 1).



Table 2. Comparison of the distances along the coast of Italy according to Pliny, Ptolemy, and measurements using Google Maps (GoogleInc., 2017). All distances are expressed in terms of Roman miles; 1 m.p.= 1480 m.

Stretches of the coast Pliny Ptolemy Difference between Googlefrom to (P) Pliny and 4 Maps

4 m.p. %(4P ) (4P ) / P 100

VarusMacra 211 219.1 214.8 8.1 3.8 % 154182MacraTiber (Ostia) 284 315.1 350.4 31.1 11 % 215240Tiber (Ostia)Cape Circei 50 53.2 53.2 3.2 6.5 % 5861CirceiSurrentum 78 155.6 224.2 77.6 99.5 % 87SurrentumSalernum 30 26.5 22.3 3.5 11.5 % 3637SalernumRhegium 237 153.7 167.8 83.3 35.1 % 200236RhegiumLocri 66 73 71.7 7 10.7 % 100LocriCape Lacinium 86 or 75 67.4 71.7 18.6 or 7.6 21.6 % or 10.1 % 8395Tarentum (Taras)Iapygia 108 88 78.9 20 18.5 % 90100IapygiaGarganum Mt 234 177.3 189.9 56.7 24.3 % 215233GarganumAncona 183 335.4 379.6 152.4 83.3 % 200225AnconaRavenna 105 88.3 88.6 16.7 15.9 % 90RavennaFormio 189 183.9 187.9 5 2.7 % 155190

The accuracy of this comparison should not be overestimated, because the routes on Google Maps have been measured rather arbitrarily. The lowerand upper values in the table refer to the shortest route across the open sea and the route along the coast, respectively.

is 225, which is pretty close to the true value of 230.However, for Ptolemy the corresponding distance amountsto 150 m.p., whereas the correct value would have been188 m.p.

Ptolemys southern Italy is distinctly squeezed betweenthe latitudes of Naples (4055 in 4; the true latitude is4050) in the north and that of the Strait of Messina (in par-ticular Cape Pelorus, 3835 in ; the true latitude is 3816)in the south. These latitudes corresponded to the so-calledklimata with the longest day of 15 and 14 3/4 h, respectively.Klimata (sing. klima) was a technical term for latitudes de-fined by the length of the longest day. These klimata were, inessence, the principal tool available to pre-Ptolemaic geogra-phers for constructing a mathematically rigorous map of theworld, at least, from Eratosthenes onwards.18 A set of theseklimata constituted the basis of the geographical system ofMarinus of Tyre, Ptolemys immediate predecessor and theprincipal source (Honigmann, 1930; Wurm, 1931). There-fore, Ptolemys latitudes of Naples and Pelorus go back, mostprobably, to Marinus or even further.

It is striking that various divergences between Ptolemysand Plinys data on the separate coastal stretches (Table 2)19

are in stark contrast with the close agreement between theirvalues for the total length of the coast: Ptolemys figures forthe perimeter of Italy and for the southern side from the

18On the system of klimata, see Honigmann (1929), Neuge-bauer (1975, p. 4345, 333336, 725733), Shcheglov (2004); onklimata as a basis of Ptolemys map, see Wurm (1931, p. 2021,30), Isaksen (2013, p. 50, Fig. 3.4).

19Similar observations have been made by Mittenhuber (2012)for Ptolemys Hispania.

mouth of the Varus to Rhegium deviate from Plinys val-ues by only 2.4 % (no. 29 in Table 1) and 3.7 % (no. 19).Hence, it is tempting to explain this by assuming that themagnitude and direction of the disagreements may have beenselected intentionally so that stretchings and compressionswould have cancelled each other out.

5.2 The Caspian Sea

The coincidence between Ptolemys and Artemidorus val-ues for the perimeter of the Caspian Sea gives us a key toexplaining its strange configuration in Ptolemys Geography,namely why it is shown as being longer from east to west (ca.8250 stades from Gangara to the mouth of the Polytimetos)than from north to south (ca. 4400 stades between the mouthsof the Rha and the Straton; see Fig. 3).

