CAMERON, ALAN, Isidore of Miletus and Hypatia: On the Editing of Mathematical Texts , 
Greek, Roman and Byzantine Studies, 31:1 (1990:Spring) p.103 

Isidore of Miletus and Hypatia: 
On the Editing of Mathematical Texts 

Alan Cameron 

Geoffrey de Ste. Croix octogenario 

EARLY IN THE SIXTH CENTURY Eutocius of Ascalon produced 
commentaries on various works of Archimedes. The best 
witness to the text, Laurentianus 28.4, offers the following 

explicit to his commentary on Book I of De sphaera et 
cylindro: 1 

EtytOKlO\) 'AcncaAroVl-cO\) \mOIlVTllla Ei~ 'to xp&tov 'troY 'ApX\.Il"OO\)~ 

XEpt o<palpa~ Kat K'UAlVOPO\), EKOOOE~ xapavayvrooeeiOl1~ 'tip M \.­
A110lCP IlTlXav\.Kip 'Io\.oropcp ilIlE'tEPCP o\.oaoKaAcp. 

The explicit to the commentary on Book II is identical except 
for the numeral. And the explicit to his commentary on Ar­
chimedes' In dimensionem circuli is identical again except for 
the title of the work commented. "Isidore the Engineer" is the 
celebrated architect Isidore of Miletus who, jointly with An­
themius of Tralles, was charged with the design of the new S. 
Sophia by Justinian in 532. The question is: what role did he play 
in Eutocius' commentaries on Archimedes? 

According to the first thoughts of J. L. Heiberg, the distin­
guished editor of so many mathematical texts, Isidore edited the 
text of Archimedes on which Eutocius' commentary was 
based.2 But in 1884 P. Tannery offered a different inter­
pretation. 3 First, he argued that the evidence of the explicits did 
not square with Eutocius' other references to contemporaries. 
The commentary on De sphaera et cylindro is dedicated 

t F in Heiberg's first edition of 1888, A in his second of 1915 (Archimedis 
opera omnia cum commentariis Eutocii lIP [Leipzig 1915] 48.26; cf 224.7, 
260.10). 

2 ·Ueber Eutokios," NJbb Suppl. 11 (1880) 359. 

3 -Eutocius et ses contemporains," reprinted in J.-L. Heiberg and H.-G. 
Zeuthen, edd., Memoires scientifiques II (I'oulouse 1912) 119. 

103 



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104 ISIDORE OF MILETUS AND HYPATIA 

respectfully to an Ammonius who can only be the influential 
philosopher who taught at Alexandria for many years at the end 
of the fifth and beginning of the sixth centuries. It has usually 
(and no doubt rightly) been assumed that Eutocius had been 
one of Ammonius' many students. The probability is increased, 
now that we know that Eutocius at one stage lectured on 
Aristotle's logic (apparently at Alexandria) and may even have 
succeeded to Ammonius' chair of philosophy.4 The later com­
mentary on Apollonius' Conica is dedicated to Anthemius, 
who is addressed in the prefaces to its four books as "dear 
friend" and so presumably a contemporary, more or less. 
According to Tannery, since Ammonius lived no later than 510 
and Isidore was a younger contemporary of Anthemius, 
Eutocius cannot have been a pupil of Isidore. 

Though embraced at once by Heiberg in his second edition of 
1915 (supra n.l: xciii), Tannery's own interpretation is so re­
markable that no summary could do it justice: 

un eleve d'Isidore de Milet aura fait, a Constantinople, une edi­
tion des trois commentaires dont il s'agit,5 commentaires publies 
a Alexandrie et ayant deja une certaine date; pour recommander 
son edition, au lieu d'y inscrire son propre nom, encore obscur, 
il l'aura mentionnee comme revue par son maitre, l'architecte de 
Sainte-Sophie. 

That is to say, some anonymous pupil of Isidore's is alleged to 
have signed his revision of Eutocius' commentaries with his 
teacher's name instead of his own. If Isidore was a younger man 
than Eutocius, then this hypothetical pupil will have been 
younger still, and his alleged revision could hardly be dated 
earlier than ca 550, obviously after Eutocius' death. 

For the moment we may leave aside that 7t<lP<lV<lytyVc.OO'KEtV 

does not mean crevise' in the sense here envisaged. But why did 
this person revise someone else's commentary anonymously 
instead of doing what every other late antique commentator 
did, appropriate its contents and republish them under his own 
name? To go no further than the subjects of this paper, 
Eutocius evidently took (unacknowledged) all that was worth 
taking from earlier commentators on Archimedes and Apol-

4 See the new text published by L. G. Westerink, -Elias on the Prior Ana­
lytics," Mnemosyne SER. 4 14 (1961) 126-39, at 129. 

5 By -three commentaries" he presumably means Eutocius' two books De 
sphaera et cylindro and the one In dimension em circuli. 



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ALAN CAMERON 105 

lonius, as Theon did (with acknowledgement) from Pappus for 
his Almagest commentary. What sense did it make for this 
anonymous to ascribe his alleged revisions to his teacher? And 
what of the reference at p.84.8 to the compass invented by 
"'Isidore our teacher," now falsely (on Tannery's hypothesis) 
;mply;ng that Eutocius was Is;dore's pupil! Tannery had the 
courage of his convictions. He did not hesitate to dismiss this 
passage too as "'an interpolation of the editor." Heiberg duly 
bracketed all four passages as interpolations in his second 
edition, and all modern scholars have concurred, notably 
Heath, Bulmer-Thomas, and Knorr.6 

But quite apart from the absurdity of the notion that this 
anonymous pupil of Isidore added no fewer than four 
references to "my teacher" without apparently realising that 
they falsely implied that it was not he, but Eutocius who had 
been Isidore's pupil, the chronological objections simply do not 
stand up. Westerink has shown that Ammonius must still have 
been alive in 520 and perhaps even a year or two later. 7 So it is 
no longer necessary, with Tannery, to place Eutocius' birth as 
early as 480. If born in (say) 490, he could have studied with 
Ammonius from ca 510. G. J. Toomer has made the attractive 
suggestion that a horoscope for 28 October 497, said in one 
manuscript that carries it to be from an astrological work by 
Eutocius, may actually be Eutocius' own horoscope. 8 If An­
themius was his contemporary (and perhaps fellow student), he 
would have been in his early forties when entrusted with the 
building of S. Sophia in 532, quite old enough to have made his 
name. That Isidore was apparently Anthemius' junior colleague 

6 Tannery's hypothesis is stated as fact in T. L. Heath's influential History 
of Greek Mathematics II (Oxford 1921) 540, whence the statement in PLRE 
II (Cambridge 1980) 439 that the allusions in Eutocius to Isidorus «the later 
architect ... are to be regarded as interpolations"; and (at disproportionate 
length) by 1. Bulmer-Thomas in the entries for both Eutocius and Isidore in 
Dictionary of Scientific Biography IV (New York 1971) 488, VII (1973) 28, 
and again in Historia Mathematica 8 (1981) 482f, rebuking J. Warren, Greek 
Mathematics and the Architects to Justinian (London 1976) 8, for ignorance 
of modern dogma. Cf W. KNORR, Textual Studies in Ancient and Mediaeval 
Geometry (Boston 1989 [hereafter 'Knorr']) 229f. 

7 Anonymous Prolegomena to Platonic Philosophy (Amsterdam 1962) xi; 
BZ 64 (1971) 10-13. 

R o. Neugebauer and H. B. van Hoesen, Greek Horoscopes (Philadelphia 
1959) L 497; 152-57, 188f; G. J. Toomer, Diocles on Burning Mirrors (Berlinl 
New York 1976) 18 n.2. 



