The Egyptians related the extension of their country with the ordering of the sky. In the sky the most important line is the Ecliptic, which is the equivalent of the tropic on Earth. All the planets move within 7, north and south, of the Ecliptic. Since the Ecliptic is at an angle of 24 (counting in round figures) with the Equator, no planet reaches a point further north than 31. For the mapping of the sky it is enough to draw a map extending up to 31 00N, assuming the Tropic and the Ecliptic to be at 2400N. The area of the sky in which the planets move was considered the inhabited part of the sky. The Egyptians conceived of the sky as a cylinder extending up to latitude 31. This part of the sky could be mapped by a Mercator projection, since the degree of longitude up to latitude 31 shrinks of only 1/7. This cylinder could be unfolded into an oblong; hence, at times, the inhabited sky and the inhabited earth is described as an oblong. The sky above latitude 31N was conceived as a huge hole, empty and uninhabited space. No stars in this area received attention except the circumpolar stars. On Earth the inhabited world, called Oikoumene, the inhabited, by Greek geographers, was conceived as extending up to latitude 3100N (or 3106N if the Tropic and Ecliptic are set at 2406N, latitude of Syene).

In mapping of the sky, the cylinder could be divided into 12 squares of 30 by 30, a square for each zodiacal constellation. The same applied to the mapping of the Earth; the Mediterranean, the Great Green for the Egyptians, was conceived as being the beginning of the empty space, corresponding to the great wasteland of the sky.

But there was the complication that the inhabited sky and Egypt extended to latitude 31N. This problem was solved by using a technique employed in land surveying. Since a square has an irrational diagonal, one substituted for it a near-square with sides related as 20:21, which has a diagonal 29. This near-square is frequently used in cuneiform mathematical calculations (called basi in Sumerian). In Mesopotamia there are temples belonging to the preliterate period (around 3000 B.C.) that have sides related as 20:21. Many Egyptian tombs of the early dynasties have this proportion. Most Greek temples were planned according to this near-square, which had acquired a cosmological meaning. In mapping the sky and the Earth, the circumference was divided into 12 near-squares of 30 of longitude and 31 30 of latitude. Hence, Egypt was conceived as extending up to latitude 3130N. The point at 3130 on meridian 3114E (the meridian of the Delta) was called Behdet, Crown. It corresponds well to the northernmost point of the estuary of the Nile. Behdet was the capital of Egypt in predynastic times.

Basically, Egypt was conceived as extending 7 north of the Tropic, to the base line of the Delta, being divided into 6 for Southern Egypt and an extra 1 for Northern Egypt.. This is the reason why in Egypt there was a cubit of 6 palms (450 mm.), as in all other cultures of the ancient world, but the official standard was the royal cubit of 7 palms (525 mm.). The king of Egypt holds in his hands the cubit of 7 palms, from which we derive the concept of scepter. This cubit represents the length of the two Egypts and also as much as Mercury (Thot, the god of measuring and mathematics) deviates from the line of the Ecliptic. The width of the zodiacal band, the great highway (hodos in Greek) in which the Sun and the planets move, which is 14, is determined by the planet Mercury that deviates the most from the Ecliptic. The movement of the planets is described as a race in a stadium, the width of the stadium with a width of 14 and a length of 360; at times the movement of the planets is described as a ball game in a similar oblong.

According to this conception, the zodiacal band is divided into 24 oblongs of 14 x 15, or for more regularity into 24 squares of 15 x 15. Two squares correspond to a constellation. This is one reason why Egypt was conceived as extending either 7 or 730 north of the Tropic. This is the reason why the Doric column has 24 faces. This is the reason why the typical Greek temple is built on a rectangle composed of two near-squares with proportions 20:21. The surface of a temple represents a constellation in the sky. The Latin word templum (derived from the Sumerian temen) makes clear that the pattern of a temple is related to the mapping of the sky; for the Latins to make a templum meant to divide the sky into a system of squares.

