As Geometer and Astronomer
It is supposed that Eratosthenes suggested to Ptolemy Evergetes the construction of the
large armillae or fixed circular instruments which were long in use at
Alexandria : but only because it is difficult to imagine to whom else they are to be
assigned; for Ptolemy (the astronomer), though he mentions them, and incidentally their
antiquity, does not state to whom they were due. In these circles each degree was divided
into six parts. We know of no observations of Eratosthenes in which they were probably
employed, except those which led him to the obliquity of the ecliptic, which lie must have
made to be 23° 51' 20''; for he states the distance of the tropics to be eleven times the
eighty-third part of the circumference. This was a good observation for the time : Ptolemy
(the astronomer) was content with it, and, according to him, Hipparchus used no other. Of his
measure of the earth we shall presently speak. According to Nicomachus, he was the inventor
of the κόσκινον or Cribrum
Arithmeticum, as it has since been called, being the well known method of detecting the
prime numbers by writing down all odd numbers which do net end with 5. and stribing ent successively the multiples of each, one after the other, so that only prime numbers
remain.
Works
Καταστερισμοί (
CatasterismiWe still possess under the name of Eratosthenes a work, entitled
Καταστερισμοί, giving a slight account of the constellations, their fabulous
history, and the stars in them. It is, however, acknowledged on all hands that this is not
a work of Eratosthenes. It has been shewn by Bernhardy in his
Eratosthenica (p. 110, &c., Berlin, 1822, 8vo.) to be a miserable compilation
made by some Greek grammarian from the
Poeticon Astronomicon of Hyginus.
Editions
This book was printed (Gr.) in Dr. Fell's, or the Oxford, edition of Aratus, 1762,
8vo.; again (Gr. Lat.) by Thomas Gale, in the Opuscula Physica et
Ethica, Amsterdam, 1688, 8vo.; also by Schaubach, with notes by
Heyne, Göttingen, 1795, 8vo.; also by F. K. Matthiae, in his Aratus, Frankfort, 1817, 8vo., and more recently by
A. Westermann, in his Scriptores Historiae poeticae
Graeci, pp. 239-267.
Short Comment on Aratus
The short comment on Aratus, attributed to Eratosthenes, and first printed by Peter
Victorius, and afterwards by Petavius in his
Uranologion
(1630, fol.), is also named in the title of both as being attributed to Hipparchus as well
as to Eratosthenes. Petavius remarks (says Fabricius) that it can be attributed to neither;
for Hipparchus is mentioned by name, also the month of July, also the barbarous word
ἀλετροπόδιον for Orion, which the more recent Greeks
never used : these reasons do not help each other, for the second shews the work to be
posterior to Eratosthenes, if anything, and the third shows it to be prior. But on looking
into this comment we find that
ἀλετροπόδιον and July
(and also August) are all mentioned in one sentence, which is evidently
* These are the only months mentioned in the comment : Orion, which the
vulgar call ἀλετροπόδιον, first rises in July, and
Procyon in August. It is not stated anywhere else in what month a star first rises, nor is
any other month mentioned at all. Probably some interpolator, subsequent to Augustus,
introduced this sentence rather to fix the astronomical characterof the new named months in his own or his reader's mind, than to give information on the
constellations. It also appears that ἀλετροπόδιον
was the word which was used by the vullgar (ἰδιώταις) for Orion, after July and August had received their imperial
names. an interpolation; and the constellation Orion is frequently mentioned under
that name. But Hipparchus certainly is mentioned.
Letter to Ptolemy
The only other writing of Eratosthenes which remains is a letter to Ptolemy on the
duplication of the cube, for the mechanical performance of which he had contrived an
instrument, of which he seems to contemplate actual use in measuring the contents of
vessels, &c. He seems to say that he has had his method engraved in some temple or
public building, with some verses which lie adds. Eutocius has preserved this letter in his
comment on book ii. prop. 2 of the sphere and cylinder of Archimedes.
