Slide #112
TITLE: World according to Eratosthenes
DATE: 194 B.C.
AUTHOR: Eratosthenes of Cyrene
DESCRIPTION: This slide shows a 19th century reconstruction of the world
view of Eratosthenes of Cyrene (275-194 B.C.). More symmetrical than accurate,
its partitions were the forerunners of parallels and meridians after Dicæarchus
(Slide #111). Geographic information that was gathered
by Alexander the Great and his successors was the primary source used by
Eratosthenes, a scholar with vision large enough to put this information
into a logical framework.
There can be no doubt that before the time of Eratosthenes the ideas of
the learned world on the subject of geography had assumed a more regular
and systematic form. And it is certain also that these had been embodied
in the form of maps, which, however imperfect, were unquestionably very
superior to anything that had preceded them. The first use of world maps
by the Greeks had been introduced at a very early period by Anaximander
(ca. 610-546 B.C. Slide #107 ), and maps of the world
were not uncommon in the time of Herodotus (ca. 489-425 B.C. Slide
#109 ), though based on the crude ideas of the period, and on hasty
assumptions that excited the ridicule of the famous historian. Nor can it
be doubted that the discoveries resulting from the conquests of Alexander
the Great (ca. 356-323 B.C.) and the extension of geographical knowledge
under his successors, would have gradually found their way into such maps;
but we know from frequent experience, even in modern times, how slowly established
errors are discarded, and how long they maintain their ground, even in the
face of more accurate information. The same thing was still more the case
in ancient times, and it is highly probable that if you could now recover
the map of the world as it was generally received in the time of the first
Ptolemies, we should find it still retaining many of the erroneous views
of Herodotus and Hecatæus (Slide #109 and Slide #108).
Eratosthenes, head of the Library at Alexandria from 240 B.C. until his
death, was known as beta to his contemporaries because they considered him
second in all his varied academic pursuits. More critical of these accomplishments
was Strabo (63 B.C.?- A.D.24, Slide #115 ) to whom
we are indebted for much of our knowledge of geography in antiquity, including
the work of Eratosthenes whose relevant works, neither of which survived,
were On the Measurement of the Earth and Geographica, Cleomedes
summarized the former, Strabo criticized the latter. Future scholars would
have a higher opinion of Eratosthenes, regarding him, "as the parent
of scientific geography" and at least "worthy of alpha" in
that subject, particularly for his remarkable measurement of the circumference
of the earth.
It appears indeed from repeated statements of Strabo that Eratosthenes made
it the object of his special attention to "reform the map of the world,"
as it had existed down to his time, and to reconstruct it upon more scientific
principles. It is this enlarged and philosophical view of the subject which
constitutes his special merit, and entitles him to be justly called "the
father of systematic geography". The materials at his command were
still very imperfect,and the means of scientific observation were wanting
to a degree which we can, at the present-day, scarcely figure to ourselves;
but the methods which he pursued were of a strictly scientific character,
and his judgment was so sound that he proved in many instances to be better
informed and more judicious in his inferences than geographers of two centuries
later.
With regard to the fundamental idea of all geography - the position and
figure of the earth - Eratosthenes adopted the views that were current among
the astronomers of his day, which had been received almost without exception
from the times of Aristotle (ca. 384-322 B.C.) and Euclid (ca. 300 B.C.).
He regarded the earth as a sphere, placed in the center of the universe,
around which the celestial sphere revolved every twenty-four hours: besides
which, the sun and moon had independent motions of their own. The obliquity
of the sun's course to that of the celestial sphere, was of course well
known; and hence the great circles of the equinoctial, and the ecliptic,
or zodiacal circle, as well as the lesser circles, called the tropics, parallel
with the equinoctial, were already familiar to the astronomers of Alexandria.
Moreover it appears that these conceptions, originally applied to the celestial
sphere, had been already transferred in theory to the terrestrial globe.
Thus the idea of the globe of the earth, as it would present itself to the
mind of Eratosthenes, or any of his more instructed contemporaries, did
not differ materially from that of the modern geographer. For all geographical
purposes, at least as the term was understood in his day, the difference
between the geocentric and the heliocentric theories of the universe would
be unimportant.
