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 The was in like manner placed by Ptolemy at a considerable distance from its true geographical position. The place of the line was well known to him as a matter of theory, but as no observations could have been made in those regions he could only calculate its place from that of the tropic, which he supposed to pass through Syene. And as he here, as elsewhere, reckoned a degree of latitude as equivalent to 500 stadia. he inevitably made the interval between the tropic and the equator too small by one-sixth; and the place of the former being fixed by observation, he necessarily carried up the supposed place of the equator too high by more than 230 geographical miles. But as he had practically no geographical acquaintance with the equinoctial regions this error was of little importance.

With Marinus and Ptolemy, as with preceding, the most important line for practical purposes was the parallel of 36° N., which, passing through the Straits of Gibraltar, Rhodes Island and the Gulf of Issus, and thus dividing the Mediterranean (as Dicaearchus and his successors usually regarded it) into two, was continued in theory along the chain of Mt Taurus till it joined the mountains north of India; thence to the Eastern Ocean it was regarded as constituting the dividing line of the inhabited world, along which the length of the latter must be measured. But so inaccurate were the observations and so imperfect the materials at command, even in regard to the best known regions, that Ptolemy, following Marinus, describes this parallel as passing through Caralis in and Lilybaeum in Sicily, the one being really in 39° 12′, the other in 37° 50′. Still more strangely he places 1° 20′ south of the dividing parallel, while it really lies nearly 1° north of it.

The problem that had especially attracted the attention of geographers from to Ptolemy was to determine the length and breadth of the inhabited world. This question had been fully discussed by, who had arrived at conclusions widely different from his predecessors. Towards the north, indeed, there was no great difference of opinion, the of  being generally recognized as that of the highest northern land, and this was placed both by Marinus and Ptolemy in 63° N., not far beyond the true position of the Shetland Islands, which had come to be generally identified with the mysterious Thule of. The western extremity, as already mentioned, had been in like manner determined by the drawn through the supposed position of the outermost of the Fortunate Islands. But towards the south and east Marinus gave an enormous extension to Africa and, beyond what had been known to or suspected by earlier geographers, and, though Ptolemy reduced Marinus' calculations, he retained an exaggerated estimate of their results.

The additions thus made to the estimated dimensions of the known world were indeed in both directions based upon a real extension of knowledge, derived from recent information; but the original statements were so perverted by misinterpretation as to give results (in map-construction) differing widely from the truth. The southern limit of the world had been fixed by and even by  at the parallel which passed through the eastern extremity of Africa (Cape Guardafui), the Cinnamon Region  and the country of the Sembritae (Sennaar). This parallel, which would correspond nearly to that of 10° of true latitude, they supposed to be situated at a distance of 3400 (340 geographical miles) from that of  (the position of which was pretty accurately known) and 13,400 to the south of Alexandria; while they conceived it as passing eastward through Taprobane (, often Ceylon plus ), universally recognized as the southernmost land of Asia. Both these geographers were ignorant of the vast extension of Africa to the south of this line and even of the equator, and conceived it as trending away west from the Cinnamon Land and then north-west to the. Marinus had, however, learned from itineraries both by land and sea the fact of this extension, of which he had conceived so exaggerated an idea that even after Ptolemy had reduced it by more than half it was still much in excess of the truth. The eastern coast of Africa was indeed tolerably well known, being frequented by and Roman traders, as far as a place called Rhapta (opposite to Zanzibar?), placed by Ptolemy not far from 7° S. To this he added a bay extending to Cape Prasum (Delgado?), which he placed in 15° S. At the same time he assumed the position in about the same parallel of a region called Agisymba, inhabited by Ethiopians and abounding in es, which was supposed to have been discovered by a Roman general, Julius Maternus, whose itinerary was employed by Marinus. Taking, therefore, this parallel as the limit of knowledge to the south, while he retained that of Thule to the north, Ptolemy assigned to the inhabited world a breadth of nearly 80°, instead of less than 60°, as in Eratosthenes and Strabo.