First of all, it is tempting to connect this anomaly withthe fact that the whole of Ptolemys map exhibits a similarstretching of all its outlines from east to west relative to themodern map.20 This stretching can largely be explained byPtolemys underestimated value for the Earths circumfer-ence. This effect is due to the principal difference betweenthe methods of measuring latitude and longitude (Shche-glov, 2016b; Grahoff et al., 2016). Latitude can be deter-mined by means of simple astronomical observations, whichhad been known to the Greeks since at least the 4th centuryBC, and starting at least with Hipparchus (2nd century BC)it was normally expressed in degrees. But it was not untilthe 18th century that an efficient and simple enough method

20On the variation in this error for different parts of Ptolemysmap, see Shcheglov (2016b).



of determining longitude was devised. For an ancient geog-rapher, the main method to find longitude was to convertdistance measurements from customary linear units (Greekstades, Roman miles, etc.) to angular units (degrees), forwhich the estimate of the Earths circumference was essen-tial. This is why an error in this estimate inevitably affectedall longitude values based on distance measurements, but hadno effect on latitude values when they had been originally ex-pressed in degrees. A too low value for the circumference ofthe Earth results in that all distances projected on its surface(i.e. converted to degrees) become proportionally overesti-mated in angular terms, which made the outlines on the mapstretch mostly in the eastwest direction (e.g. Russo, 2013;Shcheglov, 2016a, b). However, Ptolemys underestimationof the size of the Earth could have been responsible for astretching by only 17 %, which is evidently insufficient toexplain the configuration of the Caspian Sea in his Geogra-phy.

Furthermore, Ptolemys Caspian Sea is not only stretchedfrom east to west but also compressed from north to south.The only ancient estimate of the northsouth extension ofthe Caspian Sea comes from Strabo (2.1.17 C74): he definesthe meridional distance between its southernmost end and themouth entering the Ocean in the north as about ( ) 6000stades. This value matches the actual straight-line length ofthe Caspian Sea pretty well (provided that 1 stade= 185 m).However, Ptolemys latitude interval between the northern(the mouth of the Rha at 4850) and the southern (the mouthof the Straton at 40) extremities of the Caspian Sea corre-sponds to only 4417 stades (Fig. 3; of course, there is no rea-son to suppose that any of Ptolemys latitudes for the CaspianSea could have been based on actual astronomical observa-tions).

The situation is complicated by the fact that there mayhave existed a hypothetical early version of Ptolemys Geog-raphy that was based on a different estimate for the Earthscircumference, namely 252 000 stades, which was ca. 16.5 %above the true value (252000185 m= 46 620 km). This es-timate was first proposed by Eratosthenes and can be re-garded as almost generally accepted in antiquity. As has beenshown by Schnabel (1930, p. 218219), Ptolemy probablyused this value for calculating geographic longitudes in theAlmagest, one of his early works. Even more importantly,Sarre and Herzfeld (1911, p. 143153), Wurm (1937, 1940),and Shcheglov (2004, 2017) have shown, independently ofone another, that a large area on Ptolemys map was built onthe basis of Eratosthenes set of distances which were con-verted to spherical coordinates according to Eratosthenesrate of 1= 700 stades. This area covers the whole of theMiddle East, at least, between the Euphrates and the In-dus including the Caspian Sea. More importantly, Ptolemysbreadth of the Caspian Sea, when expressed in Eratosthenes700-stade degrees, corresponds to 6183 stades which closelyagrees with Strabos distance, as was noted by Wurm (1937,p. 7, 13, 1940, p. 8, 11).

It is also remarkable that, on Ptolemys map, the north-ern extremities of the Caspian Sea, as well as the northerncoast of the Pontus Euxinus, are clearly tied to the latitudeof the mouth of the Borysthenes (48 1/2), one of the sevenklimata or the key latitudes determining the structure of hismap and going back, most probably, as far as Eratosthenes(Fig. 3).21 These correspondences make it possible to sup-pose that Ptolemys meridional extension of the Caspian Seahad been originally defined as slightly more than 6000 stadesand that this distance was expressed in degrees of latitude al-ready in the early version of the map, which was based onEratosthenes value for the Earths circumference.