Measuring the Magnitude of the Earth
The greatest work of Eratosthenes, and that which must always make his name conspicuous in
scientific history, is the attempt which he made to measure the magnitude of the earth,--in
which he brought forward and used the method which is employed to this day. Whether or no he
was successful cannot be told, as we shall see; but it is not the less true that he was the
originator of the process by which we now know, very nearly indeed, the magnitude of our own
planet. Delambre says that if it were he who advised the erection of the circular instruments
above alluded to, he must be considered as the founder of astronomy : to which it may be
added that he was the founder of geodesy, without any if in the case.
The number of ancient writers who have alluded to this remarkable operation (which seems to
have obtained its full measure of fame) is very great, and we shall not attempt to combine
their remarks or surmises : it is enough to say that the most distinct account, and one of
the earliest, is found in the remaining work of CLEOMEDES.
At Syene, in Upper Egypt, which is supposed to be the same as, or near to, the town of
Assouan (Lat. 24° 10' N., Long. 32° 59' E. of Greenwich), Eratosthenes was told (that
he observed is very doubtful), that deep wells were enlightened to the bottom on the day of
the summer solstice, and that vertical objects cast no shadows. He concluded, therefore, that
Sycne was on the tropic, and its latitude equal to the obliquity of the ecliptic, which, as
we have seen, He had determined : he presumed that it was in the same longitude as
Alexandria, in which he was out about 3°, which is not enough to produce what would at
that time have been a sensible error. By observations made at Alexandria, he determined the
zenith of that place to be distant by the fiftieth part of the circumference from the
solstice, which was equivalent to saying that the arc of the meridian between the two places
is 7° 12'. Cleomedes says that he used the σκάφη, or
hemispherical dial of Berosus, in the determination of this latitude. Delambre rejects the
idea with infinite scorn, and pronounces Cleomedes unworthy of credit; and, indeed, it is not
easy to see why Eratosthenes should have rejected the gnomon and the large circular
instruments, unless, perhaps, for the following reason : There is a sentence of Cleomedes
which seems to imply that the disappearance of the shadows at Syene on the day of the summer
solstice was noticed to take place for 300 stadia every way round Syene. If Eratosthenes took
his report about the phenomenon (and we have no evidence that he went to Syene himself) from
those who could give no better account than this, we may easily understand why he would think
the σκάφη quite accurate enough to observe with at his
own end of the arc, since the other end of it was uncertain by as much as 300 stadia. He
gives 5000 stadia for the distance from Alexandriato Syene, and this round number seems
further to justify us in concluding that he thought the process to be as rough as in truth it
was. Martianus Capella (p. 194) states that he obtained this distance from the measures made
by order of the Ptolemies (which had been commenced by [Alexander](alexander-the-great-bio-1)); this writer then implies that
Eratosthenes did not go to Syene himself.
The result is 250,000 stadia for the circumference of the earth, which Eratosthenes altered
into 252,000, that his result might give an exact number of stadia for the degree, namely,
700; this, of course, should have been 694 4/9. Pliny (Plin. Nat.
2.108) calls this 31,500 Roman miles, and therefore supposes the stadium to be the
eighth part of a Roman mile, or takes for granted that Eratosthenes used the Olympic stadium.
It is likely enough that the Ptolemies naturalized this stadium in Egypt; but, nevertheless,
it is not unlikely that an Egyptian stadium was employed. If we assume the
Olympic stadium (202 1/4 yards), the.degree of Eratosthenes is more than 79 miles, upwards of
10 miles * This is not so much as the error of Fernel's measure, which
so many historians, by assuming him, contrary to his own statement, to have used the
Parisian foot, have supposed to have been, accidentally, very correct. See the Penny
Cyclopaedia, Art. " Weights and Measures." too great. Nothing is known of
any Egyptian stadium. Pliny (l.c.) asserts that Hipparchus, but for what
reason he does not say, wanted to add 25,000 stadia to the circumference as found by
Eratosthenes.
According to Plutarch (de Plac. Phil. 2.31), Eratosthenes made the sun
to be 804 millions of stadia from the earth, and the moon 780,000; according to Macrobius
(in Somn. Scip. 1.20), he made the diameter of the sun to be 27 times
that of the earth. (Weidler, Hist. Astron. ; Fabric. Bibl. Graec. vol. iv. p. 117, &c.; Delambre, Hist. de l'Astron.