But Eratosthenes had the merit of making one valuable addition to the previously
existing ideas upon this subject, by a more careful and successful measurement
than had ever been previously attempted, of the magnitude of the earth,
or circumference of the terrestrial globe. Once the idea of a spherical
earth was accepted, and that it was a perfect sphere, the measurement of
this body was a logical step, even to Greek scholars who were more given
to philosophical speculation than to quantification and experimentation.
He was not indeed the first who had attempted the solution of this problem,
which would naturally engage the attention of astronomers and geometers,
as soon as it was agreed that the earth was of a spherical form. Aristotle
refers to the calculation of "mathematicians" who had investigated
the subject (without naming them) that the earth was 400,000 stades in
circumference. This distinction may belong to Eudoxus of Cnidus (ca. 370
B.C.) who also estimated its measurement at 400,000 stades. A calculation
of 300,000 stades is credited to Dicæarchus (died 296 B.C.),
a student of Aristotle. Aristarchus of Samos (died 230 B.C.), has been called
the "Copernicus of Antiquity" because of his early espousal of
a heliocentric, rather than geocentric, view of the universe (perhaps, more
properly, Copernicus should be called the "Renaissance Aristarchus").
At a later period Archimedes speaks of 300,000 stades as the measurement
usually received, a statement apparently founded on the calculations of
Aristarchus of Samos (died 230 B.C.), one of the earlier astronomers of
the Alexandrian school. But we have no information as to the data on which
these first crude attempts were based, or the mode by which he authors arrived
at their results.
The method pursued by Eratosthenes was theoretically sound, and was in fact
identical in principle with that which has been adopted by astronomers in
modern day. The method pursued by Eratosthenes is fully stated and explained
by the astronomer Cleomedes, in his work on the Circular Motion of the
Heavenly Bodies. Both the method and the accuracy of Eratosthenes' well-known
measurement of the earth have evoked the admiration of later workers, and
his calculation is regarded as one of the greatest achievements of Greek
science. While still keeping to the geocentric views of the universe, Eratosthenes
started from the assumption that the sun was so distant that for practical
purposes one could consider its rays parallel anywhere on earth. He observed
that the rays of the sun, at midday, at the time of the summer solstice,
fell directly over Syene [modern-day Aswan] and that the vertical
rod of the sun dial (gnomon or style) would not cast a shadow (predicated
on the assumption that Syene was situated exactly under the Tropic
of Cancer). At the same time of day and year, the shadow cast by a gnomon
at Alexandria, to the north of Syene, was measured by Eratosthenes
as 1/50 of a proper 360° circle. He assumed that: Syene (S) and
Alexandria (A) lie under the same meridian circle (longitude), although
there is a difference of 2°; that rays (R1 and R2) sent down from the
sun are parallel; that straight lines falling on parallel lines make alternate
angles equal; and that arcs subtended by equal angles are similar. He accepted
a figure of approximately 5,000 stades for the distance from Syene
to Alexandria, which, according to his previous reasoning, was 1/50
of the circumference of the earth. Thus 5,000 stades x 50 equals
250,000 stades, the circumference of the earth. But as a mathematical
ploy, in order to achieve a number divisible by 60 or 360, so as to correlate
stades with his subdivisions or degrees, he emended this to 252,000 stades
[ a stade, stadion, stadia ), originally the distance covered
by a plough before turning, was 600 feet of whatever standard was used].
A conversion to modern units of measure finds Eratosthenes' calculation
to be somewhere between 45,007 km (27,967 miles) to 39,690 km (24,663 miles),
as compared to actual equatorial circumference of 40,075 km (24,902 miles),
there has always been some controversy over the equivalent modern length
of a stade as used by Eratosthenes.
The only theoretical error in this mode of calculation was in the assumption
- which was inevitable in the days of Eratosthenes - that the earth was
exactly spherical, instead of being as it really is, a slightly oblate spheroid,
and that therefore a meridian great circle was equal to that of the equator.
And the error proceeding from this cause, which would not exceed 1/300th
part of the whole, is wholly unimportant as compared with the practical
errors arising from the defective means of observation.
In the first place, it was assumed that Syene lay directly under
the tropic, it being a well-known fact that at the summer solstice the sun
could be seen from the bottom of a deep well, and that at the same time
the gnomon cast no perceptible shadow. But, though these facts were perfectly
correct as matters of rough observation, such as could be made by general
travellers, they were far from having the precise accuracy requisite as
the basis of scientific calculations. Syene is in fact situated in
latitude 24° 5' 30", or nearly 37 miles to the north of the Tropic.
