170 MATHEMATICAL GEOGRAPHY. [CHAP.
the earth amounted to 300,000 stadia, or 30,000 miles1. The
roughly approximate character of the data for this calculation,
in respect both of the points determined in the heavens, and
of the estimate of distances on the earth's surface, a portion
of which had to be calculated by sea from the reports of
navigators, necessarily involved considerable inaccuracy in the
result It is not improbable that this observation is to be
attributed to Aristotle's pupil, Dicaearchus—whose importance for
geography is shewn by his being enumerated among the greatest
masters of that science "by "Strabo at the commencement of his
work3—but it is certainly later than the time of Aristotle, since
the city of Lysimachia was not founded until 309 B.C.
The method of investigation which Eratosthenes pursued,
though less simple than this, was one which
E^stiTenes guaranteed more accurate results. The gnomon
which he used as the instrument for his observa-
tions was an upright staff set in the midst of a scaphe or bowl,
which was so arranged as to correspond to the celestial hemi-
sphere, only inverted, and was marked with lines like a dial. By
means of this he discovered that, at Alexandria at the summer
solstice, the shadow of the gnomon at midday measured one-
fiftieth part of the meridian—i.e. of a great circle of the heavens,
as measured on the scaphe. He assumes at starting the following
points—(i) that all the sun's rays fall to the earth parallel to
one another; (2) that when one straight line falls on two parallel
straight lines, the alternate angles are equal; (3) that, if arcs of
different circles subtend equal angles at the centre, they bear the
same proportion to the whole circumference of the circles of which
they are parts; so that, if one of them, for instance, is a tenth
part.of its circle, the same will be the case with the others.
He also takes it as proved that Syene and Alexandria are on the
same meridian, and that the distance between them is 5,000
stadia. He then proceeds to argue as follows. In Syene (J?),
which was regarded by the ancients as lying under the tropic,
at the summer solstice a ray of the sun (AE) when on the
meridian, falling on the point of the gnomon, would coincide
1 Berger, Geschichte der Erdkunde, Pt. a, pp. 45, 46.
3 Ibid., Pt 3, pp, vii. and 44 ; Strabo, r. i. i.