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106 ISIDORE OF MILETUS AND HYPATIA 

in the S. Sophia project9 need not mean that he was a younger 
man. According to Agathias, Anthemius was "long dead" when 
the dome of S. Sophia fell in 558. 10 The repairs were entrusted to 
Isidore's homonymous nephew, which suggests that Isidore 
too was dead. Inscriptions at Chalcis sub Belo in Syria show the 
nephew's fame as an architect established by 550 (IGLS II 348f), 
and Procopius (Aed. 11.8.25) describes work done by him at 
Zenobia in Mesopotamia "while still a young man but showing a 
natural ability beyond his years." At BP 2.5.7 Procopius re­
marks that Zenobia was "uninhabited and destitute of all good 
things," with the result that the Persians simply bypassed it 
during their invasion of 540. According to Aed. 11.8.9 it was 
precisely because it was uninhabited and no obstacle to the Per­
sians that Justinian rebuilt the city. If follows that Isidore's work 
here must be dated after 540; we might guess that he was born 
between 510 and 520. A date of ca 475 for the birth of the elder 
Isidore would accommodate all known evidence. He might 
have been 10 or 15 years older than Anthemius-and Eutocius. 
Eutocius could easily have been a pupil of both Ammonius and 
Isidore, and a contemporary of Anthemius. 

This brings us to 7tCXpcxvcxytyvromc£tv. When advancing his 
drastic interpretation of the Eutocius explicits, Tannery was evi­
dently unaware of an exactly parallel formula, appended (in the 
oldest MS., Laur. 28.18=L) to the heading to Book III of Theon's 
commentary on Ptolemy's Almagest: 11 eECOVO~ 'AAE~cxvbpECO~ 
Eie; 'to 'tpi'tov rile; J.LcxS'TIJ.Lcxnrite; Il'toAEJ.Lcxiotl Ltlv'ta~ECOe; U7tOJ.Lv'TI­
J.Lcx h:bOOECO<; 7tCXpcxvcxyvcooSEio'TIe; 'tft q>tAOOOq>q> Stlycx'tpi J.LOtl 
'y 7tcx'ti~. The parallel is more exact than has been generally ap­
preciated. In both cases the work is described as a commentary 

9 As implied by Procop. Aed. 1.1.24 and his omission in Agathias Hist. 5.9.4. 
10 Hist. 5.9.4. The often repeated claim (e.g. G. L. Huxley, Anthemius of 

Tralles [=GRBM 1 (Cambridge, Mass.) 1959] 3; O. Neugebauer, A History of 
Ancient Mathematical Astronomy II [New York 1975] 1042; Warren [supra 
n.6] 6) that he died in or even about 534 is without foundation. F. Hultsch's 
claim that -Nach seinem Tode (urn 534) fiihrte Isidoros allein sein Bau 
weiter," suggests that he has mistakenly taken the Isidore in this passage (the 
only source he cites) to refer to the elder instead of the younger Isidore. There 
is no evidence that Anthemius did not live to see the completion of S. Sophia. 

11 Book III was not published till 1943, but the subtitle was known to F. 
Hultsch, ed., Pappi Alexandrini Collection is quae supersunt III (Berlin 
1876-78) xiiif; cf A. Rome, AnnArchBrux 46 (1926) 1-14; BullAcRoyBelg SER. 

5 39 (1953) 507. 



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ALAN CAMERON 107 

by Theon and Eutocius respectively, and there is also mention 
of an "edition checked» (E1C06o£ro~ 1tapavayvro(Jedoll~) by 
some other person. In each case the name and professional 
qualification (architect/philosopher) of this other person and 
his/her relationship to the commentator ("my teacher/my 
daughter») is specihed. With four exatnples, -we tnay surely 
conclude that this was a stock formula, of which we would have 
more examples if we had modern editions of more of the 
technical writings of late antiquity. Hypatia and Isidore were 
each performing some standard activity that would be iden­
tified for contemporaries by the word 1tapavaytyvw01C£tV. 

Heiberg had noticed the parallel by the time he published his 
second edition and seemed to think that it supported the new 
interpretation of the Eutocius explicits. The exact opposite is 
the case. Hypatia was both qualified to help Theon and in­
contestably alive when he was writing. Though most famous as 
a philosopher (she is so described by Theon), Hypatia was no 
mean mathematician and astronomer: she wrote commentaries 
on Diophantus, Apollonius of Perga, and Ptolemy's Handy 
Tables. Isidore too was well qualified to help Eutocius. The 
Theon parallel surely supports the natural interpretation of the 
Eutocius explicits, namely that Isidore was indeed Eutocius' 
teacher, just as Theon was Hypatia's teacher. 

Assuming Tannery's hypothesis as fact, however, Knorr 
(527f, 807) attributes to Isidore or his hypothetical anonymous 
pupil various interpolations he detects in the original text of 
Eutocius' commentary. Whether or not such interpolations 
exist, they can no longer be ascribed to Isidore, an older man 
than Eutocius. And if they are to be ascribed to a pupil of 
Isidore, why not to Eutocius himself? Late antique commen­
taries on the classics are dangerous texts to analyze in this way. 
They are normally based on earlier commentaries and a variety 
of specialized monographs, excerpted and assembled with 
scissors and paste. Unless the commentator is both expert and 
alert, there are bound to be inconsistencies and contradictions 
between the different excerpts, written as they were over many 
centuries. And we know that when Eutocius compiled his 
commentary on De sphaera et cylindro he was a tiro (p.2.13). 

According to Theon's editor, A. Rome, Hypatia revised or 



CAMERON, ALAN, Isidore of Miletus and Hypatia: On the Editing of Mathematical Texts , 
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108 ISIDORE OF MILETUS AND HYPATIA 

edited Theon's work,12 and his hypothesis has now been carried 
much further by Knorr (756f). Rome looked for linguistic 
differences between III and other books-unsuccessfully, as 
even Knorr concluded. Knorr thought that Hypatia inserted 
new material here and there rather than revised the whole, and 
suggested the passage on division by sexagesimals at the end of 
IIL1 as an example (cf. Rome [1953: supra n.ll] 841£ n.3). The 
same procedure is also described in Books I, IV, and IX. Ac­
cording to Knorr, "stylistic discrepancies so strongly distin­
guish the account in Books III and IV from that in Book I that 
they seem hardly compatible with the hypothesis of single 
authorship." He suggests accordingly that the account in I 
derives from Theon and those in III and IV from Hypatia. He 
then finds that the author of IX, though he "explicitly draws 
from the text of III and IV and expounds the same method as 
they," is nonetheless closer to I in both style and technical 
execution. He concludes "that the author of IX is not that of III 
and IV, but of I, namely Theon; for there is no other way to 
account for the stylistic affiliation." He is thus driven to the 
paradoxical conclusion that when "writing his commentary on 
Book IX, Theon is already aware of the second (Hypatian) 
edition of Books III and IV. "13 This he explains by the 
hypothesis that Theon "delegated" the publication of his notes 
on these books to H ypatia.14 

But he has misunderstood the practice of the Neoplatonist 
commentator Ammonius to which he refers as his only parallel 
and support. Here a quite different formula is used. Asclepius 
and Philoponus state quite openly that they are publishing their 
commentaries 0.1t0 CPOlVi\C; 'AJ.lJ.lOlVio'U, which means, in effect, 
"from the lecture notes of Ammonius."lS It seems that 
Ammonius preferred to recycle his work endlessly in class 
rather than publish it (a practice not unknown among academics 

12 Commentaires de Pappus et de Theon d'Alexandrie sur l'Almageste III 
(=Studi e testi 106 [Vatican 1943]) cxvii-cxxi. 

t3 All four citations from Knorr 761£. That is to say, on stylistic grounds 
Knorr extends Hypatia'S revisions to Book IV of Theon's commentary. 

14 Tihon comes close to this position: -Theon avait charge sa fille Hypatia 
d'en faire I'edition," which goes well beyond what Theon says. See T. 
Mogenet and A. Tihon, Le <Grand Commentaire' de Theon d'Alexandrie aux 
Tables laciles de Pto!imee I (=Studi e testi 315 [Vatican 1985]) 221. 

15 See M. Richard, - 'Axo cp(tlvil~," Byzantion 20 (1950) 192; Westerink (supra 
n.6) xi. 



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ALAN CAMERON 109 

of other times and places). It was his pupils who preserved his 
work, no doubt after his death, with Philoponus (but not 
Asclepius) indicating that he had added material of his own. 
When we have versions by both Asclepius and Philoponus of 
the same lectures of Ammonius, the similarities are often very 
close. 1t. That is to say, they are reports of Ammonius' actual 
lectures, with or without additions. There is no clear indication 
that these were perceived as publications at all, much less 
publications authorized by Ammonius. Rather they were notes 
copied down by Asclepius and Philoponus in Ammonius' 
classes and later re-used by them when they were professors. 1? 