In the next place Alexandria, instead of being exactly on the same meridian
with Syene, lay in fact not less than three degrees of longitude
to the west of it: an error of no trifling moment when the distance between
the two was assumed as the basis of calculation. But a much graver error
than either of these two was that caused by the erroneous estimate of the
actual distance between the two cities. What mode of measurement had been
resorted to, or how Eratosthenes arrived at his conclusion upon this point,
we are wholly without information: but it may well be doubted whether he
had recourse to anything like actual mensuration. Indeed the difficulty
which modern experience has shown to attend this apparently simple operation,
where scientific accuracy is required, renders it highly improbable that
it was even attempted; and the round number of 5,000 stades at once
points to its being no more than a rough approximation. But even considered
as such, it exceeds the truth to a degree that one could hardly have expected,
in a country so well known as Egypt, and in an age so civilized as that
of the Ptolemies. Alexandria is in fact situated at a distance of about
530 geographical miles (5,300 stades ) from Syene, as measured
on the map along the nearest road but the direct distance between the two,
or the arc of the great circle intercepts between the two points, which
is what Eratosthenes intended to measure, amounts to only 453 miles or 4,530
stades. Eratosthenes, therefore, in fixing the length of this arc at 5,000
stades, was 470 beyond the truth. But this was not all. The difference
in latitude between Alexandria and Syene really amounts to only 7°
5', so that the direct distance between the two cities, supposing them to
have been really situated on the same meridian (as Eratosthenes assumed
them to be) would not have exceeded 4,25 miles or 4,250 stades, instead
of 5,000. His arc was therefore in reality 750 stades too long.
It is remarkable that while the terrestrial measurement was thus grossly
inaccurate, the observation of latitude as deduced from the gnomon at Alexandria
was a very fair approximation to the truth: a fiftieth part of a great circle
being equivalent to an arc of 7°12', thus exceeding by about 7' only
the true interval between Alexandria and Syene, while falling short
of that between Alexandria and the real Tropic by about 30' or half a degree.
It appears indeed almost certain that Eratosthenes himself was aware of
the imperfection of his data, and regarded the result of his calculation
only as an approximation to the truth. Hence, as mentioned above, he felt
himself at liberty to add 2,000 stades to the 250,000 obtained by his process,
in order to have a number that would be readily divisible into sixty parts,
or into degrees of 360 to a great circle.
After all it must be admitted that the calculation of Eratosthenes, considering
the disadvantages under which he labored, came surprisingly near the truth.
His measurement of 250,000 stades (the immediate result of his calculation)
would be equivalent to 25,000 geographical miles, while the actual circumference
of the earth at the equator falls very little short of 25,000 English
miles. The error in excess therefore amounted to less than one-seventh
part of the whole.
Once the value of 252,000 stades was accepted, it was feasible also
to work out the circumference of any parallel circle. Thus Eratosthenes
calculated that the parallel at Rhodes, 36°N., was under 200,000 stades
in circumference. To obtain the equivalent in stades of one degree of latitude
he had only to divide by 360, i.e., 700 stades; to obtain the equivalent
of one degree of longitude at Rhodes he could divide, say, 195,000 stades
by 360, i.e., 541.67 stades. Thus was established the basis of a
fairly accurate system of coordinates for any sectional mapping of the Mediterranean
based upon the Rhodes parallel.
Having thus laid the foundation of what has been called in modern times
"geodesy" - the determination of the figure and dimensions of
the earth, considered in its entirety, as a part of the system of the universe,
Eratosthenes next proceeded to consider that portion of it which was in
his time geographically known, or supposed to be inhabited. And here it
must be observed that the relation between the habitable world, which was
alone regarded as coming within the scope of the geographer (properly so
called), and the terrestrial globe itself, was, in the days of Eratosthenes,
and even long afterwards, a very different one from that which we now conceive
as subsisting between them. Ever since the discoveries of the great Portuguese
and Spanish navigators in the 15th and 16th centuries opened out to us new
continents, and extensions of those already known, far beyond anything that
had previously been suspected or imagined, men have been accustomed to regard
the "map of the world" as comprising the whole surface of the
globe, and including both the eastern and western hemispheres, while towards
the north and south it is capable of indefinite extension, till it should
reach the poles, and is in fact continually receiving fresh accessions.