For the sake of mapping the inhabited sky, it is enough to draw a map extending to latitude 3130N. This map can be divided into twelve near-squares with sides 30 and 31 30. The same procedure can be used in mapping Egypt and the areas to the east and west. When it became necessary to map the Earth to the north of Egypt, the extension of the inhabited earth was duplicated to 6300 N. This is the reason why Ptolemy places the limit of the Oikoumene at 63 N. On the supplementary zone 31 30N to 6300 N there was marked a supplementary line of the Tropic at 45 12N which was identified with the course of the Danube and the Po; the reference points are the mouth of the Danube and the confluence of the Ticino with the Po.

System A

The Egyptians set their basic geodetic point at the Apex of the Delta, that is, where the Nile begins to divide. This point is on the island al-Warraq, in the center of the modern city of Cairo, at 30 06N 31 14E. Hence, they chose meridian 5114E as their basic longitude. This meridian divides the Delta of the Nile into two equal parts and marks well the main course of the Nile up to its sources at the Equator, at Lake Victoria.

In fixing the basic latitudes they met with a slightly more complex problem. First of all it would have been simpler if the Apex of the Delta had been placed at exactly 3000N. They solved the problem by considering the southern limit of Egypt. The southern frontier of Egypt was formed by the Cataract of Aswan, which extends from 2406N to 2400N. Hence, Egypt south of the Apex, which was called Southern or Upper Egypt, could be reckoned to measure exactly 6 of latitude, 1/15 of the distance between the Equator and the Pole. This left 24 for the course of the Nile from the southern limit of Egypt to its sources. The 6 for the length of Southern Egypt could be reckoned either from 24 06N to 30 06N or, in round figures, from 24 00’N to 30 00’N. In trying to rationalize this shift of 6 to the north, they considered the position of the Tropic. In round figures the Tropic can be considered to be placed at latitude 24 00N, but at the time the system was established the Tropic was located at latitude 2351N. It has moved slowly south ever since; its present position is 23 27N. They related this with the fact that when one observes the shadow cast by the Sun, its position is determined by the upper margin of the solar disk, a point that is half a solar diameter (roughly 15) north of the middle point of the solar disk. This meant that when the Sun reached its highest point at the Summer Solstice, the latitude at which the Sun did not cast a shadow at noon of that day was not at 2351N, but at 2406N. Hence, they concluded that the southern limit of Egypt coincided with the Tropic, but took the Tropic as a band extending from 2351N to 2406N, with a middle point at 24 00N. Hence, the symbol for Southern Egypt is three short parallel lines crossed by a perpendicular line which represents the meridian. Then the Egyptians established a similar system at the other end of Southern Egypt. The boundary between Southern and Northern Egypt is a band of three lines each, 6 north of the corresponding lines at the Tropic.

If the  Earth were a sphere the degree of longitude would become 6/7 of the degree at the Equator at latitude 31°00’ (cos 31°-0.85717; 6/7=0.85714), but according to the actual shape of the Earth it becomes 6/7 at latitude 31° 06’. According to the presently accepted theoretical geoid the degree of longitude is 111,321 m. at the Equator and 95,406 m. at 31° 06’ at sea level. (6/7 111,321-95,418). This is the reason why there is a wavering of 06’ in the Egyptian calculations of latitude.

This wavering was related to the fact that the southern limit of Egypt in a narrow sense, the Little Cataract, extends from 24°06’ N (Philae) to 24°06’N (Syene). Southern Egypt was calculated as extending 6° of latitude, either from 24°00’N (Philae) to 30°00’N (point Pi-Hapy) or from 24°06’N to 30°06’N (Apex of Delta). Northern Egypt was conceived as being one additional degree, so that altogether the two Egypts had a length of seven degrees. This is the reason why the Pharaoh wears wears two crowns superimposed on each other, even though the concept of “crown” was associated specifically with Northern Egypt. The column originated as a symbol of Egypt: the shaft represented Southern Egypt and the capital Northern Egypt, which had the shape of a triangle. This is the reason why Vitruvius (De architectura, IV,3,4) states that the Doric column has a diameter of 2 units and a height of 14, of which the capital is one; the reason for the duplication of the height will appear below.