The situation is thus quite different from the relation of Hypatia 
to Theon or Isidore to Eutocius. 

Even if we accept Knorr's analysis of the differences between 
these four passages of Theon, his hypothesis of later editorial 
insertion is by no means the only or the most natural solution. 
Such variations and inconsistencies in the compilations of late 
antiquity are normally seen as pointers to the different sources 
employed. Knorr concedes that neither Hypatia nor Theon 
invented this method of division. To go no further back in time, 
it is described in detail by Theon's predecessor Pappus, whose 
commentary Theon pillaged heavily for his own. As a conse­
quence, most of Pappus' commentary has perished, but the so­
called Prolegomena to the Almagest preserve a fragment that 
ascribes to him the same method with the same example (360 
divided by 365 14' 48") as in Theon Book 111. 18 Knorr allows that 
Hypatia's alleged addition to Theon derives from Pappus, but 
since Pappus was Theon's own major source, this is hardly a 
safe criterion for distinguishing between Theon and Hypatia. 
Knorr's hypothesis makes it no easier than any other to under-

16 See L. Taran, Asclepius of Tralles: Commentary to Nicomachus' 
Introduction to Arithmetic (Philadelphia 1969) 10f. 

17 This practice was perpetuated among Ammonius' successors, the greater 
part of whose extant commentaries are more or less verbatim transcripts of 
lecture notes (whence the frequent problems of ascription). 

18 J. Mogenet, "La division selon Pappus d' Alexandrie," BullAcRoyBelg SER. 

S 37 (1951) 16-23; see the translation in Knorr 787-93, who describes this 
account as a "rambling mess ... more than four times longer than the account 
from Theon-Hypatia's Book III." But he allows that this is probably the fault 
of the later compiler who preserves the material-none other than Eutocius, 
according to Mogenet (L'introduction a l'Almageste [=MemAcRoyBelg 51.2 
(1956)], disputed at length by Knorr 155-211). 



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110 ISIDORE OF MILETUS AND HYPATIA 

stand why Theon allowed these inconsistencies (if such they 
are) to stand. The simplest explanation is that they derive from 
different stages of composition in a long work based on various 
sources and not consistently revised. 

In itself, the idea that a well qualified daughter might assist her 
father in the immense labour of writing a commentary on all 
thirteen books of the Almagest seems eminently reasonable. 
But the precise form of the heading to Book III seems to ex­
clude the two obvious forms this assistance might have taken: 
namely that they wrote the commentary jointly between them, 
(e.g. Knorr's hypothesis that Theon "delegated'" some books to 
Hypatia) or that Hypatia completed or revised Theon's work 
after his death, or at any rate after he had finished. 19 Whatever 
Hypatia did, she evidently did while Theon was still at work, for 
it is Theon who mentions her role, as early in so long a project 
as Book III. And even in the case of Book III, Theon still claims 
the authorship of his commentary (8EroVO<; U7t6~VTlJ.l(1). 

According to Heath, Hypatia's revision was confined to Book 
III, which "may ... account for the fact that Theon's own Book 
III disappeared from all MSS other than L'" (Laur. 28.18).20 If 
there really were two versions, it is understandable that Hy­
patia's revision might replace Theon's original. 21 But why should 
this account for copies lacking Book III altogether? According 
to Rome, Hypatia's "revision'" made the book somehow "less 
authentic. "'22 The truth is that all MSS. of Theon's commentary 
(including L) are fragmentary. L has III but (like other MSS.) 

lacks V; the other MSS. lack other books or portions of books in 
addition to III and V (the end of X, all of XI, and the beginning 
of XII). There is surely no significance in Ill's preservation by 
Lalone. J. Mogenet has recently published some scholia to 
Book III from two Vatican MSS. Some of them are more or less 
identical to Rome's text, some contain additional details or omit 
short phrases. According to Mogenet, since the Rome text 
"etait Ie resultat d'une revision faite par Hypatie, les variantes 

19 E.g. Rome (supra n.l1 [1926] cxvi) compared Hypatia'S revision of Theon 
to Theon's revision of Pappus. 

20 CR 52 (1938) 40. 
21 See the reservations about second editions in n.45 infra. 
22 Rome (supra n.l1 [1926]) 6. 



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ALAN CAMERON 111 

pourraient provenir de l'edition anterieure due au seul 
Theon. "23 But it would be remarkable indeed if the scholiast had 
quoted his source(s) with perfect fidelity.24 Some of the scholia 
are certainly much later than Theon, and it is a reasonable guess 
that some derive from Theon's own lost source Pappus. Add to 
this the numerous short lacunae in L's text of Book III, and it 
should be clear that no confidence can be placed in any attempt 
to reconstruct Hypatia in this way. 

Furthermore, Anne Tihon has recently announced the dis­
covery of most of the hitherto missing Book V of the Almagest 
commentary, in the form of scholia to the text of the Almagest 
in Vat. gr. 198.25 One of the most interesting novelties is the 
discovery that Book V is closely related to Book III, with 
several direct cross-references back to the earlier book. The 
same dates appear in the examples cited. Book III calculates the 
longitude of the sun on 5 January 323, while Book V the longi­
tude of the moon on the same date, explicitly referring to the 
calculation in Book III. That this date falls earlier than the life­
time of Theon suggests that both examples were taken over 
from Pappus. All these scholia are expressly ascribed to Theon, 
who is also given as the author of the passages cited from Book 
III. Clearly there is no support here for the hypothesis of a 
substantial revision of Book III by Hypatia. Indeed, the text of 
Book III as extant gives little enough support to the idea that it 
was revised by anybody, even Theon. In another paper Tihon 
describes it as "fort ablme, ou fort mal redige." 26 It is very singu­
lar that the only book expressly described as having been re­
vised should show the least signs of having been revised at all. 

The solution to the problem is provided by the headings to 
Books I and II of Theon's commentary, the headings that do 
not mention Hypatia: 8E(oVOe; 'AA£~avOpE(Oe; 't11e; 1tap' au'tou 
'Y£'Y£vTlIJ.Evlle; £1(060£(Oe; de; 'to 1tpiihov (O£u't£pov) 't11e; L'\)v'ta~£(Oe; 

23 - Sur quelques scolies de I' Almageste," in Le monde grec: hommages a 
Claire Preaux (Brussels 1975) 305. 

24 Compare the case of Porphyry's Homerika Zetemata, transmitted both as 
an independent text and in the form of scholia, with C enormous discrepan­
cies": N. G. Wilson, C A Chapter in the History of Scholia," CQ N.S. 17 (1967) 
245. 

25 cLe livre V retrouve du Commentaire a l'Almageste de Theon d' Alexan­
drie," AntCl56 (1987) 201-18. 

26 -Theon d' Alexandrie et les Tables Faciles de Ptolemee," A rchi'lles inter­
nation ales d'histoire des sciences 35 (1985) 121 n.37. 



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112 ISIDORE OF MILETUS AND HYPATIA 

TI'tOA,EI.UXtOU U1t0J.1VTlI.UX. According to Rome, this is "L'edition 
originale, par opposition a l'edition d'Hypatie. "27 But there are 
obvious problems here. In the first place, when Theon was 
writing his commentary on Books I-II, we might naturally 
assume that he had not yet written his commentary on III, 
much less seen it revised by Hypatia. In the second, the real 
opposition, blurred by all modern commentators, is surely 
between E1(OOOEroc; and U1t0J.1VTlJ.1Cl. According to T. L. Heath, 
for example, the heading of Book III "describes it as the 
commentary of Theon on Ptolemy's Book III 'in the recension 
of my philosopher-daughter Hypatia', while Books I and II 
have titles stating that they belong to Theon's own edition. "28 

Yet while it is at least possible to speak of a commentary of 
Theon in an edition (i.e., revision) by Hypatia, it is nonsense to 
speak of a commentary of Theon in his own edition. In the 
ordinary way, one's own books are always in one's own edition. 
Unless there are some special circumstances (a posthumous or 
revised edition), this is too self-evident ever to be worth stating 
at all. It is difficult to think of a single parallel for so strange a 
formula. There is no such reference to an ElC500t~ in the titles to 
any of Theon's other commentaries.29 In the lexicon of the 
scholar, E1(OO(Jt~ and U1tOJ.1VTlJ.1Cl normally denote two quite 
separate sorts of book, the edition of and the commentary on 
the text in question. 

