A history of Greek mathematics - Wilbourhall.org

300 HERON OF ALEXANDRIA
Pappus goes on to say that he will give four solutions, one
of which is his own ; the first, second, and third he describes
as those of Eratosthenes, Nicomedes and Heron. But in the
earlier sentence he mentions Philon along with Heron, and we
know from Eutocius that Heron's solution is practically the
same as Philon's. Hence we may conclude that by the third
solution Pappus really meant Philon's, and that he only mentioned
Heron's Mechanics because it was a convenient place in
which to find the same solution.
Another argument has been based on the fact that the
extracts from Heron's Mechanics given at the end of Pappus's
Book VIII, as we have it, are introduced by the author with
a complaint that the copies of Heron's works in which he
found them were in many respects corrupt, having lost both
beginning and end. 1 But the extracts appear to have been
added, not by Pappus, but by some later writer, and the
argument accordingly falls to the ground.
The limits of date being then, say, 150 B.C. to A. D* 250, our
only course is to try to define, as well as possible, the relation
in time between Heron and the other mathematicians who
come, roughly, within the same limits.
This method has led
one of the most recent writers on the subject (Tittel 2 ) to
place Heron not much later than 100 B.C., while another, 3
relying almost entirely on a comparison between passages in
Ptolemy and Heron, arrives at the very different conclusion
that Heron was later than Ptolemy and belonged in fact to
the second century a.d.
In view of the difference between these results, it will be
convenient to summarize the evidence relied on to
establish
the earlier date, and to consider how far it is or is not conclusive
against the later. We begin with the relation of
Heron to Philon. Philon is supposed to come not more than
a generation later than Ctesibius, because it would appear that
machines for throwing projectiles constructed by Ctesibius
and Philon respectively were both available at one time for
inspection by experts on the subject 4 ;
it is inferred that
1
Pappus, viii, p. 1116. 4-7.
2 Art. ' Heron von Alexandreia' in Pauly-Wissowa's Real-Encyclopddie
dei class. Altertumstvissenschaft, vol. 8. 1, 1912.
3
4
I. Hammer-Jensen in Hermes, vol. 48, 1913, pp. 224-35.
Philon, Mech. Spit, iv, pp. 68. 1, 72. 36.