Okytokion Huxley, George Greek, Roman and Byzantine Studies; Fall 1967; 8, 3; ProQuest pg. 203

Okytokion 

George Huxley 

THE WORK of Apollonius of Perga called Okytokion is named in 
but one of the geometer's fragments. Eutocius,1 commenting 
on estimates of the ratio of a circle's circumference to its dia­

meter, states that Apollonius gave a different value from that of 
Archimedes, one that was more accurate. A second fragment 2 was 
ascribed to the Okytokion by Heiberg. It comes from a preface and in­
vokes the Muses to sing the praises of Artemis. 

, APTEILLOOS KA€LT€ KpaTos ;goxov EVVEa KOiJpat. 

Pappus comments T6 oe KA€LT/. ~YJOLV aJlT~ TOiJ tnr0p-vrl0aT€3 in repeat­
ing the verse. I am here concerned only with the title Okytokion. 

It has long been recognized that, because dJKVTOKLOJI means 'quick­
delivery', a work so named was obviously intended to give a means of 
yielding large products by rapid multiplication; as an example of the 
method Apollonius gave the product of all the letter-numbers in his 
hexameter in the preface. But it has not been noticed, so far as I know, 
that the mention of Artemis in the verse and the name Okytokion both 
refer to lunar calculations. For dJKVToKOS is an epithet of Gf:A~JI1}, the 
moon (that is, Artemis). Thus we find her so named in a fragment of 
Timotheus of Miletus :4 

'" \ I '\', ow KvaV€OV 7TO/\OV aOTpwv 

oLa T'dJKVToKotO O€Aavas. 

The purpose of the Okytokion was, then, astronomical. Nor is this 
surprising, for though Apollonius is chiefly known today for his work 

1 Eutoc. In Archim.dimens.circ., in Archimedes ed. J. L. Heiberg III (BT, Leipzig 1915) 
p.258, 16ff. 

2 Pappus 2.22, ed. F. Hultsch I (Berlin 1876) p.24, 25ff (=Apollonius Pergaeus ed. Heiberg 
II [BT, Leipzig 1893] p.124, fr.37). 

3 Apollonius frA9 Heiberg, adfin. (=Pappus 2.17, ed. Hultsch p.20, 2). For {'1TolLvrjuan, 

vILvrjuaT€ gives better sense with KA€LT€. 

4 fr.27, D. L. Page, Poetae Melici Graeci (Oxford 1962) pA18. See also Schwenn, RE 2A.1 
(1921) 1139 S.V. SELENE. 

203 



204 OKYTOKION 

on conics, by his contemporaries he was called Epsilon, E, because of 
the likeness of that letter to the figure of the moon, concerning which 
he made accurate researches, as Ptolemaeus Chennus reported.s 
Whether or not Apollonius' estimate of the moon's distance was given 
in the Okytokion we do not know-the alleged value, 5,000,000 stades, 
is anyway almost certainly corrupt in the texts.6 Nor do we know 
that the tables of Apollonius for the moon and for lunar and solar 
eclipses 7 were prepared with the help of, or were given in, the 
Okytokion. Nor is the value of '1T used in that work recorded; all we 
are told 8 is that it was more accurate than the estimate, 3t > '1T > 3ti 
of Archimedes, who himself gave a closer estimate in his Plinthides 
and Cylinders.s More accurate Indian estimates by Kryabhana (fl. ca. 
A.D. 500) and Bhaskara,lo though they may well come from Greek 
sources, do not help here. What is clear, however, is that the Okytokion 
was not simply a work on rapid computation; it was, as the title and 
the preface were meant to show, an aid to astronomical reckoning. 

THE QUEEN'S UNIVERSITY OF BELFAST 

February, 1967 

5 Photius, Bibliotheca ed. Bekker p.151b, 18-21. See also O. Neugebauer, "The Equivalence 
of Eccentric and Epicyclic Motion according to Apollonius," Scripta Mathematica 24 (1959) 5. 

6 Hippol. Haer., in Hippolytus Werke ed. P. Wendland III (GrChrSchr 26, Leipzig 1916) 
p.41,13 (=Apollonius fr.60 Heiberg) and p.42,19. Cf Tannery, Memoires de la Societe des 
sciences physiques et naturelles ser. II, 5 (Bordeaux 1883) 254 and T. L. Heath, A History of Greek 
Mathematics II (Oxford 1921) 195. 

1 These are mentioned by Vettius Valens, Anthologiae 9.11, ed. Kroll p.354,5ff. 
8 Eutocius, loc.cit. (supra n.1). 
9 Hero, Metrika 1.26. See Heath, op.cit. 1.232-3. 
10 Cf B. L. van der Waerden, "Ausgleichspunkt, 'Methode der Perser' und indische 

Planetenrechnung," Archivefor History of Exact Sciences 1 (1961) 120-1.