Certainly this is how Theon normally used the terms. For 
example, in the course of Book I of his commentary, he 
remarks: "that sectors of equal circles are to one another as the 
angles on which they stand, I have proved in my edition of the 
Elements (OEOEtlC'tClt TtJ.1tV EV 'tft £1(OOO£t'trov r'tOtXEirov) at the end 
of the sixth book. ""30 Theon did not write a commentary on 
Euclid, but he did produce an edition of the text. And just such 

27 A. Rome, Commentaires de Pappus et de Theon d' Alexandrie sur L'ALma­
geste II (=Studi e testi 72 [Vatican 1936]) 317 n.1; cf III (supra n.12) cxvi-xxi. 

28 Heath (supra n.20) 40. So too K. von Fritz, Gnomon 15 (1939) 276: ·Die 
Oberschriften der verschiedene Bucher des Kommentares des Theon lassen 
keinen Zweifel dariiber, daB es sogar von dem Theonkommentar selbst ver­
schiedene Ausgaben oder Auflagen, die eine von Theon selbst, die andere von 
seine Tochter Hypatia besorgt, gegeben hat." 

29 A point noted but not explained by Tihon (supra n.14) 71: ·cette fois, il ne 
nous est pas precise que cet i)1t6~vl'\~a a fait I'object d'une t1(aoo~. Faut-il voir 
Ii une difference significative?" 

30 Rome (supra n.27) II 492.6ff (tr. T. L. Heath). 



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ALAN CAMERON 113 

a proposl tIOn appears in the text of almost all extant MSS. of 
Euclid~s Elements at the end of 6.33. Indeed, some of these MSS. 

are explicitly stated to be "from Theon~s edition" (h:: 'tile; SEOO­
voe; £K060£ooe;). It was not till the beginning of the nineteenth 
century, 

when Peyrard discovered that the manuscript Vaticanus Graecus 
190, which lacks that proposition and is significantly different 
from the vulgate in other respects, must be an example of the pre­
Theonic text, that it became possible to determine the nature of 
Theon's alterations of Euclid. They are many but mostly trivial 
... a very few are corrections of real mistakes in Euclid's text. 
More are due to Theon's misunderstanding the original. In some 
cases he apparently omits what he considers wrong. He makes 
frequent additions to fill what he considers gaps in Euclid's 
reasoning, even interpolating whole propositions .... On the 
whole, his edition can hardly be said to improve on the original, 
although it may well have fulfilled its purpose of being easier for 
his students to use.J1 

We now know that Theon produced similar "editions" of two 
other works of Euclid, the Data and the Optics, the latter less an 
edition (even in Theon's terms) than a simplified reworking in 
his own words; it is described in one MS. as being according to 
the "version" of Theon (£K 'tile; SEoovoe; £~T\rflo£OOC;).J2 

The possibility that Theon might have produced a similar 
"edition" of Ptolemy was long ago aired by Heiberg on the 
basis of interpolations in certain MSS.: 

ratio genus que interpolationis, quam in archetypo codicum D G 
incohatam et in utroque propagatam vidimus, peritis in me­
moriam revocabit recensionem Elementorum Euclidis a Theone 
factam.JJ 

These interpolations, he suspected, were the work of the 
school of Alexandria, "ubi Syntaxis sine dubio semper in mani-

31 G. J. Toomer, Dictionary of Scientific Biography XIII (1976) 322; cf K. 
Ziegler, -Theon (15)," RE SA (1934) 2078£; for the details, Heiberg, Euclidis 
opera V (Leipzig 1888) xxivf, li-lxxvi; Heath, The Thirteen Books of Euclid's 
Elements F (London 1926) 46-63. 

32 Toomer (supra n.31) 322f; Ziegler (supra n.31) 2078f; H. Menge, Euclidis 
opera (Leipzig 1883-1916) VI xxxii-xlix; VII xlix-I; J. L. Heiberg, Litterar­
geschichtliche Studien uber Euclid (Leipzig 1882) 129-48. For t~ilY'l(Jlc; as 
'version' see Lampe, PGL S.7). 2 (of the Septuagint). 

33 Claudii Ptolemaei opera II (Leipzig 1907) cxxvi. 



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114 ISIDORE OF MILETUS AND HYPATIA 

bus magistrorum discipulorumque mansit et docendo tracta­
batur." He quoted one or two passages from Pappus and Theon 
in the unpublished collations of F. Hultsch that agreed with 
what he considered interpolations, but conceded that full 
confirmation or refutation of his suspicion would have to wait 
until there was a critical edition of Theon's commentary. On 
the basis of his own work on the text of Theon, Rome stated 
(without detailed argument) that in his view Heiberg was right. 34 

But the situation is not as simple as it once appeared. For Gerald 
Toomer has shown that in many cases readings of D that 
Heiberg rejected must in fact be correct, often numerical com­
putations where there is no room for doubt. 35 But the lack of 
straightforward correlations between Theon's interpolations 
and one MS. or group of MSS. does not mean that they do not 
exist or cannot be detected. This after all was the situation in the 
Euclid tradition until the discovery of the sole pre-Theonic MS. 

And there too the situation is now seen to be more complex 
than Heiberg originally thought. Not only do the Theonic MSS. 
differ among themselves, each at one place or another alone 
agreeing with the Vaticanus against its fellows: the pre-Theonic 
P.Fayum 9 agrees with the Theonic MSS. against the Vaticanus. 36 

Perhaps we are in the unfortunate positon of having no pre­
Theonic Ptolemy MS. Toomer has detected a series of inter­
polations, several of them later than Pappus but all earlier than 
the copies used by the Arabic translators.37 He is too cautious to 
attribute them to Theon, but this is an obvious possibility. 

In the case of Euclid, the famous remark in the Almagest com­
mentary alerted scholars to the existence and nature of Theon's 
edi tion long before the discovery of Vaticanus 190. Under the 
circumstances, it is curious that his scarcely less explicit allu­
sions to his own edition of the Almagest have not been 
recognized. But the participle 'YE'YEVllJlEVllC; surely makes that 
inescapable. It was the "edition done" (editio facta) by himself. 
This is no more than a variation on the formula EKOOCJEWC; 
1tapavayvwCJedCJllC;, with 'YE'YEVllIlEVllC; a gloss on 1tapava­
yvwCJSdC;. So too the reference to Hypatia's edition. It was not 

34 Rome (supra n.11 [1953]) 513. 
3S G. J. Toomer, Ptolemy's Almagest (London 1984) 3; in many cases D's 

·obviously correct readings are shared by aU or part of the Arabic tradition. JJ 

36 See Heath (supra n.31) 51-54. 
37 Toomer (supra n.35) 4f and 684 for a list. 



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ALAN CAMERON 115 

her father's commentary that she edited, but the text of the 
Almagest. If it had been the commentary, why introduce the 
misleading h:boo£ro~? What we should then have expected is 
the neuter 1tapavayvroo8Ev agreeing with U1t0J.1vllJ.1a: "the 
commentary of Theon revised by ... Hypatia.'" What we in fact 
get is a genitive absolute and an antithesis between commentary 
and edition: "the commentary of Theon, with the edition 
revised by ... Hypatia. '" 

It is now possible to see exactly how the labour was divided 
between father and daughter. To start with, Theon did both text 
and commentary, but after he had completed the first two 
books he asked Hypatia to undertake the text. According to 
Rome (the only person who has looked at the MSS. for the rest 
of the commentary) there are no more such subheadings to 
Books IV-XIII.38 So there is no way of telling whether she 
prepared the text of the remaining ten books. But the natural 
assumption is that Theon found the task of both text and 
commentary too much for him, and persuaded Hypatia to take 
over the text for the rest of the project. It will not (of course) 
have been any more of a critical edition in the modern sense 
than Theon's of Euclid. It was just a simplified and 'corrected' 
text for the use of students-the same students who (according 
to the preface to Book I of Theon's commentary) had asked 
him to publish his lecture notes in that form. Naturally they 
wanted a reliable text to go with Theon's commentary. Hypatia 
had doubtless worked through the text of the Almagest many 
times with her father, so it cannot have been too difficult for 
her to produce a version that would harmonize with his views. 