With the Greek geographers on the contrary, from Eratosthenes to Strabo,
the known or habitable world was conceived as a definite and limited portion
of the earth's surface, situated wholly within the northern hemisphere,
and comprised within about a third of the extent of that section. Towards
the north and south a was conceived that the excessive cold in the one case,
and the intolerable heat in the other, rendered those regions uninhabitable,
and even inaccessible to man. That there might be inhabitants of the southern
hemisphere beyond the torrid zone, or that unknown lands might exist within
the boundless and trackless ocean that was supposed to extend around two-thirds
of the globe from west to east, was admitted to be theoretically possible,
but was treated as mere matter of idle speculation, much as we might at
the present day regard the question of the inhabitants on Mars.
In his Geographica Eratosthenes discussed the best method of drawing
a map of the inhabited area of the earth as known. The first task of the
geographer therefore, according to the notions then prevailing, was to determine
the limits and dimensions of the map of the world which was to form the
subject of his special investigations. This question, which was taken up
by Eratosthenes at the beginning of his second book, had already been considered
by several previous writers, who had arrived at very different results.
On one point indeed they were all agreed, that the length of the habitable
world, from west to east, greatly exceeded as breadth, from north to south.
Democritus, two centuries before Eratosthenes, had asserted that it was
half as long again as a was broad, and this view was adopted by Dicæarchus,
though recent discoveries had in his day materially extended the knowledge
of its eastern portions. The astronomer Eudoxus on the other hand maintained
that the length was double the breadth; Eratosthenes went a step farther
and determined the length to be more than double the breadth, a statement
which continued to be received by subsequent geographers for more than three
centuries as an established fact. According to his calculation the length
of the known world from the Atlantic to the Eastern Ocean amounted
to 74,000 stades, while as breadth from the parallel of the Cinnamon
Country [Ethiopia/Somaliland] to that of Thule [Iceland ?] did
not exceed 38,000 stades.
Therefore, as with earlier map construction, the length of the oikumene
greatly exceeds the width, though by what proportion depends on how much
of the northern, eastern and southern extremities was regarded as inhabited.
It is clear from Strabo that Eratosthenes used an orthogonal projection.
Rather than a rectangle, he thought of the oikumene as tapering off at each
end of its length, like a chlamys [short Greek mantle]. Moreover
Strabo tells us that to the above total of 74,000 stades Eratosthenes,
using another mathematical ploy, added 2,000 at each end, to prevent the
width being more than half the length. On the parallel of Rhodes, this total
of 78,000 stades corresponds to about 140° longitude, which is
roughly the distance from Korea to the west coat of Spain.
As approximations to sizes and shapes of parts of the world, Eratosthenes
first divided the inhabited world by a line stretching from the Pillars
of Hercules [Straits of Gibraltar] to the Taurus Mountains and
beyond, then subdivided each of these two sections into a number of irregular
shapes, or sphragides, which literally meant 'an official seal' and
later was extended to represent a plot of land numbered by a government
surveyor, then by extrapolation to a numbered area on a map. India he suggested
drawing as a rhomboid, Ariana [the eastern part of the Persian Empire]
as approximating a parallelogram. We do not know the total number of sphragides
and have shapes recorded only for some. Taprobana Island, a misplaced
Ceylon/Sri Lanka, and the short-cutting of Africa and India in the south
were the result of the misconception that the equatorial waters were too
hot to be navigated.
Eratosthenes undoubtedly conceived, in accordance with the prevalent belief
in his day, that the Ocean was found immediately to the east of India, and
that the Ganges flowed directly into it. Just to the north of the Ganges
the great mountain chain of Imaus, which he regarded as the continuation
of the Indian Caucasus and the Taurus, descended (according
to his ideas) to the shores of the Eastern Ocean; and he appears
to have given the name of Tarnarus to the headland which formed the
termination of this great range. From that point he supposed the coast to
trend away towards the north-west, so as to surround the great unknown tracts
of Scythia on the north, but sending in a deep inlet to the south
which formed the Caspian Sea.