In the administrative division of Egypt the area between Memphis and the Apex, from 2951N to 3006N, was a special nome that did not belong either to Northern or Southern Egypt. The reason for this is that the boundary could be set at 30 00N, a convenient round figure; it is the latitude of the biggest pyramid, the pyramid of Cheops. It could also be set at 3006N, the real beginning of Northern Egypt. The latitude 2351N was chosen for the location of the first capital of united Egypt, Memphis. The geodetic point for this capital was marked by a hemispheric stone placed at the point called Sokar on the basic meridian 3114E (the same Sokar is preserved by the modern village of Saqqarah).

The Egyptians assumed that the rest of Egypt, that is, Lower or Northern Egypt, extends exactly 1 north of the Apex of the Delta. They marked the Delta on the ground as a triangle that has the height of 1. Hence, the basis of the Delta runs along parallel 3106N. Egypt as a whole, Northern and Southern Egypt, has a length of 7 of latitude. Here, again it would have been more convenient if the basis of the Delta was on latitude 3100N. But they were able to give a specific significance to latitude 3106N by noticing that if the Earth were a sphere the degree of longitude would have length of 6/7 of its length at the Equator at latitude 3100N, but given the actual shape of the Earth it acquires this length at latitude 3106N.

The triangle of the Delta was made to extend 124 east and west of the basic meridian of Egypt. In this way the angles came to correspond perfectly with the eastern and western boundary stations on the coast. The Delta was considered as composed of two triangles with sides related as 5:7 (5 is the latitude and 7 the longitude). But since they knew that the degree of longitude becomes shorter by 1/7 at latitude 3106N, the relation between the height of the Delta and each semibasis of it is 5:6.

For all these reasons the Egyptians came to give particular significance to the factor 7 in their calculations of length. Whereas, the rest of the ancient world used a cubit of 6 palms (a palm is 4 fingers), the Egyptians adopted as their standard unit of length a cubit of 7 palrms, called royal cubits. This cubit is divided into 7 palms and 28 fingers. The multiple of the cubit is the stadion of 500 cubits; the stadion was conceived as a double-minute of march, assuming that in a second one made a full step of 2 1/2 cubits (5 cubits in a double-second). Fifty stadia made a unit called itr, river measure by the Egyptians and schoinos by the Greeks; a schoinos is 7,862.22 m. The schoinos was considered equivalent to an hour of navigation on the Nile. In practical reckonings a degree was calculated as 14 schoinoi. But in more exact reckonings the degree was calculated as 14.1 schoinoi to a degree, that is, 110,857 m. to a degree. According to our present reckonings the degree of latitude is 110,848 m. at latitude 3000.

The two values for the degree were linked with the two figures for the latitude of the Tropic. The Tropic was assumed to be at 356 schoinoi from the Equator (336 = 6 x 7 x 8). By the round figure of 14 schoinoi to the degree, there is obtained the round figure of 24 00N for the Tropic. By the accurate figure of 14.1 schoinoi to the degree there is obtained the figure of 2349.8N. It is possible that that this was the most exact figure for the Tropic. Possibly the figure for the Tropic was rounded to 2351N in order to make it 15 less than 2406N, whereas the diameter of the sun is slightly more than 30.

The Egyptians reckoned that the total length of Egypt from latitude 2400 N to latitude 3106N was exactly 100 schoinoi (14.1 x 706 = 100.110). This length was divided into 14 schoinoi for Northern Egypt and 86 schoinoi for Southern Egypt.