Interestingly, 6183 stades is quite close to the quotient of20 000 stades (the perimeter of the Caspian Sea according toArtemidorus; no. 32 in Table 1) divided by . If this coinci-dence is not accidental, and if the circumference of 20 000stades and the meridional extension of slightly more than6000 stades were the two parameters that determined theoutlines of the Caspian Sea from the very beginning, then itmathematically implies that in the early Eratosthenic ver-sion of Ptolemys map the sea must have had a round shape.We may suppose that, when Ptolemy had accepted a smallervalue for the Earths circumference instead of Eratosthenes252 000 stades, the meridional extension of the Caspian Sea,being expressed in degrees, remained unchanged, whereasits circumference was recalculated to the 500-stade degrees,which made the sea stretch from east to west and take theshape it has on Ptolemys map today.

There is a difficulty, however, in that other ancient sourcesnever compare the Caspian Sea with a circle.22 On the con-trary, they often use quite different comparisons: a sickle orthe horns of the crescent, or a mushroom cap.23 But thischoice of metaphors might be due to the fact that, unlikePtolemy, other sources considered the Caspian Sea as a gulfof the Ocean. Anyway, a circle seems to be the simplest andthe most obvious figure that comes to mind to describe theshape of an unexplored sea or gulf about which almost noth-ing was known.24

21On Eratosthenes as a source of Ptolemys seven klimata, seeHonigmann (1929) and Shcheglov (2004).

22In contrast to, for example, the Persian Gulf which was de-scribed as round and similar to a human head, see Agathem.3.12:

21

; Mela, Chorogr., 3.71: reddit formam capitis hu-mani; Plin. 6.108: humani capitis effigie.

23Agathem. 3.13: (crescent-shaped); Curt. Ruf. 6.4.16:. . . lunae maxime similem, quum eminent cornua, quum eminentcornua, nondum totum orbem sidere implente; Plin. 6.38: . . . lunatisobliquatur cornibus . . . sicilis, ut auctor est M. Varro, similitudine;Iordan. Getica 5.30: ab Oceano euroboro in modum fungi, pri-mum tenui, posthaec latissima et rotunda forma exoritur; the samecrescent-like shape of the Caspian Sea is seen on the so-called Tab-ula Peutingeriana, see http://www.cambridge.org/us/talbert/mapb/TP2000seg11.jpg or http://peutinger.atlantides.org/map-a.

24Remarkably, there are two other seas that have regular roundedshapes in Ptolemys Geography: the Bay of Ganges (modern Bay


http://www.cambridge.org/us/talbert/mapb/TP2000seg11.jpghttp://www.cambridge.org/us/talbert/mapb/TP2000seg11.jpghttp://peutinger.atlantides.org/map-a


Table 3. Length of the Red Sea coast according to Artemidorus, Eratosthenes, Ptolemy, and measurements using Google Maps (Google Inc.,2017). All distances are expressed in stades; 1 stade= 185 m.

Stretches of the coast Distance Difference between Difference between(stades) 4 and Artemidorus 4 and Google Maps

Eratosthenes and Ptolemy Google stades % stades %Artemidorus (D) Maps (GM)

4 (4D) (4D)/ (4GM) (4GM)/D 100 GM 100

HeroonpolisPtolemais 9000 7575 7864 81088189 1,425 15.8 533614 6.57.6HeroonpolisBerenice 4180 3266 3366 4324 914 21.9 1058 24.5BerenicePtolemais 4820 4310 4497 37843865 510 10.6 445526 11.513.9PtolemaisDeire 6500 7944 8211 47004843 1444 22.2 27662909 57.161.9

5.3 The Red Sea

The general configuration of the Red Sea (or, in ancientterms, the Arabian Gulf) on Ptolemys map is determinedby the latitudes of four points: Berenice, Ptolemais Theron,Adulis, and Ocelis (Fig. 3).25 The length of the African coastfrom Heroonpolis (the northernmost point) to Deire (situatedopposite to Ocelis) in Ptolemys work is exactly the same asin Artemidorus (in 4 it is only 0.1 % or 19 stades shorter, in it is 3.7 % or 574 stades longer; see Table 1). However, thelengths of the separate coastal stretches recorded by Eratos-thenes and Artemidorus relate to Ptolemys data as follows.

