X^HI 
MENSURATION: HERON OF ALEXANDRIA 
Controversies as to Heron’s date. 
The vexed question of Heron’s date has perhaps called 
forth as much discussion as any doubtful point in the history 
of mathematics. In the early stages of the controversy much 
was made of the supposed relation of Heron to Ctesibius. 
The Belopoe'ica of Heron has, in the' best manuscript, the 
heading "Hpcovos Ktijctl^lov BeXonouKa, and from this, coupled 
with an expression used by an anonymous Byzantine writer 
of the tenth century, o A&Kprjubs KrrjcrifSLos o rov AXe£avSpecos 
"Hpcovos KaQ-qypTrjs, 1 Ctesibius of Ascra, the teacher of Heron 
of Alexandria ’, it was inferred that Heron was a pupil of 
Ctesibius, The question then was, when did Ctesibius live'? 
Martin took him to be a certain barber of that name who 
lived in the time of Ptolemy Euergetes II, that is, Ptolemy VII, 
called Physcon (died 117 b.c.), and who is said to have made 
an improved water-organ 1 ; Martin therefore placed Heron at 
the beginning of the first century (say 126-50) b.c. But 
Philon of Byzantium, who repeatedly mentions Ctesibius by 
name, says that the first mechanicians {Teyvlrou) had the 
great advantage of being under kings who loved fame and 
supported the arts. 2 This description applies much better 
to Ptolemy II Philadelphus (285-247) and Ptolemy III Euer 
getes I (247-222). It is more probable, therefore, that Ctesibius 
was the mechanician Ctesibius who is mentioned by Athenaeus 
as having made an elegant drinking-horn in the time of 
Ptolemy Philadelphus 3 ; a pupil then of Ctesibius would 
probably belong to the end of the third and the beginning of 
the second century b.c. But in truth we cannot safely con 
clude that Heron was an immediate pupil of Ctesibius. The 
Byzantine writer probably only inferred this from the title 
1 Athenaeus, Deipno-Soph. iv. c. 75, p. 174 b-e: cf. Vitruvius, x. 9, 13. 
2 Philon, Meehan. Synt., p. 50. 38, ed. Schone. 
3 Athenaeus, xi. c. 97, p. 497 b-e.