This system was slightly modified when the Egyptians began to measure lands to the north of Egypt. For the purpose of measuring to the north of their country the Egyptians fixed the northermost point of Egypt at the northernmost point of the Delta. This is a point of latitutude 3130N on the main Axis of Egypt (3114E) called Behdet, crown,; Behdet was the capital of Egypt in predynastic times. Behdet had the advantage of being 730 (1/12 of 90) north of the southern limit of Egypt. It was also 15 00 or 1/6 of 90 north of the point where the Blue Nile and the White Nile merge at Khartoum (1630N). the distance between latitude 2400N and latitude 3130N was recalculated as 106 schoinoi; because this makes the degre equal to 14.15 schoinoi, that is, 111.172 m. to the degree. According to our present reckonings the degree of latitude at latitude 4500N, the middle point between the Equator and the Pole, is 111.131 m.

The world north of Egypt was mapped by taking parallel 4500N as the main line. At that latitude a degree of longitude reckoned on the basis of 14.14 schoinoi or 707 stadia, becomes 10 schoinoi or 500 stadia (707 x cos 45=707 x 0.70711=499.927). However, the basic parallel was shifted to 4512N, for the usual reason that given the actual shape of the earth, the degree of longitude becomes 500 stadia at that latitude. Parallel 4512N was identified with a line marking the northern shore of the Black Sea, the mouth of the Danube, the lower course of the Danube, the lower course of the Adige, the middle course of the Po up to its junction with the Ticino.

For the purpose of mapping the world north of Egypt, the distance from the Equator to Behdet, 31 30, was duplicated to 6300. Latitude 6300N remained the extreme northern limit of the mapped world throughout ancient history; it is the most northerly latitude in Ptolemys Geography.

Latitude 6300N was considered the latitude at which there begins the world that has eternal light during the summer. It is true that technically the day of 24 hours starts further north, but even today the Norwegians consider as important the twilight zone below the Arctic Circle. Norwegian practice is to consider that light lasts as long as the upper margin of the sun is less than 4 below the horizon.

There was also another reason for setting the extreme northern limit of Egypt at 3130N. In mapping the sky the Egyptians divided the sky into two parts. One was the sky in which the sun, the Moon and the planets move: this was considered the inhabited part of the sky; the rest was considered a wasteland in which nothing moves, where there is no life. The planets move in a band that extends 7 north and south of the Ecliptic; this is determined by the planet Mercury, the god of measurements, which has the maximum deviations from the Ecliptic. Hence, the inhabited part of the sky extends only to 3100N, assuming the angle of the Ecliptic to be 2400. The sky could be represented by a cylinder; the rest of the sky, above latitude 3100N was considered an empty unmeasured hole. This concept was extended to the earth: there is the inhabited part of the earth, the Oikoumene, and the empty, unmeasured and unmapped part (the eremon of the Greeks). Hence, Egypt on earth extends as far north of the Tropic as the movement of the heavenly bodies extends north of the Ecliptic. Originally the Mediterranean, the Great Green for the Egyptians, was considered the equivalent of the wasteland of the sky.

But the figure of 31 was an odd figure. However, it was standard practice of ancient mathematics to convert the square which has an irrational diagonal into a near-square (called basi in Sumerian) with proportions 20:21, because thereby there is obtained a rational diagonal. The oldest temples of Mesopotamia, belonging to the period that precedes the origin of writing, are planned by such a near-square. I have discovered tahat almost all Greek temples are planned by such a near-square. On the same principle the band of the Oikoumene in the sky or on earth, can be divided into 12 near-squares lof 30 of longitude and 3130 of latitude. This gives a near--square to each constellation of the zodiac. Temples were planned on the same principle because they correspond to the division of the sky. In the sky the Oikoumene was left ending at latitude 3130N, but on eath it was duplicated to extend to latitude 6300N. Hence, on earth the eremon was made to begin north of 6300N.

