Guest post from
Sonja Brentjes

A few weeks ago I
posted a couple of reviews of recent volumes published from the Brethren of
Purity’s epistles series. In part of it, I made a number of blunders which
Sonja Brentjes pointed out and suggested I should correct. It's a pleasure to have her as a guest on my blog. To do that, here is
her review of the volume on epistles 1 and 2.

*Epistles of the Brethren of Purity. On Arithmetic and Geometry. An Arabic Critical Edition and English Translation of EPISTLES 1 & 2*, Edited and Translated by Nader El-Bizri, with a Foreword. Oxford: Oxford University Press in association with The Institute of Ismaili Studies, 2012.

This book is part of
the larger project to produce a critical edition of the 52 epistles composed
presumably in the 10

^{th}century (one dating proposal considers also the first half of the 11^{th}century) by a group of men, called the Brethren of Purity, who lived probably in Basra, may have been of Persian origin and may have adhered to Shiʿi or more specifically Ismaili beliefs (such an adherence is claimed by both the Imami Shiʿa and the Ismailis as the second institutional publisher of the series indicates, but doubted by some academics). The book’s editor and translator, Nader el-Bizri, is also the current chief editor of the entire project.
The present book
contains the first two of the 52 epistles treating number theory according to
Nikomachos of Gerasa (2

^{nd}c) and elementary Euclidean geometry combined with geometrical knowledge of the craftsmen in Arabic and an English translation. Before the translation is the Foreword, mentioned on the book cover, an introduction and a so-called technical introduction. After the English translation follows an appendix to the second epistle, a selected biography, a subject index and a geographical index of places. Before the Arabic edition come an Arabic appendix and two indices (subject matter, names).
There are three
previous translations of the first epistle (two in German (Dieterici 1868,
reprint 1969, Brentjes 1984) and one in English (Goldstein 1964)) and one
German translation of the second (Dieterici 1865 (vol. III), reprint 1969) as
well as several editions of the entire corpus (Bombay 1887-89, Cairo 1374/1928, Beirut 1957, Beirut-Paris 1995) and partial editions. None
of the editions is considered to be a critical one. Hence the effort of the Institute of Ismaili Studies to prepare such a critical edition. Here begin, however,
the problems. Not only is there today widespread doubt in general that
something like an urtext can indeed be reconstructed for any text and author,
there is also serious doubt that such a project is possible at all in particular
for the epistles of the Brethren as Paul E. Walker explained in his talk at
this year’s meeting of the American Oriental Society in Portland, March 15-18
(What was the original form of the

*Rasā᾿il Ikhwān al-**Ṣ**afā᾿*?). In his abstracts, he states the following:” A recent project undertaken by the Institute of Ismaili Studies and a team of scholars aims to produce a critical edition of this text. However work so far has revealed major problems with establishing the exact nature of the original work. The oldest and best manuscripts do not agree. Information in the existing Bombay-Cairo- Beirut edition suggests strongly that that version is itself Fatimid (or based on a Fatimid era copy). It thus may predate all of the known mss. Wide discrepancies among these textual sources indicate surely that there never was a single version of the Epistles, but instead a jumble of alternates with various additions and alterations perhaps contributed by early editors and copyists, even by the Ikhwān themselves.“ (http://www.umich.edu/~aos/2013/Abstracts2013.pdf, p. 51)
El-Bizri was aware of the difficulties presented by
the different textual versions, but chose the oldest complete manuscript (MS
Istanbul, Süleymaniye, Atif Efendi 1681 (dated 578h, i.e. 1182) as his basis
for the edition and translation, which he altered at times by adding marginalia
or passages from six other manuscripts and one printed edition (Beirut 1957).
The problem with his approach is that he admits clearly that none of the other
six manuscripts nor the text of the Beirut edition have the text of Atif Efendi
1681 as their archetype. He concludes that no stemma can be established (pp.
58f). In relationship to the two epistles published in this book, this
evaluation applies, according to el-Bizri, in particular to the second one on
geometry. Moreover, el-Bizri states clearly that Atif Efendi 1681 itself does
not always offer the most reliable text (p. 51). These comments support Walker’s
stance that a critical edition of the epistles is impossible. In regard to the
two epistles presented in this book, el-Bizri emphasizes that the difficulties
and differences concern in particular the part on geometry (p. 59). Hence, any
reader of the work should be aware that what s/he will be reading is just one
among several possible variants of the second epistle.