Table 3 shows that the northsouth stretch from Heroonpo-lis to Ptolemais is ca. 1425 stades shorter in Ptolemy than ac-cording to Artemidorus, while the next one turning to the eastfrom Ptolemais to Deire is ca. 1444 stades longer.26 Similardeformations of these stretches are exhibited by Ptolemys

of Bengal) and the Great Bay (the Tongking Gulf); see e.g. Stck-elberger and Grahoff (2006, p. 896897, 902903).

25In Ptolemys Geography, Berenice is situated at the latitude ofSyene (2350), Ptolemais at the latitude of Meroe (1630 in 4and in Canon of the noteworthy cities 14.2 or 1625 in ), whichcorrespond to the klimata with the longest day of 13 1/2 and 13 h,respectively. Such arrangement of these points goes back as far asEratosthenes (F IIB3738, IIIA18 Berger = F 4142, 59 Roller) or,at least, Hipparchus (F V4V5 Berger = F 4647 Dicks = Strab.2.5.36 C133). Adulis (Almagest 2.6.4 Heiberg p. 105106) andOcelis (Geogr. 8.22.7) were presumably connected with the klimaof the 12 3/4 h day (1230) in the early version of Ptolemys map(see Wurm, 1931, 2324), but in the final version they have beenshifted to the latitudes of 1140 (4 and Canon of the noteworthycities 14.2) or 1120 () and 12, respectively. Modern latitudesof these points (according to the database of http://pleiades.stoa.org)are as follows: Berenice: 2355, Ptolemais: 1813, Adulis: 1513,Ocelis: 1243, Deire: 1226.

26Artemidorus gave 9000 stades for the distance from Heroon-polis to Ptolemais, and thence 6500 to Deire (Agathem. 3.14).However, according to Pliny (6.164), Artemidorus values for thefirst distance was 9500. Eratosthenes gave also 9000 stades fromHeroonpolis to Ptolemais, thence 4500 to Deire (F IIIB48 Berger=F 95 Roller= Strab. 16.4.4 C768), 4820 from Berenice to Ptolemais

map relative to the modern map (Table 3).27 As in the caseof Italy, the compression of the northsouth coastal segmentcan be accounted for by Ptolemys erroneous estimate of thecircumference of the Earth, but the stretching of the segmentPtolemaisDeire by exactly the same amount seems suspi-cious and requires some additional explanation.

6 Conclusions and further perspectives

The main conclusion of our study is intuitively expectableand in this sense unsurprising, namely that Ptolemys Geog-raphy was most likely based on some ancient periploi sim-ilar to those known from other sources. What seems unex-pected and much more important is that our study has re-vealed a close numerical agreement between Ptolemys Ge-ography and the other periploi-based sources in the data onthe length of relatively long coastlines (over 10 000 stades):in most cases the differences between Ptolemys data and theother sources fall between +4 and 1 %. This observationcan provide a new insight into the genesis of Ptolemys Ge-ography and the history of ancient geography in general.

A major challenge we face now is how to reconcile thisstriking agreement between Ptolemys data and the othersources with the equally striking contradictions betweenthem in the short coastal stretches of which the long onesconsist (as was demonstrated by the example of Italy). Inother words, with increase in the coastline lengths beingcompared, different discrepancies between Ptolemy and theother sources compensate one another until an almost com-plete agreement is reached. But what factors determined thistransformation? Could it be intentional, or just accidental,and to what extent? This question compels us to revisit ourunderstanding of Ptolemys methods and the relevancy ofour methods of examining his work. For the time being, we

(F IIB3738 Berger = F 4142 Roller = Plin. 2.183; 6.171), and,accordingly, 4180 from Heroonpolis to Berenice.