There is a famous text of Egyptian geography which is found inscribed on three different measuring rods and of which other copies seem to exist. Even though the rods are of later periods, the text of the inscription is considered to have been drafted in the Old Kingdom because of its lingusitic style. The text says that from Behdet to the Apex of the Delta there are 86 schoinoi. Egyptologists have not been able to make sense of this text, because they have declared a priori that a calculation in terms of differences of latitude was impossible. Hence, they have dismissed these documents as gibberish without even trying to test their figures in terms of latitude.

The basic geodetic system of Egypt consists of a meridian, 3114E, and of the triangle of the Delta. But from the two outer angles of the Delta there were lowered two meridians, parallel to the main meridian, which mark the eastern and the western limit of Egypt. With these two meridians Egypt acquires the shape of a rectangle. All the geographical positions of Egypt and of the lands surrounding Egypt were calculated in relation to these three meridians and the triangle of the Delta.

It is possible to establish with certainty when this geodetic system was established, because on the two sides of the throne of the Pharaoh of Egypt there was a design that represents it. This design appears, with slight variations, on all the representations of an Egyptian pharaoh sitting on the throne. The earliest statues known to us belong to the Fourth Dynasty, but we have evidence that the design existed earlier. Egyptologists are quite familiar with this design which they call Unity of Egypt, but they have never explained it. It represents the scheme by which the geodetic system of Egypt was established.

The design Unity of Egypt is related to the column. The column, which is familiar to us through Greek temples, originated in Egypt as a symbol of Egypt or of the Oikoumene. The shaft of the column represents Egypt up to latitude 3000N, whereas the capital represents the addition of the Delta or northern Egypt. The tapering of the column reflects the shrinking of the degree of longitudes. The fluting of the column represents the meridians. The proprotions used by the Greeks in building their columns were based on the patterns of Egyptian geodesy.

To the system that had just been described there were added some further refinements. One was to calculate that the Main Axis of Egypt cuts the Nile at the Second Cataract, which was considered the southern limit of Egypt in a wide sense, at latitude 2151N. By this reckoning the capital of Memphis is 8 north of the border and Egypt as a whole, excluding the band between 2951N and 3006N (the band corresponding to the band of the Tropic), comes to be 9 or 1/10 of 90. But it was found that more exact measurements could be obtained by following meridian 3228E, which is the Eastern Axis of Egypt. This meridian cuts the Nile near Khartoum, the junction of the White Nile with the Blue Nile, at exactly latitude 1630N, exactly 1500 south of Behdet. This meridian does not pass through the Cataract of Aswan (it passes slightly to the west of it), but it cuts the Nile at exactly 2300N. Hence, the legal boundary of Egypt was shifted from the Cataract at Asswan to a point 1 south of it, point 2300N 3238 E, called Sacred Sycamore, which remained the legal boundary of Egypt up to Roman times. By this reckoning Southern Egypt has a length of 7.

The choice of latitude 2300N as the legal southern limit of Egypt had also another explanation.

When the Egyptians began to set up their geodetic system there had benn already in existence another geodetic system which was based on meridian 954E. This meridian goes from the Equator, cutting the easternmost point of the Gulf of Guinea to the Norwegian coast of Orkedal, SW of Trondheim. This meridian remained always the meridian zero of ancient geography, except for small modifications resulting from the efforts to adjust it to the Egyptian geodetic system. The first geodetic point set in Egypt was at the Cataract of Aswan, which is at 3254E and hence 2300 east of the basic meridian.

As a result the Egyptians remained always concerned with the problem of giving a rationale to this figure of 23. One of the methods was to set the southern limit of Egypt at 2300N, so that Egypt could be linked with the basic geodetic point 000, equivalent to 954E, by a geodetic square of 23 by 23.

Next, the Egyptians shifted the basic geodetic point to the Island of So Tom in the Gulf of Guinea which is at 2351 West of the Main Axis of Egypt. They assumed that the line of the Ecliptic is marked on the earth, as it is marked on some globes today. They say that the Ecliptic crosses the Equator at the Island of So Tom and crosses the Tropic at 2351N, 3114E. Hence, the Ecliptic became the diagonal of a square that has its SW angle at So tom and its NE angle at the mentioned point.