Of the northern shores of Asia or Europe he had really no more knowledge
than Herodotus, but, unlike that historian, he assumed the fact that both
continents were bounded by the Ocean on the north; a fact which is undoubtedly
true, but in a sense so widely different from that supposed by Eratosthenes
that a can hardly be held as justifying his theory. In fact the conclusion
of Eratosthenes was mainly based upon the erroneous belief that the Caspian
communicated with the Ocean to the north in the same manner that the Persian
Gulf did to the south; a view which was adopted by all geographers for a
period of three centuries, on the authority of Patrocles.
It was doubtless from the same authority that Eratosthenes derived his statement
as to the dimensions of the Caspian Sea, as well as that concerning the
outflow into it of the rivers Oxus and Iaxartes, which he
asserts "... was well known to the Greeks". Yet the erroneous
idea of its communication with the Ocean to the north sufficiently shows
how questionable the information possessed by the Greeks really was.
His ideas of the geographical position and configuration of India were also
in great measure erroneous. As mentioned above, he conceived it to be of
a rhomboidal form, which may be regarded as a rough approximation to the
truth, and he even knew that the two sides which enclosed the southern extremity
were longer than the other two. But as he supposed the range of Imaus that
bounded the country to the north to have its direction from west to east,
while the Indus flowed from north to south, he was obliged to shift around
the position of his rhomb, so as to bring the other two sides approximately
parallel to the two thus assumed. Hence he conceived the projecting angle
of India to have a direction towards the south-east instead of the south,
and even supposed it to advance farther towards the east than the mouth
of the Ganges. He appears in fact to have obtained, probably from the information
collected by Patrocles, a correct general idea of the great projection of
India in a southerly direction towards Cape Comorin, but was unable to reconcile
this with his previously conceived notions as to its western and northern
boundaries, and was thus constrained altogether to distort its position
in order to make it agree with what he regarded as established conclusions.
It was doubtless from the same source that he had learned the name of the
Coniaci, as the people inhabiting this southernmost point of India; a name
which hence forward became generally received, with slight modifications,
by ancient geographers.
Physical geography, in the modern sense of the term, was still quite in
its infancy in the days of Eratosthenes, and it cannot be said that he did
much to impart to it a scientific character. In treating the mountain chains
of Asia as one continuous range, to which he applied the name of Taurus,
he may be regarded as having made a first attempt, however crude, at that
systematic description of mountain ranges to which we now give the name
of orography. He also arrived at a sound conclusion concerning the
causes of the inundation of the Nile, a subject that must naturally have
engaged the attention of a geographer resident in Egypt. On the other hand
he stated a strange hypothesis, that the surplus waters of the Euphrates
were carried by subterranean channels to Coele, Syria, and thence again
underground so as to feed the streams which broke out near Rhinocorura
and Mount Casius.
Eratosthenes also adopted, and apparently developed at considerable length,
an idea first suggested by the physical philosopher Strato, that the Mediterranean
and the Euxine [Black] Seas had originally no outlet, and stood in
consequence at a much higher level, but that they had burst the barriers
that confined them, and thus given rise to the Straits of the Bosphorus,
the Hellespont and that of the columns. In proof of this theory he
alleged the presence of marine shells far inland in Libya, especially
near the temple of Jupiter Ammon, and on the road leading to it, as well
as the deposits and springs of salt that were also found in the Libyan
deserts.
This map of the known world was a very striking achievement and may be considered
to be the first really scientific Greek map. Although the dimensions are
not known exactly, as it was presented to the Egyptian court a may be assumed
to have been fairly large. It must have been drawn as closely as possible
to scale, and its influence on subsequent Greek and Roman cartography was
tremendous. Indeed, with Ptolemy's inaccurate alterations to the overall
dimensions of the world and the oikumene, it can be said to have
affected world maps right down to the Age of Discovery.
LOCATION: (this map only exists as reconstruction)
REFERENCES:
Bagrow, L., History of Cartography, p. 33.
*Bricker, C., Landmarks in Mapmaking, p. 13.
*Brown, L.A.,The Story of Maps, p. 51.
*Bunbury, E., History of Ancient Geography, pp. 618-660.
*Dilke, O.A.W., Greek and Roman Maps, pp. 33.
Harley, J.B., The History of Cartography, Volume One, pp. 154-57,162, 381.
Raisz, E., General Cartography, p. 9.
Thrower, N.J.W., Maps and Man, p. 17.
*illustrated