Eratosthĕnes
（Ἐρατοσθένης). A distinguished contemporary of Archimedes, born at Cyrené, B.C. 276. He possessed a variety of talents seldom united in the same individual. His mathematical, astronomical, and geographical labours are those which have rescued his name from oblivion, though he was, besides, famous for his athletic prowess. The Alexandrian school of sciences, which flourished under the first Ptolemies, had already produced Timochares and Aristyllus; and Eratosthenes had not only the advantages arising from the instruments and observations of his predecessors, but the great Alexandrian library, which probably contained all the Phœnician, Chaldaic, Egyptian, and Greek learning of the time, was intrusted to his superintendence by the third Ptolemy (Euergetes), who had invited him to Alexandria.The only work attributed to Eratosthenes which has come down to us entire is entitled Καταστερισμοί, and is merely a catalogue of the names of forty-four constellations, and the situations in each constellation of the principal stars, of which he enumerates nearly five hundred, but without one reference to astronomical measurement. We find Hipparchus quoted in it, and mention made of the motion of the pole, that of the polar star having been recognized by Pytheas. These circumstances, taken in conjunction with the vagueness of the descriptions, render its genuineness extremely doubtful.
If Eratosthenes be really the author of the Καταστερισμοί, it must have been composed merely as a vade mecum, for we find him engaged in astronomical researches far more exact and more worthy of his genius. By his observations he determined that the distance between the tropics, that is, twice the obliquity of the ecliptic, was 11/83 of an entire circumference, or 47¡ 42' 39", which makes the obliquity to be 23¡ 51' 19.5", nearly the same as that supposed by Hipparchus and Ptolemy. As the means of observation were at that time very imperfect, the instruments divided only to intervals of 10', and as corrections for the greater refraction at the winter solstice, for the diameter of the solar disc, etc., were then unknown, we must regard this conclusion as highly creditable to Eratosthenes. His next achievement was to measure the circumference of the earth. He knew that at Syené the sun was vertical at noon in the summer solstice; while at Alexandria, at the same moment, it was below the zenith by the fiftieth part of a circumference: the two places are nearly on the same meridian (error 2¡). Neglecting the solar parallax, he concluded that the distance from Alexandria to Syené is the fiftieth part of the circumference of the earth; this distance he estimated at five thousand stadia, which gives two hundred and fifty thousand stadia for the circumference. Thus Eratosthenes has the merit of pointing out a method for finding the circumference of the earth. But his data were not sufficiently exact, nor had he the means of measuring the distance from Alexandria to Syené with sufficient precision.
Eratosthenes has been called a poet, and Scaliger, in his commentary on Manilius, gives some fragments of a poem attributed to him, entitled Ἑρμῆς, one of which is a description of the terrestrial zones. It is not improbable that these are authentic.
That Eratosthenes was an excellent geometrician we can not doubt, from his still extant solution of the problem of two mean proportionals, preserved by Theon , and a lost treatise quoted by Pappus, De Locis ad Medietates.
Eratosthenes appears to have been one of the first who attempted to form a system of geography. His work on this subject, entitled Γεωγραφικά (Geographica), was divided into three books. The first contained a history of geography, a critical notice of the authorities used by him, and the elements of physical geography. The second book treated of mathematical geography. The third contained the political or historical geography of the then known world. The whole work was accompanied with a map.
Eratosthenes also busied himself with chronology, and suggested the Julian calendar, in which every fourth year has 366 days. Some remarks on his Greek chronology will be found in Clinton's Fasti Hellenici (vol. i. pp. 3, 408); and on his list of Theban kings, in Rask's work on the ancient Egyptian chronology (Altona, 1830).
The properties of numbers attracted the attention of philosophers from the earliest period, and Eratosthenes also distinguished himself in this branch. He wrote a work on the duplication of the cube—Κύβου Διπλασιασμός—which we only know by a sketch that Eudoxus has given of it, in his treatise on the Sphere and Cylinder of Archimedes. Eratosthenes composed, also, another work in this department, entitled Κόσκινον, or “the Sieve,” the object of which was to separate prime from composite numbers. Eratosthenes arrived at the age of eighty years, and then, becoming weary of life, died by voluntary starvation (B.C. 196). The best editions of the Καταστερισμοί are that of Schaubach, with notes by Heyne (Göttingen, 1795), and that of Matthiae, in his Aratus (Frankfurt, 1817). The fragments of Eratosthenes have been collected by Bernhardy in his work Eratosthenica (Berlin, 1822), and the poetical remains separately by Hiller (Leipzig, 1872). See, also, Berger, Die geographischen Fragmente des Eratosthenes (Leipzig, 1880).