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successively the multiples of each, one after the other, so that only prime numbers remain.
We still possess under the name of Eratosthenes a work, entitled Karao-repier/jof, 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 Eratostlienica (p. 110, &c., Berlin, 1822, 8vo.) to be a miserable compilation made by some Greek grammarian from the Potticon Astronomicon of Hyginus. 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, Gottingen, 1795, 8vo.; also by F. K. Matthiae, in his Aratus, Frankfort, 1817, 8vo., and more recently by A. Westermann, in his Scriptores Historiae poeticae Gfaeci, pp. 239—267. 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 aAerpoTro-Siov 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 shews it to be prior. But on looking into this comment we find that dherpoirotiiov and July (and also August) are all mentioned in one sentence, which is evidently* an interpolation; and the constellation Orion is frequently mentioned under that name. But Hipparchus certainly is mentioned. ' 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 he adds. Eutocius has preserved this letter in his comment on book ii. prop. 2 of the sphere and cylinder of Archimedes.
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 pro-
* These are the only months mentioned in the comment: Orion, which the vulgar call d\€Tpoiro-Sioi', 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 character of the new named months in his own or his reader's mind, than to give information on the constellations. It also appears that d\€Tpoir6<5iov was the word which was used by the vulgar (iSizoTais) for Orion, after July and August had received their imperial names,
cess 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'm 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 cleo-medes.
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 concludedj therefore, that Syene 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 er/ca^r;, 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 aKdtyrj 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 Alexandria to 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 694f. Pliny (H. N. ii. 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.