For the purpose of mapping the world east and west of Egypt, there was chosen as main line parallel 3600N, which marks the division between Africa and Europe, the southern coast of Asia Minor, the main line of the mountains in Asia, and the key line in China. The people of Mesopotamia assued that the main band of the world extends from 3600N to 3000E, because this fit excellently the geography of that country. They drew these two parallels from Gibraltar to the Chinese coast. The band was divided into squares with a height of 6 of latitude and 712 of longitude. Assuming that the degree of longitude shrinks to 5/6 at that latitude (cos 3333==5/6), each square is a perfect square in terms of actual length of the degree.

When the Egyptians adopted this system they counted 3 squares of 712 of longitude west of the Western Axis of Egypt, setting their meridian zero at 814E. The new meridian zero is 23 west of the Main Axis of Egypt.

The new meridian was justified by relating it to the sources of the Danube. This is the reason why Herodotus and Aristotle say that Europe extends as far west as the sources of the Danube. Today we place the sources of the Danube at Donaueschingen where the Brigach is increased by some underground sources, but the sources of the Brigach are at 814E.

When King Darieos set up a capital for the newly established Persian Empire, he chose Persepolis, which is in a most impractical position and came to be used merely as a ritualistic capital. But the new capital was based on a geodetic point, determined by the tomb of the king, which is exactly on parallel 3000N and 3 units of 712 east of the Eastern Axis of Egypt and 2300 east of the Main Axis of Egypt. Hence, the meridian of Persepolis balanced in relation to Egypt the meridian zero east of Egypt.

System B

At the beginning of the Middle Kingdom the geodetic system was revised by putting the emphasis on the Eastern Axis of Egypt. A new capital was established at Thebes on meridian 3238E. In front of the place where this meridian cuts through the water of the Nile, there was set the temple of Ammon which became the main temple of Egypt. The main room of this temple is exactly at 2/7 of the distance from the Equator to the Pole. In this room the god Ammon was represented by a hemispheric stone similar to the stone that used to be at the point Sokar (Sokar too was a god) at Memphis. The reason for choosing a latitude of 2545N, 2/7 of the distance between the Equator and the Pole, was that in the ancient world it was standard practice to calculate trigonometric functions by dividing the arc into seven parts. The cosine of 2545 is 0.90095, or practically 0.90.

Given this value of the cosine, in the geodetic system of Thebes calculations were made by a stadion of 1111.11 stadia to the degree. This unit was chosen because according to it the degree of longitude is 1000 stadia at the latitude of Thebes. This stadion is based on a foot of 332.0387 mm.; this is the standard foot in cuneiform mathematical texts; 300 such feet make a stadion (minute of march); the schoinos is reckoned as 60 stadia (a double hour of march). The foot of this system is 9/8 of Roman foot. The schoinos (6000 feet) is 5,992.90 m.; it is quite close to 4 Roman miles (a mile is 5000 Roman feet) or 5,918.91 m. (the Romans calculated 75 miles to the degree). The stadion of this system is that used by Aristotle when he states that the circumference of the Earth is 400,000 stadia. This system has the advantage of fitting better into sexagesimal reckoning: In a rough computation a degree can be computed as 18 schoinoi.

But in more exact reckoning it was computed as 18.5 schoinoi or 1110 stadia; the absolutely precise figure was 1111 stadia. Traditionally the length of Egypt was taken as 100 schoinoi; now, this length was applied to the distance (523) between Thebes and Pelusion, at latitude 3106N. The distance (243) between Thebes and the Sacred Sycamore at 2300N was reckoned as 50 schoinoi. Hence, according to the system of Thebes, Egypt has a total length of 150 schoinoi (9000 stadia).