That this is what the subtitles to Theon's commentary mean is 
put beyond reasonable doubt by the subtitles to all four books 
of Eutocius' commentary on the Conica of Apollonius of Perga 
(II 168,290,314,354 Heiberg): Eut01dou 'A(J1(aAroVltOU d~ to a' 
[W, y', 5'] troy 'A1tOAAvroiou KOOVtKroV tll~ Kat' au'tov EKbOo£ro~. 
As with Books I and II of Theon, Eutocius cannot be saying 
that this is his own edition of his own commentary. Who else's 
edition could it be? There can be no question (as Heiberg saw 
already in his paper of 1880) that Eutocius is referring to his 
own commentary and his own edition of the text of Apollonius. 

38 Rome (supra n.27) II 318 n.1: • A partir du 4 e livre ces mentions dis­
paraissent. " 



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116 ISIDORE OF MILETUS AND HYPATIA 

The edition is referred to quite explictly in the preface to Book 
IV: 

Book IV, my dear friend Anthemius ... is particularly elegant and 
clear for readers, thanks to my edition with its commentary; the 
notes39 make up for anything left unsaid.-40 

It seems clear from these words that Eutocius' work included 
an edition of the text as well as a commentary. One of the three 
Banu M usa brothers, who commissioned the Arabic translation 
of Books I-VII in the ninth century, collated the Eutocian 
version of I-IV against a pre-Eutocian text, and found "that the 
errors in these were fewer than in the original." The first four 
books of their translation (all that Eutocius edited) "came out 
according to the restoration of Eutocius, and the following ac­
cording to the composition of Apollonius. "41 The brothers re­
peatedly apply the terms "restore" and "correct" to his labours 
on the text. 

In his commentary Eutocius frequently cites alternative ver­
sions to be found "in some copies" (tv UCHV a.vu'Ypacpo~, as he 
writes in the first three books, contenting himself thereafter 
with an aAAc.o<; ).42 In explanation of these variants, he refers to a 
passage in Apollonius' own dedicatory letter to Eudemus, 
which deserves to be quoted in full: 

I dare say you have not forgotten my telling you that I under­
took the investigation of this subject at the request of Naucrates 
the geometer at the time when he came to Alexandria and stayed 
with me, and that, after working it out in eight books, I com-

39 Heiberg (supra n.2: 375) once conjectured Ka'taypacpat, -diagrams," for 
the MSS. napaypacpai, which he rightly kept in his edition (interpreting -breves 
illas not as, quibus in codd. mathematicorum propositiones usurpatae vel ipsius 
operis vel Euclidis citantur," 355 n.l). This would have implied that diagrams 
were not common in texts of the period, which is hardly credible (diagrams 
were certainly used in early mathematical texts, as papyri and some other evi­
dence clearly prove: K. Weitzman, Illustrations in Roll and Coder [Princeton 
1970] 47ff). 

40 t(JU ~£ xaph:v Kat (Jacp£~ 'to"i~ £v'tuyxavou(Jt Kat JlaAt(J'ta ano 'til~ TtJlE'ti­
pa~ £K06(JECJ)~. Kat o-u~£ (JXOAtCJ)v ~£"i'tat· 'to ya.p Ev~iov ai napaypacpat nAT}-
po\'xnv. 

41 Both quotations are from their long and informative preface as translated 
by G. J. Toomer, Apollonius, Conics Books V to VII: the Arabic Translation 
of the Lost Greek Original in the Version of the Banii Musa II (New York 
1990) 620-28. 

42 Passages collected by Heiberg (supra n.3) 361£. 



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ALAN CAMERON 

municated them to him at once, somewhat too hurriedly, with­
out a thorough revision (as he was on the point of sailing), but 
putting down all that occurred to me, with the intention of re­
turning to them later. Wherefore I now take the opportunity of 
publishing each portion from time to time, as it is gradually 
corrected. But, since it has chanced that some other persons also 
who have been with me have got the first and second books 
before they were corrected, so do not be surprised if you find 
them in a different shape.43 

117 

Eutocius inferred, perhaps over-optimistically,44 that his 
variants derived from these various versions by Apollonius: 45 

Since there were several editions, as Apollonius himself says in 
the preface, I thought it better to put them together from what­
ever source came to hand and place the clearer version in the text 
to help the understanding of beginners; and to indicate the varia­
tions on the proofs outside [sc. in the margin].46 

Here he is describing the principles on which he constructed 
his text as well as his commentary. He even enunciates his 
critical principles: he has put the "clearer" version in the text. 
That is to say, he used his judgement, not manuscript evidence, 
to decide between variants. As the Banii Miisa put it, "he 
employed his intelligence in what he could not correct ... until 
he discovered the proof for it." Rejected variants he placed 
"outside," by which he evidently means in the margin. 47 There 

43 Tr. T. L. Heath, Apollonius of Perga: Treatise on Conic Sections (Cam­
bridge 1896) lxix. 

44 II lvii Heiberg: "sive, quod veri similius est, magistris debetur, qui libro 
ApoIIonii in docendo utebantur, quo modo in codicibus reliquorum 
mathematicorum ortae sunt demonstrationes alterae." 

45 Modern writers often make the anachronistic assumption that revised 
editions drive their predecessors off the market. The truth is that authors had 
no way of controlling the dissemination of a work once it had left their 
hands. The best known case is Cicero's Academica, where (non-overlapping) 
parts of both editions have survived: see Philipps on in M. Gelzer, W. Kroll, R. 
Philippson, and K. Buchner, "M. Tullius Cicero," RE 7A (1939) 1128-35. 

46 1t!..£wvcov 5£ oUCJrov h:MCJI:'cov, ro.;; lCal. aiyto.;; <pT1CJtV EV 'til f:1ttCJ'toAil, a~etvov 
i]'Y'1CJa~TJv CJuvayayeiv aU'ta.;; ElC 'troY EIl1tt1t'tov'tcov, 'ta O'a<pEO''t£pa 1tapa­
't19£~vo.;; £v 'tip PT)'T:ip 5ta 'tTtv 'troy eiCJayo~tvcov eu~ape1<Xv, i:1;c0gev 5£ £v 'toi.;; 
O''l>V'te'taYIlEVOtC; OXOAlotC; E1ttO'TJllaive09<Xl 'tOUC; Ota<popouc; (roc; dlCOC;) 'tp01tOUC; 'troy 
<l1t05dl;ecov. 

47 Heiberg (supra n.3: lviii) also argues that some of the lacunae in Eutocius 
point to the text having been written in the margins and so particularly 
vulnerable to physical damage. 



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118 ISIDORE OF MILETUS AND HYPATIA 

has been some debate in recent years about when scholia came 
to be written in the margins of classical texts rather than in 
separate monographs. It has usually been assumed that the 
practice developed in late antiquity; others have preferred to 
postpone it until the development of minuscule script in the 
eighth and ninth centuries. 48 The debate centres less on the 
purely technical aspect (the location of explanatory notes on the 
same page as the text) than on the abridgement for the purpose. 
Here in the case of Eutocius we seem to have an indisputable 
example; his commentaries clearly represent an abridgment of 
the work of innumerable predecessors. 49 

We should not overrate Eutocius' editorial skills. His edition 
was no doubt modelled on those of Theon, aimed at students 
rather than scholars. His frequent citation of variants does not 
in itself prove that he collated MSS. systematically. It is likely that 
the more important variants were already indicated with an 
liAAOO<;; in the margins of scholarly MSS. The Aristotelian com­
mentators frequently discuss variant readings, and though they 
occasionally collated MSS., it is clear that the texts they used often 
carried variants. 5o Nonetheless, whatever his method and 
sources, there can be no question that Eutocius produced his 
own text of Books I-IV of Apollonius' Conica. 

So in all four examples of the £1(000£00<;; formula from Eu­
tocius' Apollonius commentary and in all three from Theon's 
commentary on the Almagest the reference is to a text. The 
same is surely true of the three more examples from Eutocius' 
commentaries on Archimedes. So Heiberg's first thoughts 
were best. Isidore did not revise Eutocius' commentaries, he 
edited the text on which his commentaries were based. 

48 See Wilson (supra n.24) 244-56, and -The Relation of Text and Commen­
tary in Greek Books," in Atti del Convegno internazionale «Illibro e il testo», 
Urbino, 20-23 settembre 1982, edd. C. Questa and R. Rafaelli (Urbino 1984) 
105-10. 

