19.- MATHEMATIC AND CARTOGRAPHIC EVIDENCES
As methodology to compare the distances given by Eratosthenes (Strabo, Bk. I, c. IV, 5) with those that appear in the Ancient Map, lacking of an explicit scale, it would be enough to measure in millimeters, on the general map attributed to Ptolemy, the distance that there appears between Canopos and Carthago and then to compare it with the 13,500 furlongs indicated by Eratosthenes as existing among them. See fig. 9.
9.- Detail of the “Ancient Map”, with longitudinal segments.
Well, practiced the diverse operations on a photocopy
of the general map, taken of the already mentioned edition made in Rome in
1478, we reached the following conclusions:
Canopos (today Abu Qir), the most western mouth of the river Nile. Because Carthago does not appear specially indicated in the general Letter, we will locate it next to a located African peninsula, in the current Tunisia, to the south of the western end of Sicily, since Strabo says that Eratosthenes located Carthago in the same meridian that Rome (Strabo, Bok.. I, cap. IV). By determining this point, we find 60 mm. for the distance Canopus-Carthago. As this distance corresponds to 20º or 14,000 furlongs, you could conclude that the 13,500 furlongs indicated by Eratosthenes were taken of this map. In this way, a degree is equal to 3 mm. in the map and a millimeter to 225 furlongs of 700 to the degree.
According to the current gradation, Carthago would have been located at 10º05 ' L.E.G. and Canopos at 30º05 ' L.E.G., it is to say at 20º or 14,000 furlongs, figure extraordinarily close to the 13,500 indicated by Eratosthenes. It is necessary to conclude that the Ancient Map was calculated in relation to 700 furlongs to the degree and not over 500 like Ptolemy supposed to follow Marinus of Tyrus.
Carthago-Pilars of Heracles. Eratosthenes supposed “at least” 8,000 furlongs, equivalent to 11º30 ', in circumstances that appear 60 mm. in the map or 13,500 furlongs. In the reality there is 15º45 ', it is to say 11,025 furlongs from 700 to the degree.
Canopos-River Nile. In the reality there are 2º between Canopos and the main or more oriental mouth of the Nile, degree 32 L.E.G., that is to say 1,400 furlongs. Eratosthenes only estimated 1,300 and in the map 6 mm.appear, it is to say 1,350 furlongs.
Satelite image of the Delta of the Nile River
Nile-River Euphrates. If it is considered to the city of Thapsacus like representative point of the Euphrates to be located on their margins at 36ºL.N.-38º L.E.G. and, as such, the continuity of the axis Pilars of Hercules-Rhodes-Issic Gulf (Iskenderun or Alexandretta Gulf), we find 6º of longitudinal distance between both rivers, equivalent to 4,200 furlongs, but Eratosthenes counted 5,000 furlongs because in the map appear 20 mm., corresponding to 4,500 furlongs.
River Euphrates-Caspian Gates (Gorge of Sirdara). As this narrow pass crosses Elbruz Mounts in 52º30 ' L.E.G., approximately at 60 km. to the east of Teheran and always on the parallel 36, there would be 14º30 ' from Thapsacus, it is to say 10,100 furlongs, almost identical quantity to the 10,000 furlongs indicated by Eratosthenes. In the map, 43 mm., equivalent to 14º or 9,675 furlongs
Caspian Gates-River Indus. Eratosthenes showed 14,000 furlongs for this distance, that is to say 20º, which it really exists between the Caspian Gates and the origen of the river Indus, at 72º L.E.G. and always in 36º L.N. In the map 63 mm. or 14,175 furlongs are shown to the river Coa, also called Cophen, corresponding to the current river Chitral (also called Konar), affluent of the river Kabul that converges with the Indus.
River Indus- the narrowest part of India. Eratosthenes affirmed “that the longitude from the most narrowest part in India to the river Indus is of 16,000 furlongs” They would correspond to 22º50 ', almost 23º that counted from the degree 72 L.E.G. they would arrive to the degree 95 L.E.G. that is in fact the most eastern point reached by the river Brahmaputra. In the map there are 71 mm. or 15,975 furlongs from the river Coa, the most western tributary of the Indus, until the Bepyrrus Mons (Bepyrrus Mount), corresponding to the current Mounts Naga located between India and Burma (Myanmar) . Here the “India Extra Gangem” (“India beyond the river Ganges” or “Transgangetic India”) or the narrowest part of India began.