Anc. ; Petavius, Uranologion.) [[A. DE
M.](author.A.DE.M)]
Erastosthenes' contributions to Geography
With regard to the other merits of Eratosthenes, we must first of all mention what he did
for geography, which was closely connected with his mathematical pursuits. It was
Eratosthenes who raised geography to the rank of a science; for, previous to his time, it
seems to have consisted, more or less, of a mass of information scattered in books of travel,
descriptions of particular countries, and the like.
Works
ΓεωγραφικάAll these treasures were accessible to Eratosthenes in the libraries of Alexandria; and
he made the most profitable use of them, by collecting the scattered materials, and uniting
them into an organic system of geography in his comprehensive work entitled
Γεωγραφικά, or as it is sometimes, but erroneously, called,
γεωγραφούμενα or
γεωγραφία. (
Strab. i. p.29, ii. p. 67, xv. p.
688; Schol.
ad Apollon. Rhod. 4.259, 284, 310.) It consisted of three
books, the first of which, forming a sort of introduction, contained a critical review of
the labours of his predecessors from the earliest to his own times, and investigations
concerning the form and nature of the earth, which, according to him, was an immovable
globe, on the surface of which traces of a series of great revolutions were still visible.
He conceived that in one of these revolutions the Mediterranean had acquired its present
form; for, according to him, it was at one time a large lake covering portions of the
adjacent countries of Asia and Libya, until a passage was forced open by which it entered
into communication with the ocean in the west. The second book contained what is now called
mathematical geography. His attempt to measure the magnitude of the earth has been spoken
of above. The third book contained the political geography, and gave descriptions of the
various countries, derived from the works of earlier travellers and geographers. In order
to be able to determine the accurate site of each place, he drew a line parallel with the
equator, running from the pillars of Heracles to the extreme east of Asia, and dividing the
whole of the inhabited earth into two halves. Connected with this work was a new map of the
earth, in which towns, mountains, rivers, lakes, and climates were marked according to his
own improved measurements. This important work of Eratosthenes forms an epoch in the
history of ancient geography; but unfortunately it is lost, and all that has survived
consists in fragments quoted by later geographers and historians, such as Polybius, Strabo,
Marcianus, Pliny, and others, who often judge of him unfavourably, and controvert his
statements; while it can be proved that, in a great many passages, they adopt his opinions
without mentioning his name. Marcianus charges Eratosthenes with having copied the
substance of the work of Timosthenes on Ports (
περὶ
Διμένων), to which he added but very little of his own. This charge may be
well-founded, but cannot have diminished the value of the work of Eratosthenes, in which
that of Timosthenes can have formed only a very small portion. It seems to have been the
very overwhelming importance of the geography of Eratosthenes that called forth a number of
opponents, among whom we meet with the names of Polemon, Hipparchus, Polybius, Serapion,
and Marcianus of Heracleia.
Editions
The fragments of this work were first collected by L. Ancher, Diatribe
in Fragm. Geograph. Eratosth., Göttingen, 1770, 4to., and afterwards by G. C.
F. Seidel, Eratosth. Geograph. Fragm. Göttingen, 1789, 8vo. The
best collection is that of Bernhardy in his
Eratosthenica. ἙρμῆςAnother work of a somewhat similar nature, entitled
Ἑρμῆς (perhaps the same as the
Καταστερισμοί mentioned above), was written in verse and treated of the form
of the earth, its temperature, the different zones, the constellations, and the like.
(Bernhardy,
Eratosth. p. 110, &c.)
ἨριγόνηAnother poem, Ἠριγόνη, is mentioned with great
commendation by Longinus. (De Sublim. 33. 5; comp. Schol. ad Hom. Il. 10.29; Bernhardy, l.c. p. 150,
&c.)
As Philosopher, Historian, and Grammarian
Eratosthenes distinguished himself also as a philosopher, historian, and grammarian.