49 For a list of the earlier texts read and cited by Eutocius see Heiberg (supra 
n.2: 363-71), concluding that he was -ein sehr fleiBiger Sammler von weit 
ausgedehnter Belesenheit" (363); Bulmer-Thomas (supra n.6) IV 489ff. But his 
Apollonius commentary is less substantial, providing much less of historical 
value than the Archimedes commentary: cf. Toomer (supra n.41) xvi. 

50 See the evidence for De caelo alone assembled by P. Moraux, -Notes sur 
la tradition indirecte du 'de caelo' d' Aristote, " Hermes 82 (1954) 145-82, and 
in his edition, Aristote du ciel (Paris 1965) clx-<lxvi. 



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ALAN CAMERON 119 

Once more, however, we should not overestimate this edi­
tion. We need not believe, with E. Stein, that Isidore "distin­
guished himself» as editor of Archimedes; or with C. Fabricius 
that it is Isidore we have to thank for the "rescue» of the 
principal MSS. of Archimedes. 51 

Large claims have been made for the "School of Isidore." 
According to H. Hunger, he played an important role in the 
transmission of the text of both Archimedes and Euclid. 52 It is 
worth taking a closer look at the only piece of evidence that 
links him to Euclid. The author of the so-called fifteenth book 
of Euclid's Elements demonstrates how to inscribe certain regu­
lar solids inside certain others (for example, a cube in an octa­
hedron) and how to determine the angle of inclination between 
faces meeting in an edge of these solids. The method was to 
construct various isosceles triangles, and the rules for drawing 
them are attributed to "Isidore our great teacher. »53 There is no 
reason to doubt the usual assumption that this is Isidore of 
Miletus and that the author of the treatise was a pupil of his, 
writing in the early sixth century. 54 After briefly quoting Isi­
dore's formulation of his rules, the anonymous proceeds to 
explain them in more detail, on the grounds that "the distin­
guished man» was content once they seemed self-evident to 
himself (54.If Heiberg). The implication is that Isidore had not 
published his own discovery. He may well have given brilliant 
and popular classes on the ancient mathematicians. He may 
even have played a part in the revival of interest in their 
writings, which may in turn have led to a demand for copies, 
both in Constantinople and Alexandria. But Heiberg's further 

51 E. Stein, Histoire du Bas-Empire II (Paris 1949) 457; C. Fabricius, RE 9 
(1916) 2081; much the same in K. Ziegler, Kl. Pauly 2 (1975) 1462. 

52 Heiberg (supra n.31) 156; H. Hunger, Die hochsprachliche profane Litera­
tur der Byzantiner II (Munich 1978) 230. 

53 Heiberg (supra n.32) 50.21 with 67 n.1.; a clear summary of Isidore's rules 
in Heath (supra n.31) lIP 519f. 

54 Heiberg (supra n.31) 156. To Heiberg's case against the alternative pos­
sibility, that Book XV is by Damascius and that the teacher is the Athenian 
scholarch Isidorus, may be added Damascius' malicious remark (Vita Isidori 
218, ed. C. Zintzen [Hildesheim 1967]=Epit. Photo 164) that Isidorus excelled 
Hypatia not only as a man does a woman but also as a true philosopher does 
a geometrician. The implication is surely that this Isidorus was not a 
geometrician. 



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120 ISIDORE OF MILETUS AND HYPATIA 

suggestion55 that Isidore was also responsible for the formation 
of a corpus of Archimedes' writings probably goes too far. 
After all, as the same Heiberg conceded, Eutocius seems to 
have known only the three works of Archimedes on which he 
wrote commentaries-and Isidore perhaps only the first two. 56 
Since another six have survived,57 it does not look as if the 
School of Isidore conducted a very thorough search. There is 
certainly no evidence that he did anything for the text of Euclid. 
Nor, after Theon and Proclus, can he be credited with a revival 
of interest in Euclid. 

Even the often repeated claim that "it was in the school of 
Isidorus that [Archimedes'] treatises were turned from their 
original Doric into the ordinary language" is not borne out by 
the evidence.58 On the one hand, the way Eutocius draws atten­
tion to the antiquated terminology and the "partial preservation 
of Archimedes' own Doric" in an "old book" he found (p. 
130.29f) suggests that both dialect and terminology had already 
been largely modernized before Isidore's day. On the other 
hand, he quotes a handful of Doric forms in his commentary on 
De sphaera et cylindro that are no longer to be found in our 
MSS.59 Evidently the systematic suppression of Dorisms was 
later than Eutocius' day. 

The only work attributed to Isidore is a commentary, on one 
of the most practical works of the eminently practical Hero of 
Alexandria, his KaJlapudt ("On Vaulting"). Isidore was a highly 
successful builder, and in an age when so many churches were 
being built, we can hardly doubt that this commentary owed 
more to Isidore's own experience in building vaults than to 
study of the MSS. of Hero. 60 All we know of it comes from 

55 Archimedis opera lIP xcv: -eius temporis studiis debetur, quod opera 
Archimedis, quae singulatim ferebantur aut in bibliothecis latebant, undique 
conquirebantur. nonnulla in corpusculum mechanicorum recepta sunt." 

56 Heiberg (supra n.2) 359, and see 123 infra. 
57 Not to mention fragments and another that survived long enough to be 

translated into Arabic. 
58 Heath (supra n.6) 25; cf. Bulmer-Thomas (supra n.6 [1981]) 482. 
59 J. L. Heiberg, ·Ueber den Dialekt des Archimedes," NJbb Suppl. 13 

(1884) 543. 
60 -The relevance to Haghia Sophia is obvious," according to Warren (supra 

n.6: 8), but the work in which Eutocius refers to it cannot have been written 
later than ca 520. Vaults had been the staple of Roman architecture since 
Trajan, e.g. W. L. MacDonald, The Architecture of the Roman Empire 2 I 
(New Haven 1982) 180f. Isidore had doubtless been building them all his life. 



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ALAN CAMERON 121 

another of his pupils, Eutocius, who in Book II of his Archi­
medes commentary refers to it for the description of a special 
compass Isidore had invented for drawing parabolas (p.84.8). It 
does not survive, and we cannot even be certain that it was a 
published work. At this period, the word U7t0JlvllJlu often 
denotes nothing lTIore than lecture notes taken down by a 
student/,l and Eutocius was certainly Isidore's student. 

Anthemius too has come in for extravagant praise over the 
years. According to an architectural historian (Warren [supra 
n.6] 12), "Isidorus the elder and his nephew stood with 
Anthemius on the ultimate peak of Greek mathematics. Their 
efforts raised it a little higher." A more qualified critic wrote 
recently of his "bombastic style and mathematical ineptitude. "62 

The claims for originality and even brilliance once made for his 
discussion of burning-mirrors in On Remarkable Mechanical 
Devices63 (of which only a fragment survives in the original) 
have suffered a sharp blow from Toomer's publication of the 
classic Greek treatment of the subject, Diocles' On Burning 
Mirrors. Not only are Anthemius' demonstrations clumsy by 
comparison; he appears not even to have known Diocles' book, 
despite Eutocius' knowledge of it. 64 For an architect he was no 
doubt a competent mathematician, and he certainly knew how 
to apply his knowledge to subjects great and small. A complete 
Arabic translation (unpublished) of On Remarkable Mechanical 
Devices continues with methods for constructing fairground 
distorting mirrors. 65 And Agathias lists a series of mechanical 
jokes he played on his unfortunate neighbour in Constan­
tinople, including dazzling him with mirrors and a simulated 
earthquake caused by steam-power.66 Hunger's claim (supra 
n.S2: 230) that he "commented on Nicomachus" seems to be a 

61 For example, almost none of the numerous extant commentaries by Am­
monius and Olympiodorus were published; what we have are copies made 
from their lectures «bto cprovi1~) by students: Richard (supra n.D) 191-222. 

62 Toomer (supra n.8) 20. 
63 Text and commentary in Huxley (supra n.10). 
64 Toomer (supra n.8) 18, 187-201. 
65 Toomer (supra n.8) 20, supplemented by private information. The dis­

covery of the Arabic version puts out of court the much discussed issue 
(Huxley [supra n.10] 20-33) whether the so-called Fragmentum mathemati­
cum Bobiense was part of Anthemius' book. 