This system was fitted to sexagesimal reckoning, the system used in scholarly work; but, for this very reason, it never became popular in Egypt. It is importatn to us because it is the system followed by Herodotus in his description of Egypt. Up to now scholars have never tried to explain the figures used by Herodotus, because they have excluded a priori that he could speak of differences of latitude and longitude. Hence, they have dismissed Herodotus figures as absurd; and, further, in order to explain how he could submit absurd figures, they have accused him of being a liar when he reports of having visited the whole of Egypt. The prevailing opinion is that Herodotus never saw Egypt beyond the Delta.

System C

When the Assyrians conquered Egypt in the seventh century B.C. they reformed the system of measures of Egypt in order to bring it into agreement with their own and thereby manifest their dominion. The system introduced by the Assyrians continued to be used under the successive foreign rulers of Egypt: Persians, Greeks and Romans. The first step was to substitute for the traditional Egyptian cubit a new official unit, which was the cubit used in Mesopotamia, the cubit of 532.7017 mm (9/5 of Roman foot). In order to keep the traditional length of 100 schoinoi, the basis of the Delta was shifted from 3106N to 3112N; thereby the length of Egypt became 712 (1/50 of 360). In practical reckoning one could still go by the traditional figure of 14 schoinoi (700 stadia) to the degree. But in more accurate reckonings the degree is 13.888 schoinoi.

The shifting of the basis of the Delta to latitude 3112N had the purpose of linking Egypt more intimately with the non-Egyptian geodetic systems. The mapping of Europe and Asia on the two sides of the Black Sea was based on parallel 4500N, but this meridian had been modified into parallel 4512N. One reason for this is that the degree of longitude at this latitude had the length that it would have at latitude 4500N if the Earth were a sphere. For this reason there was a general shift of 12 to the north in the calculation of the geodetic lines north of Egypt. For a similar reason the Egyptians had set the basis of the Delta 6 north of parallel 3100N, but now they had to accept a shift that does not conform to the geography of Egypt itself.

The new latitude of 3112N broke the political isolation of Egypt by making it depend on a foreign geodetic system. Hence, it was used to establish the position of Alexandria, when Alexander the Great decided to set up a new capital for Egypt on the sea, that is, as much as possible in contact with the outer world.

Current scholarship keeps repeating that the circumference of the Earth was first measured by Eratosthenes, the Greek who was put in charge of the library of Alexandria. But actually the opposite is true: Eratosthenes merely cited some old Egyptian information about the circumference of the Earth without understanding it too well.

Eratosthenes claims to have found out that a degree of latitude is 700 stadia; but this is nothing but the most traditional Egyptian datum: 14 schoinoi of 50 stadia. Then, he claims that on a more accurate reckoning he found the circumference of the Earth to be 250,000 stadia instead of 252,000. In this case, too, he merely quotes the Assyrian system of 13.888 schoinoi (694.444 stadia) to the degree.

When the Assyrians established their system the Tropic must have been at about latitude 2345N, with the result that the latitude at which the Sun does not cast a shadow at the Summer Solstice must have been at about 2400N, the southern limit of Egypt. Hence, Eratosthenes repeated the information that the Sun does not cast any shadow at the southern limit of Egypt.

He further claims to have found out by observation that when the Sun does not cast any shadow at the southern limit of Egypt, it casts a shadow of 712 at Alexandria. The instrument that he is said to have used would not permit a reckoning precise to the minute; half a degree would be the maximum. furthermore, at his time the point without shadow was somewhat to the south of latitude 2400N.

In reality, Eratosthenes had read the old Egyptian data (more than 2000 years old) to the effect that the Tropic is at latitude 2351N and that the Sun does not cast any shadow at Elephantine (2406N). He did not understand the necessity of adjusting the figures according to the apparent semi-diameter of the Sun and affirmed to have found out that at Elephantine, which according to him is at the Tropic and at 2351N, the Sun does not cast any shadow at the Summer Solstice. He claims to have found that Alexandria is 712north of 2351N. He could not even determine the latitude of Alexandria.

Since he did not understand that the data obtained by shadow observation have to be corrected by the semidiameter of the sun, he confused into one the three old Egyptian data about the position of the Tropic.