Narrowest part of India-East End of the Oecumene. Eratosthenes said “that the part of the India that extends toward the ends has three thousand more furlongs”, and later on that it was necessary to add “other two thousand toward the East”. Thus, for Eratosthenes, the east end of the oecumene was located at 5,000 furlongs, equivalent to 7º, toward the east of the meridian of the Bepyrrus Mons, reaching, in the 19° L.N., the Gulf of Tonkin in Vietnam, located in 105º L.E.G. But as the Ancient Map shows, 69 mm., that is to say 15,525 furlongs or 22° as existent to the east of the Bepyrrus Mons, you would arrive to the meridian 117 L.E.G. in the Sea of China.
When arriving to this last point of the count of Eratosthenes, it should be remembered that he supposed that between Carthago and the Pilars of Heracles, there would not be less than 8,000 furlongs , in circumstances that the map indicated 60 mm. or 13,500 furlongs. As in the reality there is 15º45 ', it is worth to say 11,025 furlongs from 700 to the degree, it should be added 3,000 furlongs of the western Mediterranean estimated by Eratosthenes to the 72,800 furlongs that he would have calculated between the Strait and the oriental end of the oecumene, reaching this way at 75,800 furlongs or 108°.
However, as the Ancient Map gives an extension of 88,700 furlongs, that is to say 126°, it is appreciated that the calculations of Eratosthenes were short in 18°.
In relation to the distances given by the Ancient Map, it should be pointed out emphatically that in this, the Mediterranean Sea corresponds exactly to the third part of the oecumene. This concept was not lost completely and during the Middle Ages, the correlated maps only to the Mediterranean were denominated “maps T in O", abbreviation of the Greek (Tritemoris Oikoumenes") that in Latin version would be Tertia [Pars] Orbis", that is to say “the third part of the inhabited Orb”.
It should be pointed out that Strabo said that Eratosthenes considered to the extension of the oecumene as a little bigger than the third of the terrestrial globe. Well then, that concept makes it a little bigger than 120° and Eratosthenes could deduce it adding at the 108° continental already referred 13° or 9,100 furlongs that there exist between the Pilars of Heracles and the Island of Iron (Ferro Island), the most western in the Canary Islands. This deduction is supported by Eratosthenes, said (Strabo, Bok. I, c. IV, 5) “it must be added still the bend of Europe outside of the Pilars of Herácles, opposed to the Iberian and that it leans toward the Sunset, that is not smaller than 3,000 furlongs” and, in a following passage (Strabo, Bok.. I, c. IV, 5) “to these longitudes he also adds other 2,000 furlongs toward the West.”
Dracon's Tree in the Ferro Island
The remarkable agreement of the geographical knowledge of the ancient people with astronomy and the arithmetic, would authorize to think that if we assign the zero meridian to the Chinese coast, the zodiacal sign Taurus would reach until the grade 30 in which the river Tarim is sucked down by the sands in the China province of Sinkiang (Xinjiang); the sign of Gemini would embrance from the degree 30 up to the 60, where the “twins” rivers Syr Darya and Amu Darya end in the Sea of Aral. Then the sign of Cancer would embrace from the degree 60 up to the 90 that it covers the oriental part of the Mediterranean, abundant in crustaceans like the “crab” and in mollusks like the murex that gave the purple color to the Phoenician fabrics. Next, the sign of Leo would embrace from the degree 90 up the 120, so that it seems to refer to the great “lion” represented in the Sphinx. After Leo, the sign of Virgo would embrace from the degree 120 to the 150 and it would seem to mention to the not very well-known Atlantic Sea, until then “virgin.” From the degree 150 to the 180, it would correspond the sign of Libra, the Scales, because its needle of the pointer would be equivalent to the half of the Earth from the Chinese coasts.
Before concluding the study of the surprising similarity among the longitudinal measures pointed out by Eratosthenes with those shown in the Ancient Map, it would also be necessary to examine the measures of latitude, as Strabo (Strabo, Bok. I, c. IV, 2) has told us. See fig. 10.
10.- Detail of the “Ancient Map”, with latitudinal segments.
Meroe-Alexandria. Eratosthenes showed 10.000 furlongs. In the map 43 mm. from Alexandria at the beginning of the island Meroe that corresponds 15°18 ' according to the scale of 3 mm. per degree that has been using. As Alexandria is located 31°11 ' L.N. and Meroe in 16°55 ' L.N., there is a difference of 14°16 ' that according to the this scale, 42,8 mm. would be equal, that which implies an exact interrelation between the map and Eratosthenes. See fig. 11.
11.- Map of Egypt and Marmarica. Greek manuscript of Vatopédi.