66 Hist. 5.7f; E. Darmstaedter, • Anthemios und sein "kiinstliches Erd­
beben- in Byzanz," Philologus 88 (1933) 477-82. 



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122 ISIDORE OF MILETUS AND HYPATIA 

confusion with Anthemius' contemporary and fellow-citizen 
Asclepius of Tralles. There is no evidence that he took pupils or 
edi ted texts. 

There is a widespread view that Isidore and Anthemius were 
"more scientists than architects." According to Krautheimer, 
for example, "Experienced master builders of 537 must have 
stood aghast at the disregard of sound building practices by 
those two non-professionals to whom the Emperor had en­
trusted his greatest building." 67 There is no basis whatever for 
this opinion. A passage of Pappus to which G. Downey drew 
attention bears out for late antiquity Vitruvius' famous claim 68 

that architects were expected to have a sound theoretical 
training: "the man who has been trained from his youth in the 
aforesaid sciences [geometry, mathematics, astronomy] as well 
as practised in the aforesaid arts [metalwork, carpentry, paint­
ing], and in addition has a versatile mind, will be, they say, the 
best inventor of practical devices and the best builder. "69 Pap­
pus conceded that very few reached this ideal; those that did 
were known by the honorable title mechanicus ( Illlxavlx6~). 
The inscription from Chalcis sub Belo (IGLS II 348) celebrates 
Isidore's homonymous nephew as IlE'YaA01tpE1tEO''t(X'tO~ lA­
Ao{)O''tpto~ xat 1l1lxavlx~. 

Procopius (Aed. 1.1.24) makes it clear that Justinian put An­
themius in charge of the new S. Sophia because he was "the 
most learned in the art of building" (llllXavlxll), and Agathias 
(Hist. 5.8.3 [p.171.7 Keydell]) describes him as a builder by pro­
fession ('tExVn). It should be noted that Isidore is already 
described as Illlxavlx6~ in the explicits to Eutocius' De sphaera 
et cylindro, a first publication of his youth (p.2.13), that is to say 
ca 510/515, when Isidore cannot have been more than 35.70 

There is no reason to doubt that Isidore was a practicing, pro-

61 R. Krautheimer, Early Christian and Byzantine Architecture) (New York 
1979) 215, 220. 

68 De Arch. 1.1.3, not always taken seriously: see MacDonald (supra n.60) 
138. 

" F. Hultsch (supra n.l1) III 1022-24=1. Thomas, Selectwns Illustrating the 
History of Greek Mathematics II (Loeb ed., London 1941) 614-17, with G. 
Downey, ·Pappus of Alexandria on Architectural Studies," Isis 38 (1948) 
197-200, and ·Byzantine Architects: Their Training and Methods," Byzan­
tion 18 (1946--48) 99-118. 

70 On the question of ages and dates see supra 2. 



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ALAN CAMERON 123 

fessional architect all his life, teaching pupils in the intervals 
between commissions. 

Inasmuch as it may be essentially Isidore's text of Archimedes 
we read today, he may be said to have played a central role in 
the transmission of the text. But, like Theon's Ptolemy and 
Eutocius' Apollonius, it -w-as surely a text that rested on 
Isidore's own judgment rather than collation of MSS. Since this 
was the text that had formed the basis of Eutocius' study of 
Archimedes in Isidore's school, it is hardly surprising that he 
should have used it as the basis for his own commentary. But 
this does not mean that he saw it as the last word on the text of 
Archimedes. At p.130.29f he announces a spectacular discovery 
of his own: that "old book" containing theorems which, despite 
some corruptions, seemed to correspond to a promise of 
Archimedes unfulfilled in extant editions and explained quite 
otherwise by previous commentators. The terminology and 
traces of Doric convinced him (as they have convinced 
modern students 71 ) that he had actually found a missing 
fragment of Archimedes/2 

This brings us at last to the meaning of napava:ytyvrooKEtV. A 
search of the computer files of the Thesaurus Linguae Graecae 
allows this rare word to be traced from fourth-century Athens 
down to the age of Theon and Eutocius. Its standard, well docu­
mented meaning is 'read aloud for the purpose of checking or 
comparing one document against another'. 

Particularly revealing is a passage in Ps.-Plutarch (Lives of the 
Ten Orators 841F ): Lycurgus enacted a law that the tragedies of 
Aeschylus, Sophocles, and Euripides should be written out and 
kept in the public archives (tae; tpayq>oiae; auto>v £v KOtVCP 
ypa'l'aJlEVO'Ue; <j)'\)A.a.ttEtV); and that the city clerk read them out 
to the actors to compare their texts; and that it be unlawful to 
depart from the authorized text in acting (Kat tOV tile; nOAEOOe; 
ypaJlJlatEa napavaytyvrooKEtV tOLe; unOKptvo'UJlEVOte;' OUK £~­
ELvat yap (nap ') aUtae; imoKpivE08at). Bernardakis' supple­
ment seems to be the neatest way to obtain the required sense: 
Lycurgus' law was evidently intended to stop "the growing cor-

71 Heath (supra n.6) 540f; P. M. Fraser, Ptolemaic Alexandria (Oxford 1972) 
II 578. 

72 Nor is this the only occasion on which Eutocius collated MSS. He goes on 
to quote Dionysodorus' solution of this same problem (153.15f), noting that 
the corruptions of the text were present in every MS. he had inspected. 



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124 ISIDORE OF MILETUS AND HYPATIA 

ruption of the tragic texts by actors' interpolations. ~73 What the 
clerk did was read out the authorized text so that actors could 
check their versions against it. Then there is Porphyry's quota­
tion of a letter from Longinus to himself complaining that his 
copies of Plotinus' writings are full of errors: "I should be very 
glad if you could send me accurately written copies, simply to 
read for the purpose of comparison ('tou 1tapavayvoovat Jlovov) 
and then return ~ (Plot. 19.29, tr. Armstron g). This sense is 
common in the Attic orators: e.g. Aeschin. In Ctes. 201, 'tOUC; 
VOJlOUC; 'tip 'VllCPlOJla'tt 1tapavayvoovat ("read by way of com­
parison"74); 250, 'tCxC; E1tlO'tOACxC; aAAtlAolC; 1tapavaytyvooKoUOlV 
("read and compare with each other"'). So often of reading 
documents (usually laws) aloud: Dem. De Cor. 267, J,Lap'tuplac; 
... 1tap' aC; 1tapavclyvro6l Kal ou J,LOt 'tac; PtlOElC;; Aeschin. In 
Ctes. 187, 1tapavclyvro6l OTt Kal 0 y£ypacpE K't1l0lcpoov; De fa Is. 
leg. 60, 1tapavclyvro6l Otl JlOl Kal 'to ~llJloo6£vouc; vilCPlOJla; 91; 
Isoc. Paneg. 17; Polyb. 2.12.4, 'tCx 1tE1tpaYJ,L£va OlE~llA6ov Kal'tCxC; 
ouv6tlKaC; 1tapav£yvrooav; cf 3.21.5, 15.25.5; III Mace. 1.12, 'tou 
oE VOJ,LOU 1tapavayvroo6Ev'tOC;; Diod. 1.70.9, 73.4; 15.3.6; Philo In 
Flacc. 100; Jos. Vito 260, AJ 10.58; Apollod. Bib/. 2.64; Euseb. 
Praep.Evang. 8.5.1; Athanasius PC 28.912, 944; Basil PC 31.1437; 
Joh. Chrys. PC 55.611, 614. In many of these passages there is a 
clear implication that the text is beng read publicly so that 
everyone can check what it says: for example, Libanius Decl. 
16.1.49: olov, Ei 1tapavoJlrov ypacpTt 'to KPlVOJlEVOV EO'tt, 1tapav E­
yvooo6Ttoav ot. VOJ,LOl. 'tCx 'tou 'V1lcplOJla'toc; PtlJ,La'ta Ei Olacprovlav 
'ttvCx EXEt, JlEJla6tlKa'tE. Compare also Letter to Aristeas 299, an 
account of how everything Ptolemy said and did during his 
audiences was written down and "read out'" (1tapavaYlvoooE'tal) 
the following day, "and if any procedure is found incorrect it re­
ceives rectification" (tr. Hadas). 