Philosophical Works
Eratosthenes' acquirements as a philosopher are attested by the works which are attributed
to him, though we may not believe that all the philosophical works which bore his name were
really his productions. It is, however, certain that he wrote on subjects of moral
philosophy, e. g. a work Περὶ Ἀγαθῶν
καὶ Κακῶν (Harpocrat. s. v.
ἁρμοσταί; Clem.
Al. Strom. iv. p. 496), another Περὶ Πλούτον καὶ
Πενίας (D. L. 9.66; Plut. Themist. 27), which some believe to have been only a portion of the preceding work,
just as a third Περὶ Ἀλυπίας, which is mentioned by
Suidas. Some other works, on the other hand, such as Περὶ τῶν
κατὰ Φιλοσοφίαν Αἱρέσεων, Μελέται,
and Διάλογοι, are believed to have been erroneously
attributed to him. Athenaeus mentions a work of Eratosthenes entitled
Ἀρσινόη (vii. p. 276),
Epistles (x. p.
418), one
Epistle addressed to the Lacedaemonian Agetor (xi. p. 482),
and lastly, a work called
Ἀρίστων, after his teacher
in philosophy. (vii. p. 281.)
Historical Works
His historical productions are closely connected with his mathematical pursuits. He is
said to have written on the expedition of Alexaxander the Great (Plut. Alex. 3, 31, &c.; Arrian, Arr. Anab. 5.5.3); but the statements quoted from it belonged in
all probability to his geographical or chronological work. Another on the history of the
Galatians (Γαλατικά), of which the 33rd book is quoted
by Stephanus of Byzantium (s. v.
Ὕδρηλα), was undoubtedly the work of another
Eratosthenes. (Schmidt, de Gall. Exped. p. 15, &c.; Bernhardy, l.c. p. 243, &c.) There was, however, a very important chronological
work, entitled
Χρονογραφία or
Χρονογραφιῶν, which was unquestionably the production of our Eratosthenes. In
it the author endeavoured to fix the dates of all the important
events in
literary as well as political history. (Harpocrat.
s. v.
Εὔηνος;
Dionys. A. R.
1.46; Clem. Alex.
Strong. i. p. 145.) This work, of which some
fragments are still extant, formed a comprehensive chronological history, and appears to
have been held in high esteem by the ancients. Apollodorus and Eusebius made great use of
it, and Syncellus (p. 96c.) has preserved from it a list of 38 kings of the Egyptian Thebes.
(Comp. Bernhardy,
l.c. p. 243, &c.) Another work, likewise of a
chronological kind, was the
Ὀλυμπιονῖκαι. (
D. L. 8.51;
Athen. 4.154; Schol.
ad Eurip. Hecub. 569.) It contained a chronological list of the victors in
the Olympic games, and other things connected with them. (Bernhardy, p. 247, &c.)
Grammatical Works
Among his grammatical works we notice that On the Old Attic Comedy
(Περὶ τὴς Ἀρχαίας Κωμῳδίας), sometimes simply
Περὶ Κωμῳδίας, or Κωμῳδιῶν), a very extensive work, of which the twelfth book is quoted. It
contained everything that was necessary to arrive at a perfect understanding of those
poetical productions. In the first part of the work, Eratosthenes appears to have entered
even into discussions concerning the structure of theatres, the whole scenic apparatus, the
actors, their costumes, declamation, and the like; and it is therefore not improbable that
the Ἀρχιτεκτονικός (Schol. ad
Apollon. Rhod. 1.567, 3.232) and σκευογραφικός
(Pollux, 10.1), which are mentioned as separate works, were only portions of the first part
of his work on the Old Comedy. After this general introduction, Eratosthenes discussed the
works of the principal comic poets themselves, such as Aristophanes, Cratinus, Eupolis,
Pherecrates, and others, entering into detailed criticism, and giving explanations both of
their language and the subjects of their comedies. We still possess a considerable number of
fragments of this work (collected in Bernhardy, l.c. pp. 205-237); and
from what he says about Aristophanes, it is evident that his judgment was as sound as his
information was extensive. He is further said to have been engaged in the criticism and
explanation of the Homeric poems, and to have written on the life and productions of that
poet; but nothing certain is known in this respect.