27However, a part of this deformation is due to the fact thatPtolemy and his predecessors placed Ptolemais 2 too far to thenorth of Marsa Aqiq, its modern counterpart.


http://pleiades.stoa.org


may only suggest a preliminary explanation. Most plausibly,Ptolemys map was constructed not bottom-up when itsoutlines would have been drawn successively point by pointlike beads are strung on a thread, but top-down when thecartographer first drew the general outlines determined bylong distances, and only after that he inserted minor details,fitted into the general picture. This assumption can be corrob-orated in part by the three cases (Italy, the Caspian Sea, andthe Red Sea) where Ptolemys Geography exhibits a propor-tional shortening of the northsouth sections of coastline andstretching of the neighbouring eastwest sections relative tothe distances recorded in other sources. Whereas the short-ening of the northsouth sections was definitely caused byPtolemys underestimate of the circumference of the Earth,the stretching of the eastwest sections is hard to explain, un-less by assuming that the cartographer deliberately compen-sated the shortening. Of course, three cases are not enoughfor definitive conclusions, and the issue awaits further inves-tigation.

Data availability. Ptolemys coordinates are taken from the elec-tronic database attached to the newest edition of the Geography(Stckelberger and Grahoff, 2006).



Appendix A: Plinys third gulf of Europe

In addition to the materials presented in Table 1, one caseneeds to be considered separately. Pliny (4.1), without in-dicating his source, estimates the perimeter of the so-calledthird gulf of Europe from the Acroceraunia Promon-tory (modern Karaburun) to the Hellespont (Dardanelles)at 1925 m.p.= 15 400 stades without minor gulfs (praeterminores sinus). Since it is not known which gulfs he regardedas minor, it is hazardous to rely on this evidence. Neverthe-less, we can try, as an experiment, to measure the coast fromthe Acroceraunia to Sestos (as the major point on the Helle-spont) in Ptolemys Geography without the most prominentof the minor gulfs mentioned by Pliny (Fig. A1).28 With-out these gulfs, the coastline length measures 15 778 stadesin4 or 15 714 stades in, which is quite close to Plinys fig-ure. When measured including all the gulfs, it would amountto 21 552 stades in 4 or 21 589 in .

28The Ambracian Gulf (between Nicopolis and Leucas), theCorinthian (between capes Antirrhion and Drepanon), the Messe-nian (between capes Akritas and Tainaros), the Laconian (betweencapes Tainaros and Malea), the Argolic (between capes Malea andSkyllaion), the Thermaic, Toronic, and Singitic gulfs (of course, thischoice is rather arbitrary).

Figure A1. The outlines of Plinys third gulf of Europe onPtolemys map (4 recension) without the minor gulfs (shownwith yellow).



The Supplement related to this article is available onlineat https://doi.org/10.5194/hgss-9-9-2018-supplement.

Competing interests. The author declares that he has no conflictof interest.

Acknowledgements. I would like to thank Pascal Arnaud, Geor-gia Irby, Roel Nicolai, Eugene Rodin, and two anonymous refereeswhose comments greatly improved parts of the article. This workwould be impossible without help from Alexandra Elbakyan andher project Sci-Hub.

This article is a part of the research project Internal Structuresof Ptolemys Map supported by the Russian Foundation for BasicResearch (grant 15-01-00005).

Edited by: Giovanni P. GregoriReviewed by: Roel Nicolai, Pascal Arnaud, Georgia Irby, andtwo anonymous referees

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http://etheses.dur.ac.uk/10374https://drive.google.com/open?id=0ByHnqj0cHCZMU3pQOWJtcDgzVFkhttps://drive.google.com/open?id=0ByHnqj0cHCZMU3pQOWJtcDgzVFkhttps://drive.google.com/open?id=0ByHnqj0cHCZMdmNpdkE2NEJxQTQhttps://drive.google.com/open?id=0ByHnqj0cHCZMdmNpdkE2NEJxQTQhttps://drive.google.com/open?id=0ByHnqj0cHCZMZVdOQ3hDMWJRbnMhttps://drive.google.com/open?id=0ByHnqj0cHCZMZVdOQ3hDMWJRbnM

AbstractIntroductionPeriploi among the sources of Ptolemy's GeographyMethod of comparisonComparison of the coastline lengths in Ptolemy's Geography and in other sourcesThe influence of Ptolemy's erroneous estimate of the circumference of the EarthItalyThe Caspian SeaThe Red Sea

Conclusions and further perspectivesData availabilityAppendix A: Pliny's third gulf of EuropeCompeting interestsAcknowledgementsReferences

the length of coastlines in ptolemy’s geography and in ... · 10 d. a. shcheglov: the length of...

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