Next, Eratosthenes claims that Alexandria is on the meridian of Elephantine, whereas they are apart by about 3 of longitude. Finally, he implies that a survey on the ground found an orthodromic distance of 5000 stadia between Elephantine and Alexandria. This claim cannot be taken seriously, since not even the great empires of Egypt, Assyria and Persia would have been able to conduct a survey on the ground for more than one degree.

The demonstration that Eratosthenes did not proceed to any degree of measurement and quoted ancient data without fully understanding it, has been submitted more than once, but scholars continue to repeat that he measured the length of the degree and hence the circumference of the Earth, because the alternative is to admit that this was done in pre-Greek times, a fact that official scholarship wants to deny for a priori reasons.

Eratosthenes could not find his way among the old Egyptian data. He says that Elephantine is at the Tropic and says that the Tropic is at 2351N, but also says that Elephantine is at a distance of 16,800 stadia from the Equator. This means that, by the rough figure of 14 schoinoi (700 stadia) to the degree, the Tropic is at 2400N. But by the old Egyptian accurate figure of 14.1 schoinoi (705 stadia) to the degree, the Tropic is at 2351N. Here, Eratosthenes quotes figures based not on the Egyptian cubit of his time, but on the old Pharaonic cubit. By the cubit of Eratosthenes time, 16,800 stadia would have placed the Tropic and Elephantine at 2412N.

Eratosthenes confused different data belonging to separate geodetic systems, but he came to the correct results because the Egyptians had tried to preserve the same figures for the length of Egypt in all systems. By the oldest system the interval between Elephantine at 2406N and the latitude of Alexandria, 5112N, is 5000 stadia, stadia calculated by the old Pharaonic cubit (706 x 705 stadia = 5005.5 stadia).

System C of geodesy was related to a new interpretation of the Delta that fitted better the needs of Mediterranean traders. The Delta is conceived as extending 106N of the Apex, to latitude 3112N, and then extending for 106 in either direction. Thereby the Delta comes to be composed of two isosceles triangles. The hypothenuses of these two triangles correspond to the Canopic and Pelusiac branches of the Nile. This is called the Delta that can be circumnavigated.

The western limit of the Delta became the point 3112N 3008E which provided a better anchor point for the system of geodetic squares drawn in the Mediterranean west of Egypt. The first geodetic square ended on the meridian Cythera (2256E), the southernmost point of Greece. The next geodetic square ended at 1544E, the tip of Italy on the Straits of Messina. But most important was that meridian zero became 832E which is the axis of the main trade route of Europe. According to the current opinion of archeologists this trade route came into existence about 2000 B.C.

In the Mediterranean the meridian marks the western coast of Sardinia. But the texts describe the trade route as ascending the Adriatic Sea, reaching the San Gottardo Pass through the Po and the Ticino. Descending to the Rhine along the course of the Reuss; since this is the most difficult part of the road, it is described in great detail. The route continues north through the Weser river, reaching the mouth of the Elbe, and then moves along the western coast of the peninsula of Jutland. The texts mention amber in relation to this route and archeologists have traced this route in terms of findings of amber.

The establishment of this new meridian zero is probably related to the decline of the original meridian 954E which marked the route from the Gulf of Guinea to the Mediterranean. This decline may be related to the dessication of the Sahara. But the Carthaginians continued to use meridian 954E as their basic line. In the Alps this meridian indicates the route through the Adda to Passo Bernina, descending through Engadin.

The Romans for reasons of security set their main camp in Switzerland at Vindonissa on the Reuss in order to close the route of meridian 832 E, and reopened the older route of the Engadin. However, medieval texts refer to this route as Via Mala.

Texts of the early first millennium B.C. still describe the route all the way from Norway to the Gulf of Guinea, but the description of the African part is sketchy. Furthermore, the Gulf of Guinea is described as savage and decayed, stating that earlier it was the center of a great maritime trade.