A history of Greek mathematics - Wilbourhall.org

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108 ERATOSTHENES
out of 83 contained in the whole meridian circle'. 1 The
mean of Ptolemy's estimates, 4 7° 42' 30", is of course nearly
ll/83rds of 360°. It is consistent with Ptolemy's language
to suppose that Eratosthenes adhered to the value of the
obliquity of the ecliptic discovered before Euclid's time,
namely 24°, and Hipparchus does, in his extant Commentary
on the Phaenomena of Aratus and Eudoxus, say that the
summer tropic is very nearly 24° north of the equator'.
'
The Doxographi state that Eratosthenes estimated the
distance of the moon from the earth at 780,000 stades and
the distance of the sun from the earth at 804,000,000 stades
(the versions of Stobaeus and Joannes Lydus admit 4,080,000
as an alternative for the latter figure, but this obviously
cannot be right). Macrobius 2 says that Eratosthenes made
the 'measure' of the sun to be 27 times that of the earth.
It is not certain whether measure means ' solid content ' or
'
diameter ' in this case ; the other figures on record make the
former more probable, in which case the diameter of the sun
would be three times that of the earth. Macrobius also tells
us that Eratosthenes's estimates of the distances of the sun
and moon were obtained by means of lunar eclipses.
Another observation by Eratosthenes, namely that at Syene
(which is under the summer tropic) and throughout a circle
round it with a radius of 300 stades the upright gnomon
throws no shadow at noon, was afterwards made use of by
Posidonius in his calculation of the size of the sun. Assuming
that the circle in which the sun apparently moves round the
earth is 10,000 times the size of a circular section of the earth
through its centre, and combining with this hypothesis the
datum just mentioned, Posidonius arrived at 3,000,000 stades
as the diameter of the sun.
Eratosthenes wrote a poem called Hermes containing a good
deal of descriptive astronomy ; only fragments of this have
survived. The work Catasterismi (literally placings among
'
the stars ') which is extant can hardly be genuine in the form
in which it has reached us ; it goes back, however, to a genuine
work by Eratosthenes which apparently bore the same name
alternatively it is alluded to as KardXoyoi or by the general
1
2
Ptolemy, Syntaxis, i. 12, pp. 67. 22-68. 6.
Macrobius, In Somn. Scip. i. 20. 9.