Erato'sthenes
（
Ἐρατοσθένης), of Cyrene, was, according to Suidas, the son of Aglaus, according to others, the son of Ambrosius, and was born B. C. 276.
He was taught by Ariston of Chius, the philosopher, Lysanias of Cyrene, the grammarian, and Callimachus, the poet.
He left Athens at the invitation of Ptolemy Evergetes, who placed him over the library at Alexandria. Here he continued till the reign of Ptolemy Epiphanes.
He died at the age of eighty, about B. C. 196, of voluntary starvation, having lost his sight, and being tired of life.
He was a man of very extensive learning : we shall first speak of him as a geometer and astronomer.
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
We 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
1 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); 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
2 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.]
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
All 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.
Another 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.)
Another 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.
Further Information
For more complete lists of the works attributed to Eratosthenes, see the
Eratosthenica of Bernhardy.
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