ERATOSTHENES. 



EKCILLA T ZTJNIOA, ALONSO. 



7M 



promotion of education in Bud and Heidelberg. He had published 

 at the former town in 1565 a work ' De DUorinune Logica et Scientue 

 Demonstrative.' He alao wrote several work* ou medical aoience. 



fEnoh und Qruber, AUgtmeiue Encyclopedic; Adam us, Vita Ger- 

 MMonua Htdieonu*, 107-109.) 



KRATO'STHEXES, a distinguished contemporary of Archimedes, 

 iasaid to have been born at Cyrene in the year B.C. 276. He ponessed 

 a Tariety of talrnU teldom united in the tame individual, but not all 

 in the aame eminent degree ; his mathematical, astronomical, and geo- 

 graphical laboan, are those which hare rescued his name from oblivion. 



The Alexandrian school of science*, which nourished under the first 

 Ptolemies, bad already produced Timoohares and Aristyllus, whose 

 solstidsl observations, made probably by the shadows of a gnomon, 

 and by the armillary circles imitatire of thoee of the celestial vault, 

 retained considerable credit for centuries afterwards, though from 

 these methods of observation they must have been extremely rude 

 and imperfect. 



Eratosthenes had uot only the advantages arising from the instru- 

 ments and observations of his predecessors, but the great Alexandrian 

 library, which probably contained all the Phoenician, Chaldaic, 

 Egyptian, and Greek learning of the time, was entrusted to his 

 superintendence by the third Ptolemy (Euergetes), who invited him 

 to Alexandria ; and we have proof in the scattered fragments which 

 remain to us of this great man. that these advantages were duly 

 cultivated to his own happiness and the progress of infant astronomy. 



The only work attributed to Eratosthenes, which has come down to 

 as entire, is entitled 'Catasterismi,' and is merely a catalogue of the 

 names of forty-four constellations, and the situations in each constella- 

 tion of the principal stars, of which he enumerates nearly five hundred, 

 but without one reference to astronomical measurement: we find 

 Hipparchiis quoted in it, and mention made of the' motion of the pole, 

 that of the polar star having been recognised by Pytheas. These 

 circumstances, taken in conjunction with the vagueness of the 

 description*, render its genuineness extremely doubtful ; at all events, 

 it is a work of little value. It may be seen in the Oxford edition of 

 Aratus,' and was repubUshed by Shaubach, with notes by Heyne 

 (QotL, 1795). A more correct edition of the text was published by 

 K. K. MatthiK, in his edition of ' Aratus' (Frankfurt, 1817, 8vo) ; and 

 by A. Weshrmann, in his ' Scriptores Historic Poeticw Graeci,' pp. 

 839-267. 



If Eratosthenes be really the author of the treatise 'Catasterismi,' 

 it must have been composed merely as a ' vade mecuin,' for we find 

 him engaged in astronomical researches far more exact and more 

 worthy of his genius. By his observations he determined that the 



Uipparchus and Ptolemnjus. A* the means of observation we're at that 

 time very imperfect, the in-tnmieuU divided only to intervals of 10', 

 and correction* for the greater refraction at the winter solstice, for 

 the diameter of the solar disc, &c., then unknown, we must regard 

 thin conclusion as highly creditable to Eratosthenes. 



His next achievement was to measure the circumference of the earth, 

 lie knew that at Syene (now Assouan) the sun was vertical at noon 

 in the summer soUtice ; while at Alexandria, at the same moment, it 

 wa* below the zenith by the fiftieth part of a circumference : the two 

 place* are nearly on the same meridian (error 2) ; neglecting the solar 

 parallax, he concluded that the distance from Alexandria to Syene is 

 the fiftieth part of the circumference of the earth; this distance he 

 JrtimaUd at 5000 stadia, which gives 250,000 stadia for the circum- 

 ference : the following diagram will explain the principle of this 

 admeasurement : 



C the centre of the earth, A Alexandria, Syene, 8 the un, <ZAS 

 b. A of four riRht angle., <A8C the sun's parallax, which is very 

 mall ...< ACS is very nearly = ZAS; therefore distance A*C = ii of 

 circumference of earth. 



Thus Eratosthenes has the merit of pointing out a method for 

 finding the circumference of the earth : but his data were not suffi- 

 ciently exact, nor had he the means of measuring the distance At with 

 sufficient precision. 



Eratosthenes has been called a poet, and Scoliger, in his commentary 

 on Manilius, give* some fragment* of a poem attributed to him, entitled 

 ' Hermes, or de Zonis,' one of which is a description of the terrestrial 

 zones : it is not improbable that these are authentic ; the chronii 1-rs 

 as well as philosophers of all nations, in a state of incipient civilisation, 

 have called in the aid of metre to popularise their labours. Erato*- 

 tbenes is therefore entitled to the name of a versifier rather than a 

 poet, like his precursor Manetho, who wrote 'AToTfAeoTumitcl (effect* 

 or influences), a mixture of astrology and astronomy ; one of whose 

 lines, containing the names of the sun and planets, may be taken a* a 

 specimen : 



Zew'Aprjj Tltupiij MTJKT; KfxWt'HAio; 'Ep/^s. 



