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August 16    Scripture

People - Ancient Greece: Eratosthenes
Ancient Greek mathematician, elegiac poet, athlete, geographer, astronomer, and music theorist.

Eratosthĕnes in Harpers Dictionary of Classical Antiquities (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).
http://tiny.cc/abebv


Eratosthenes in Wikipedia Eratosthenes of Cyrene (Ancient Greek: Ἐρατοσθένης, IPA: /eratostʰénɛːs/; English: /ɛrəˈtɒsθəniːz/; c. 276 BC[1] – c. 195 BC[2]) was a Greek mathematician, elegiac poet, athlete, geographer, astronomer, and music theorist. He was the first person to use the word "geography" and invented the discipline of geography as we understand it.[3] He invented a system of latitude and longitude. He was the first person to calculate the circumference of the earth by using a measuring system using stades, or the length of stadiums during that time period (with remarkable accuracy). He was the first person to prove that the Earth was round. He was the first to calculate the tilt of the Earth's axis (also with remarkable accuracy). He may also have accurately calculated the distance from the earth to the sun and invented the leap day.[4] He also created a map of the world based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy. According to an entry[5] in the Suda (a 10th century reference), his contemporaries nicknamed him beta, from the second letter of the Greek alphabet, because he supposedly proved himself to be the second best in the world in almost every field.[6] Life Eratosthenes was born in Cyrene (in modern-day Libya). He was the third chief librarian of the Great Library of Alexandria, the center of science and learning in the ancient world, and died in the capital of Ptolemaic Egypt. Eratosthenes studied in Alexandria, and claimed to have also studied for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the second librarian, Apollonius of Rhodes, in that post.[7] He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies, Cleomedes credited him with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the sun at noon on the summer solstice in Alexandria and on Elephantine Island near Syene (now Aswan, Egypt). Eratosthenes criticized Aristotle for arguing that humanity was divided into Greeks and barbarians, and that the Greeks should keep themselves racially pure, believing there was good and bad in every nation.[8] By 195 B.C, Eratosthenes became blind. He died in 194 B.C, at the age of 80–82. Eratosthenes' measurement of the earth's circumference Eratosthenes calculated the circumference of the earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun would be 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the meridian arc distance from Alexandria to Syene must be 1/50 of the total circumference of the earth. His estimated distance between the cities was 5000 stadia (about 500 geographical miles or 800 km) by estimating the time that he had taken to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m,[9] which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion"[10] of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%.[11] Although Eratosthenes' method was well founded, the accuracy of his calculation was limited.[citation needed] The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is slightly north of the Tropic of Cancer, is not directly south of Alexandria, and the sun appears as a disk located at a finite distance from the earth instead of as a point source of light at an infinite distance.[citation needed] There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable, especially for travel along the non-linear Nile which was traveled primarily by boat. Given the margin of error for each of these aspects of his calculation, the accuracy of Eratosthenes' size of the earth is surprising.[citation needed] Eratosthenes' experiment was highly regarded at the time, and his estimate of the earth’s size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later. Other astronomical distances Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the sun to be "σταδίων μυριάδας τετρακοσίας και οκτωκισμυρίας" (literally "of stadia myriads 400 and 80,000") and the distance to the moon to be 780,000 stadia. The expression for the distance to the sun has been translated either as 4,080,000 stadia (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974–1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad. This testimony of Eusebius is dismissed by the scholarly Dictionary of Scientific Biography. It is true that the distance Eusebius quotes for the moon is much too low (about 144,000 km) and Eratosthenes should have been able to do much better than this since he knew the size of the earth and Aristarchus of Samos had already found[citation needed] the ratio of the moon's distance to the size of the earth. But if what Eusebius wrote was pure fiction, then it is difficult to explain the fact that, using the Greek, or Olympic, stadium of 185 m, the figure of 804 million stadia that he quotes for the distance to the sun comes to 149 million kilometres. The difference between this and the modern accepted value is less than 1%.[12] Scribal errors in copying the numbers, either of Eusebius' text or of the text that Eusebius read, are probably responsible. The smaller of the foregoing two readings of Eusebius (4,080,000 stadia) turns out to be exactly 100 times the terrestrial radius (40,800 stadia) implicit in Eratosthenes' Nile map and given in the 1982 paper by Rawlins (p. 212) that analysed this map (see Further Reading). Greek scholars such as Archimedes and Posidonius normally expressed the sun's distance in powers of ten times the Earth's radius. The Nile map – Eusebius consistency is developed in a 2008 Rawlins paper. The data would make Eratosthenes' universe the smallest known from the Hellenistic era's height, and made the sun smaller than the earth. His indefensible lunar distance would require the moon to go retrograde among the stars every day for observers in tropical or Mediterranean latitudes, and would predict that half moons occur roughly 10° from quadrature. The Eusebius-confirmed 1982 paper's empirical Eratosthenes circumference (256,000 stadia instead of 250,000 or 252,000 as previously thought) is 19% too high. But the 2008 paper notes that the theory that atmospheric refraction exaggerated his measurement (a theory originally proposed in the 1982 paper, applied to either mountaintop dip or lighthouse visibility) is thus bolstered as the explanation of Eratosthenes' error. This is because accurately measuring the visibility distance of the Alexandria lighthouse (then world's tallest, built at Eratosthenes' location and during his time) and computing the Earth's size from that should have given a result 20% high from refraction, very close to his actual 19% error. The 2008 paper wonders if the 40,800 stadia estimate originated with Sostratus of Cnidus (who designed the lighthouse), and offers a reconstructive speculation that the lighthouse was about 93 meters high, which is much below previous suppositions. Prime numbers Eratosthenes also proposed a simple algorithm for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes. Works * Περὶ τῆς ἀναμετρήσεως τῆς γῆς (On the Measurement of the Earth)[13] (lost, summarized by Cleomedes) * Geographica (lost, criticized by Strabo) * Arsinoe (a memoir of queen Arsinoe; lost; quoted by Athenaeus in the Deipnosophistae) * A fragmentary collection of Hellenistic myths about the constellations, called Catasterismi (Katasterismoi), was attributed to Eratosthenes, perhaps to add to its credibility. Named after Eratosthenes * Eratosthenes (crater) on the moon * Eratosthenian period in the lunar geologic timescale * Eratosthenes Seamount in the eastern Mediterranean Sea
http://en.wikipedia.org/wiki/Eratosthenes


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