There are also several examples in late writers 75 of the gerun­
dive 1tapavayvroo'ttKoC;, where the reference is to a document 
required to be formally read aloud: e.g. Palladius Dial. de vita 
loan. Chrysos. p.47.20 Coleman-Norton, 1tapavayvroo'ttKoV 
EX0J,LEV J,Lovov· 1tOl..,oa'tE au'to avayvroo61lval; and Photius Bib/. 
cod. 162 (l05a.20 Bekker, II 129 Henry», Eypa'VEv E1tlO'tOATtV 

7J R. Pfeiffer, A History of Classical Scholarship (Oxford 1968) 82; Ptolemy 
III is later said to have borrowed this authorized text and never returned it. 

74 So T. Gwatkin and E. S. Shuckburgh in their still useful commentary of 
1890. 

75 See Lampe, PGL S.'V. (p.l022). 



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ALAN CAMERON 125 

EUOEJ3tcp (1tUPUVUyvroO'tl1(OV OE 1(UAEl 'tllv E1ttO'tOATtV), OP1(Ot<; 
ul)'tov d<; 't1)v 'tuu'tll<; avayvrootv E1(1(UAoUJlEVO<;. Evidently the 
letters are to be read aloud so that there should be no mis­
understanding; in the second case the writer actually binds the 
recipient with an oath to do so. 

So from first to last the word seems to imply reading with 
care and accuracy. If a single English word has to be picked to 
translate it, 'check' or 'revise' might be best, so long as a caveat 
is added. There does not seem to be a single text that suggests 
revision in the sense of addition or expansion,76 the sense re­
quired if either Hypatia or Isidore had added new material to 
the commentaries of Theon and Eutocius respectively in the 
way envisaged (for example) by W. Knorr. Indeed, in the case 
of the laws and Christian texts specified in virtually all the texts 
listed above, the purpose of the reading is precisely to establish 
that nothing has been added or altered. But it would be a 
perfectly satisfactory word to characterize the careful reading 
and checking that went to produce the sort of editions here 
under discussion. It corresponds to the primary meaning of 
Latin recognoscere, "to examine, check (a document), in order 
to establish authenticity, accuracy, etc." 77 

The linking of two names in all the headings and explicits 
under discussion might bring to mind the numerous subscrip­
tiones in Latin MSS. dating from this period where the owner 
names the man who has collated the text with him; he is often a 
professor, and is named as a sort of guarantee of the purity of 
the text. For example Vettius Agorius Basilius Mavortius ... legi 
et ut potui emendavi conferente mihi magistro Felice oratore 
urbis Romae (Hor. Epodes); Felix ... emendabam contra 
legente Deuterio scholastico (Martianus Capella).78 But the 
parallel is not exact. The subscriptores in these MSS. are not the 
authors, but (often aristocratic) owners, anxious to ensure that 
their calligraphic copies had an accurate text. The only way to 

76 Theon's supplements to Euclid do not count as additions of substance. 
77 OLD s.v. 1b (p.1583). So already the first thoughts of Heiberg (supra n.2: 

359). While acknowledging that the basic meaning of 1tapavay\yvcOO'1C£tv was 
"nebenbei Ie sen, d.h. conferiren," he reckoned that "hiervon is aber kein 
we iter Schritt zu der Bedeutung: eine Ausgabe mit andern vergleichen, eine 
Text recension besorgen." In his edition (supra n.1: IIP xciii n.1) he glossed the 
word "' recognoscere vel recensere." 

78 I have discussed these two cases in CP 81 (1986) 320ff; for other examples 
see J. E. G. Zetzel, Latin Textual Criticism in Antiquity (N ew York 1981) Ch. 
x. 



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126 ISIDORE OF MILETUS AND HYPATIA 

do this was to hire a competent person to collate every word 
against another copy certified as reliable. And the subscrip­
tiones almost invariably use one or both of the words emendare 
or conferre, making it clear that correction and collation is the 
point of the activity. Neither Theon nor Eutocius uses either of 
the two standard Greek equivalents, Otop8ouv and a.v'tt~aA.­
AEtV.79 

Hypatia and Isidore did more than proofread somebody else's 
text. They constituted their own, an activity for which 1[ClPClVCl­

'Y1:yvcOO1Cnv became the technical term. It was evidently a new 
term. Its absence from the voluminous Homer scholia 80 is 
proof enough of this. It is not a term ever applied to what 
Zenodotus, Aristophanes, or Aristarchus did to the text of 
Homer. This is perhaps because it was a different sort of 
activity. The text of Homer was judged by the criteria of 
'fittingness', MS. attestation, or linguistic usage; variants in Aris­
totle likewise by the last two criteria in addition to philosophical 
considerations. Both groups of scholars were trying to establish 
what their author wrote and what it meant. In the writings of 
the mathematicians an altogether different criterion was para­
mount: mathematical correctness. Was the proof right? The 
mathematicians were read quite simply to learn mathematics. 
To this end mistakes were naturally corrected. If a demonstra­
tion could be improved, it was. Not even the language was 
sacrosanct; as Eutocius' discussion of his new Archimedes frag­
ment shows him well aware, both dialect and even terminology 
were modernised. The point was to produce a text that the 
professor's students could read and understand. The purpose of 
their studies was utilitarian. Some of them would go on to 
become architects. Practical considerations were understand­
ably predominant. There was no reason why Otop8ouv should 
not have served for this sort of editing as well, but it is not 
surprising that a different term came to be used. 

Of course, Hypatia may have contributed more to her 
father's enterprise than a corrected text. Since she never mar­
ried, she may (as in Kingsley's novel Hypatia) have continued 
to live in his house. They had no doubt discussed the problems 

79 R. Devreesse, Introduction a l'etude des manuscrits grecs (Paris 1954) 83ff, 
123f; LS] s.vv.; E. G. Turner, Greek Manuscripts of the Ancient World 2, ed. P. 
J. Parsons (=BICS Suppl. 46 [London 1987]) 15f. 

80 It is not registered, at any rate, in J. Baar, Index zu den Ilias-Scholien 
(Baden-Baden 1961). 



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ALAN CAMERON 127 

of the Almagest over many years, and Theon may have 
included many of her ideas. But that is a possibility based on 
general considerations of probability; it is not implied by what 
Theon says in the heading to Book III. 

As for Isidore's contributions to Eutocius, that is a different 
matter. On the one hand, Eutocius did study Archimedes with 
Isidore and perhaps copied his text from Isidore's personal 
exemplar. Obviously we should expect to find some of Isi­
dore's ideas in Eutocius' commentary. On the other hand, to 
judge from his one reference to Isidore in his commentary 
(p.84.8) and the scrupulous account of an original contribution 
of Isidore by the anonymous author of Euclid XV, we should 
not expect to find Eutocius presenting original ideas of Isidore 
as his own. Furthermore, nothing Eutocius says suggests that 
Isidore was directing the work that resulted in his commentary, 
was present while he did it, or criticised it before publication. 
On the contrary, it was not to Isidore that Eutocius dedicated 
his De sphaera et cylindro, but to Ammonius (p.2.1S Heiberg), 
whom he praises as no less a mathematician than a philosopher. 
There is good evidence for Ammonius' mathematical expertise, 
and another of his pupils, Olympiodorus, writes competently 
on astronomy.81 All four books of the later commentary on the 
Conica of Apollonius are dedicated in the warmest terms to 
Anthemius. The commentary on In dimensionem circuli, based 
on Isidore's text, has no dedication at all. The commentary on 
De planorum aequilibriis is dedicated to an unidentifiable "most 
noble Peter'" and the explicits in the same Florentine MS. that in 
the other three works mention Isidore's edition here say only 
"Commentary of Eutocius of Ascalon .... '" Apparently Isidore's 
edition did not include this work. The available evidence does 
not suggest that he was the "onlie begetter'" of Eutocius' studies 
on Archimedes. 82 

COLUMBIA UNIVERSITY 
September, 1990 

81 Neugebauer (supra n.10) 1037, 1043ff. 
82 I am grateful to Jacqueline Long, Henry Mendell, Dirk Obbink, Anne 

Tihon, Gerald Toomer, and Alex Tulin for comments on an earlier draft; and 
above all to Wilbur Knorr for generously showing me the relevant parts of his 
Textual Studies in Ancient and Medieval Geometry before publicaton.