A history of Greek mathematics - Wilbourhall.org

304 HERON OF ALEXANDRIA
And first we will show how we can measure an
Hipparchus.
interval of time by means of the regular efflux of water,
a procedure which was explained by Heron the mechanician
in his treatise on water-clocks.'
Theon of Alexandria has a passage to a similar effect. 1
first says that the most ancient mathematicians contrived
a vessel which would let water flow out uniformly through a
small aperture at the bottom, and then adds at the end, almost
in the same words as Proclus uses, that Heron showed how
this is managed in the first book of his work on waterclocks.
Theon's account is from Pappus's Commentary on
the Syntaxis, and this is also Proclus's source, as is shown by
the fact that Proclus gives a drawing of the water-clock
which appears to have been lost in Theon's transcription from
Pappus, but which Pappus must have reproduced from the
work of Heron. Tittel infers that Heron must have ranked
as one of the more ancient ' ' writers as compared with
Ptolemy. But this again does not seem to be a necessary
inference. No doubt Heron's work was a convenient place to
refer to for a description of a water-clock, but it does not
necessarily follow that Ptolemy was referring to Heron's
clock rather than some earlier form of the same instrument.
An entirely different conclusion from that of Tittel is
reached in the article ' Ptolemaios and Heron ' already alluded
to. 2 The arguments are shortly these. (1) Ptolemy says in
his Geography (c.
He
3) that his predecessors had only been able
to measure the distance between two places (as an arc of a
great circle on the earth's circumference) in the case where
the two places are on the same meridian. He claims that he
himself invented a way of doing this even in the case where
the two places are neither on the same meridian nor on the
same parallel circle, provided that the heights of the pole at
the two places respectively, and the angle between the great
circle
passing through both and the meridian circle through
one of the places, are known. Now Heron in his Dioptra
deals with the problem of measuring the distance between
two places by means of the dioptra, and takes as an example
1
Theon, Comm. on the Syntaxis, Basel, 1538, pp. 261 sq. (quoted in
Proclus, Hypotyposis, ed. Manitius, pp. 309-11).
2
Hammer-Jensen, op. cit.