The wretched doggrel arising from forcing names, scientific terms, and 

 reasonings into verse, may be judged by some ridiculous productions 

 of the kind in our own language. 



That Eratosthenes was an excellent geometer we cannot doubt, from 

 hi* still extant solution of the problem of two mean proportionals, 

 preserved by Theon, and a lost treatise quoted by Pappus, ' De Loci* 

 ad Medietates,' on which Montucla has offered some conjectures, 

 ' Histoire des Math.,' an. vil, p. 280. 



Eratosthenes appears to have been one of the first who attempted 

 to form a system of geography. His work on this subject, entitled 

 ' Geographic* ' (Vtwypaipucd), was divided into three books. The first 

 book contained a history of geography, a critical notice of the autho- 

 rities used by him, and the elements of physical geography. The 

 second book treated of mathematical geography, and contained the 

 method above explained, by which he determined the earth's circum- 

 ference. The third book contained the political or historical geography, 

 arranged according to the three great divisions of the known globe, 

 Europe, Asia, and Libya. The whole work was accompanied with a 

 map of the known world. The geography of Eratosthenes is lost ; the 

 fragments which remain have been chiefly preserved by Strabo, who 

 was doubtless much indebted to him. 



Eratosthenes also busied himself with chronology. The reader 

 will find some remarks on his Greek chronology in Clinton's ' Fasti 

 Helleuici ;' and on his list of Theban kings, by K, Rusk, in his little 

 work on the ancient Egyptian chronology, German translation, 

 Altona, 1830. 



The properties of numbers attracted the attention of philosophers 

 from the earliest period, and Eratosthenes also distinguished himself 

 in this branch by a work which he denominated K^KKICUI', ' Cril.i urn,' 

 or ' Sieve,' the object of which is to separate prime from composite 

 numbers, a curious memoir ou which was published by Horsley in the 

 'Philosophical Transactions,' 1772. The principle of the method is 

 to reject all the multiples of the primes, tabulating first all the odd 

 numbers ; the multiples of 3 will be found with intervals of two places, 

 those of 5 with intervals of 4, aud by placing a mark over each such 

 multiple, none but prime numbers will remain after this shifting. 

 The same method, which is indeed indirect, but comparatively rapid 

 in application, has been employed by Ladislaus Chernac, in forming a 

 table of primes from 1 to 1,020,000, in a treatise published in 1811 : 

 the following example will explain the method : 



3, 5, 7, 9, 11, 13, 15, 17, 19, 81, 23, 25, 27, 29, 31, 33, 85, 37, 39, 41 , 



43, 45, 47, 49. 



By actually trying this method it will bo seen how readily the 

 composite numbers are marked out, and we may terminate the operation 

 when our commencing number exceeds a third of the last number in 

 the table. 



Eratosthenes arrived at the age of eighty years, aud ultimately 

 becoming weary of life, died by voluntary starvation. (Suidas, 

 ' Eratosthenes.') Montucla, with bia usual naiveUS, says it would 

 have been more philosophical to await death " de pied ferine." 



(Montucla, Jlittoirc del Math., p. 239 ; Dclambre, Uul. de CAilro- 

 nomie Ancienne. p. 86 ; Lalande, MM. Aaron, in art. ; Sententice dr. et 

 Lot. tit I'octii Min., RadtdjAi Wintertoni, Cambridge, 1700 ; Pragma** 

 Or. el Lot., by Shaubach, Qottingen; Aralta, Oxford edition, 1872; 

 Horsley, Traett aud Memoir in Phil. Tratu., 1772; Cataitcritmi, Heyne ; 

 C'riorim Arith., by L. Chernac; Gtograpkicorut* fragmenla, 1787; 

 Eutocius, Commentary on Arckimedet. The edition of the Fragment* 

 of Eratosthenes, by Bernhardy (Berlin, 1822, 8vo), does not contain 

 the ' Catasterismi.' See CLEOUBDH.) 



EKCILLA Y ZUNIGA, ALONSO, the author of the ' Araucana/ 

 an epic poem, and better known out of Spain than many other 

 Spaui*h works of greater merit. Alonso was the third son of a cele- 

 brated lawyer, Fortun Garcia, lord of the castle of Eroilla, and was 

 born at Madrid in 1533. His mother, Doha Leouor de Zuiiiga, 

 became a widow the following year, and being appointed 'guard* 

 dauias ' to the wife of Charles V., noon obtained far her son a place 

 among the page* of the prince of Asturias, afterwards Philip II. At 

 the age of fourteen, Erciila attended that prince through Italy, 

 Germany, and the Netherlands, in a pompous progress of which the 