Alexandria-Hellespontus, today Dardanelles Strait. In the map there is 29 mm.that correspond 6,525 furlongs or 9° 19 '. In the reality, there are 8°49 ' or 6,172 furlongs among Alexandria, located at 31°11 ' L.N. and the southern end of the Dardanelles Strait, located at 40°00 ' L.N. For this distance Eratosthenes marked 8,100 furlongs, equivalent to 11°34 ', what implies that he exceeded approximately in two degrees.
Hellespontus-mouths of the river Borysthenes, today Dnieper.
If the mouth of the Dnieper is located at 46°30 ' L.N., there would be a difference of 6°30 ' or 4,550 furlongs regarding the southern end of the Dardanelles Strait, located at 40°00 ' L.N. In the map appear 22 mm., corresponding to 4,950 furlongs or 7°04 '. Nevertheless, Eratosthenes indicated 5,000 furlongs, which implies a slight error of 450 furlongs or 38 '.
Mouths of the Borysthenes-parallel that crosses through Thule. In the map appear 40 mm., equivalent to 9,000 furlongs or 12°51 ', among the mouth of the river Borysthenes, located at 46°30 ', and the parallel one that goes by Thule, reason why this corresponds to the parallel one 60. However it is not like this, since when fixing Eratosthenes 11,500 furlongs, that is to say 16°25 ' , it reaches to the degree 63 as it is read in the map, which takes to suppose that it is built keeping a right projection. The reference of Eratosthenes to the degree 63 suggests that in this matter he followed Pytheas of Marseille very closely, to whom unfortunately Strabo disqualified without serious arguments, losing for the geographical science the historical value of a very important part of his journey.
It is also of interest to notice that the Ancient Map not only locates Thule at the degree 63, but it also locates its western end at 5° to the west of the meridian that goes by Marseille. According to the current gradation, the city of Marseille is located 5°21 ' L.E.G., that is to say in the same meridian that the city of Bergen, in the western end of Norway, not far from the region of Telemark, name that without a doubt derives Thule. In this manner, it is unavoidable the conclusion that Thule could never be Iceland, so this is located in the same meridian to that of the Canary Islands, it is to say in the degree 18 L.O.G.
It was known from immemorial times that at sunset on the day of the summer solstice over Syene (current Aswan, at the feet of the first waterfall of the Nile), the deep wells appeared with their entirely illuminated mirrors of water and in their walls, there was no shade marked. Notice that now the Tropic is located at 71 km. toward the South.
Of this circumstance so special Eratosthenes should have deduced that if in that moment he measured in Alexandria the shade angle that projects the sun over some poles or sundial, sufficiently big as to obtain equivalent shade angles to minutes, he could check the total of the equatorial circumference by multiplying the existent space between Alexandria and Syene for the times that such angle is the 360° of the circumference.
According to Cleomedes that is the only author that detailed the method of Eratosthenes in his scientific part, he would have found that the shade angle measured at noon in Alexandria of the summer solstice, was equal to 7°12 ' respect to Syene. As these sexagesimal 7°12 ' (decimals 7°20 ') they are equal to 50th part of the circumference, Eratosthenes should multiply by 50 the existent distance between Alexandria and Syene to obtain the measure of the equatorial circumference. However, Cleomedes believed that Eratosthenes had used the figure of 5,000 furlongs as the distance among these two cities, because this was the one that traditionally was considered, and this way Eratosthenes would have obtained 250,000 furlongs for the maximum circumference of the Earth.
Cleomedes missed his opinion, because Eratosthenes really used the figure of 5,040 furlongs, as a result of transforming the 7°12 ' or 7° 1/5 into furlongs from 700 to the degree. In this way, Eratosthenes obtained 252,000 furlongs that is the product of multiplying 5, 040 furlongs for 50. As you can see, Eratosthenes did not arrange any figure with so much nimbleness as it has repeated tirelessly
It is also interesting to point out that Eratosthenes found that there was 3,750 furlongs between Rhodes and Alexandria. We estimate that this quantity, he could obtain it when observing that in the Ancient Map, appear 15 mm. among these cities. Well then, according to our method of determining the scale in that the map was built we would have to multiply these 15 mm. for the 225 furlongs that on average fit in a millimeter. As a result of this, 3,375 furlongs are obtained. . As in the current atlas, It appears a latitudinal difference of 5°15 ' or 5°1/4 among both cities that multiplied by the 700 furlongs that fit in a degree, it yield a total of 3, 675 furlongs, it is demonstrated once again, that Eratosthenes faithfully stuck to the Ancient Map to let know the distances that he estimated interesting to state.