It had been a common belief among, from the earliest attempts at , not only that the length of the inhabited world greatly exceeded its breadth, but that it was more than twice as great, an unfounded assumption to which their successors seem to have felt themselves bound to conform. Thus, while extending his Africa unduly southward, exaggerated still more grossly eastward. Here also he really possessed a great advance in knowledge over all his predecessors, the trade with  having led to an acquaintance, though of a vague and general kind, with regions east of the  and, the limits of Asia as previously known to the. Marinus had learned that traders proceeding eastward from the Stone Tower (near the Pamir?) to Sera, the capital of the Seres (inland China?), occupied seven months on the journey; thence he calculated that the distance between the two points was 36,200 or 3620 s. Ptolemy, while he points out the erroneous mode of computation on which this conclusion was founded, could not correct it b any real authority, and hence reduced it summarily by one half. He therefore placed Sera (Singanfu?), the easternmost point on his map of Asia, 45° from the Stone Tower, which again he fixed, on the authority of itineraries cited by Marinus, at 24,000 stadia or 60° of longitude from the Euphrates, reckoning in both cases a degree of longitude (in this latitude) as equivalent to 400. Both distances were greatly in excess, independently of error arising from graduation. The distances west of the Euphrates were of course comparatively well known, nor did Ptolemy’s calculation of the length of the Mediterranean differ very materially from those of previous Greek geographers, though still greatly exceeding the truth, after allowing for the permanent error of graduation. This last, it must be remembered, would be cumulative, the longitudes being computed from a fixed point in the west, instead of being reckoned east and west from Alexandria, which was undoubtedly the mode in which they were really calculated. These causes of error combined to make Ptolemy allow 180° long., or 12 hours’ interval, between the Fortunate Islands meridian and Sera (really about 130°).

But in thus estimating the length and breadth of the known world, Ptolemy attached a very different sense to these terms from that which they had generally borne. Most earlier and “&thinsp;cosmographers&thinsp;” supposed the inhabited world to be surrounded on all sides by sea, and to form a vast  in the midst of a circumfluous. This notion (perhaps derived from the ic “&thinsp;ocean stream,” and certainly not based upon direct observation) was nevertheless in accordance with truth, great as was the misconception involved of the continents included. But Ptolemy in this respect went back to, and assumed that the land extended indefinitely north in the case of eastern , east, south-east and north in that of Asia, and south, south-west and south-east in that of Africa. His boundary line was in each of these cases an arbitrary limit, beyond which lay the, as he calls it. But in Africa he was not content with this extension southward; he also prolonged the continent eastward from its southernmost known point, so as to form a connexion with south-east Asia, the extent and position of which he wholly misconceived.

In this last case derived from the voyages of recent navigators in the  a knowledge of extensive lands hitherto unknown to the  world, and Ptolemy acquired more information in this quarter. But he formed a false conception of the bearings of the coasts thus made known, and of the position of the lands to which they belonged, and, instead of carrying the line of coast northwards from the Golden Chersonese (Malay Peninsula) to the Land of the Sinae (sea-coast China), he brought it down again towards the south after forming a great bay, so that he placed Cattigara—the principal emporium in this part of Asia, and the farthest point known to him—on a supposed coast of unknown extent, but with a direction from north to south, and facing west. The hypothesis that this land was continuous with southernmost Africa, so as to enclose the Indian Ocean as one vast lake, though a mere assumption, is stated by him as definitely as if based upon positive information. It must be noticed that Ptolemy’s extension of Asia eastwards, so as to diminish by 50° of longitude the interval between easternmost Asia and westernmost, fostered ' belief that it was possible to reach the former from the latter by direct navigation, crossing the.

Ptolemy’s errors respecting distant regions are one thing; it is another thing to discover, in regard to the Mediterranean basin, the striking imperfections of his geographical knowledge. Here he had indeed some well-established data for latitudes. That of Massilia had been determined, within a few miles, by, and those of , Alexandria and were approximately known, all having been observation-centres for distinguished. The fortunate accident that Rhodes lay on the same parallel with the enabled Ptolemy to connect the two ends of the Inland Sea on the famous parallel of 36° N. Unfortunately Ptolemy, like his predecessors, supposed its course to lie almost uniformly through the open sea, ignoring the great projection of Africa towards the north from  westward. The erroneous position assigned to Carthage being supposed to rest upon astronomical observation, doubtless determined that of all North Africa. Thus Ptolemy’s Mediterranean, from Massilia to the opposite point of Africa, had a width of over 11° of latitude (really 6°). He was still more at a loss in respect of longitudes, for which he had no trustworthy observations; yet he came nearer the truth than previous geographers, all of whom had greatly exaggerated the length of the Inland Sea. Their calculations, like those of Marinus and Ptolemy, could only be founded on the imperfect estimates of mariners; and Ptolemy, in translating these conclusions into scientific form, vitiated his results by his system of