Beyond this matter
of principle, the Arabic texts and their English translations suffer under
severe shortcomings that reflect el-Bizri’s lack of experience in history of
mathematics in Antiquity and Islamicate societies, as a translator of a
technical text and as an editor. Moreover, he misunderstood or misinterpreted
more than once Arabic passages and mathematical statements. Since these
shortcomings permeate the entire book, the space provided for the review does
not suffice for presenting a list of all these different kinds of mistakes.
They are particularly frequent in the chapter on number theory, where almost
every other page contains several of them. Some of the problems become already
visible in the introductions. There, el-Bizri relies primarily on a few works
of the historian of mathematics in Islamicate societies Roshdi Rashed, whose
historiographical positions and modernizing transformations of medieval
mathematics are not shared by many colleagues in the field. Due to his
unfamiliarity with the subject matter and the historiographical issues at
stake, el-Bizri’s summary even trivializes Rashed’s judgments.

The Arabic text and
its English translation are marred by numerous kinds of mistakes and wrong
decisions, the English translation more so than the Arabic edition. They show
el-Bizri’s severe lack of expertise as editor, translator and historian of
mathematics. The available space for reviewing does not allow me to give a
survey of these mistakes with examples. Thus I decided to describe them in a
general manner without specific examples.

1.
Mistakes
in the Arabic texts

The mistakes in the
Arabic texts result primarily from the editorial position taken by el-Bizri and
the unclear procedures he followed. They encompass questionable decisions
concerning the inclusion of marginalia and alternative readings, decisions to
preserve clearly wrong sequences of textual passages, omissions of most likely
original passages and the occasional modernizing changes of the medieval text. In
addition, there are several typing and vocalization errors.

2.
Mistakes
in the English translation

The mistakes in the
English translation in contrast are manifold. They concern wrong decisions in
regard to mathematical terminology, the lack of understanding of medieval technical
language as well as historical changes in grammar or semantic, the omission of parts
of the Arabic text, which indicate shortcomings in proofreading, and the
replacement of medieval numerical notations by modern forms. The desire to
produce a flowing english text has misled the translator to disregard issues of
content.

a.
Mathematical
terminology, misunderstood medieval technical language and historical changes
of language

The content of the
two epistles is elementary and well known through English translations of its
Greek fundaments in Euclid’s

*Elements*and Nicomachus’*Introduction to Arithmetic*. As in the case with decisions on editorial issues, el-Bizri chose different approaches when translating. In a number of cases he translated, correctly so, literally, while in other cases, where such a literal rendering would have suited the text and its sources equally well, he replaced the terms by unusual expressions that have no background in the sources nor in modern mathematical language.
The opposite variant
of inappropriate decision when translating can also be found, namely when translating
one of two related Arabic technical terms not literally, but according to its
mathematical meaning and contemporary naming, but the second, in contrast, in a
literal manner, which does not make sense mathematically.

The third case, more
often appearing than the two previous ones, is the wrong translation, either
literal or interpretively, of a mathematical term.

b.
Omissions
and additions

Several omissions of
passages extant in the Arabic edition document in the English translation
highlight the lack of care when proofreading. The continued additions to the
translation, clearly marked by square brackets, of elementary mathematical
explanations, elementary textual content already provided by the text itself in
earlier passages and undisputed, well-established Arabic mathematical terms
with their Greek, incorrectly transliterated equivalents are as a rule
superfluous, at times false and should be placed in those cases, where they are
valid, in the footnotes or be discussed in a commentary.

c.
Problems
in regard to content

This lack of
expertise comes also to the fore in el-Bizri’s problems with comprehending the
language of the two epistles and its transformation into a modernized English
text. A continuously occurring issue is the interpretation of expressions
standing for finite or infinite repetitition of procedures. Phrases like
bāligha mā bāligha do not indicate infinite, but finite repetitions.
Expressions like ilā lā nihāya, however, mark clearly infinity. In some cases
like the summation of series the confusion between these two types of
expressions yields wrong mathematical statements in the English text. In addition to such mistakes that probably
result from applying modern understandings to medieval concepts substantial
mistranslations of longer passages also occur.

3.
Mathematical
mistakes

Some of the
mathematical mistakes are the result of wrong translating decisions, while
others stem from a desire to adapt medieval statement to forms taught in
secondary schools today. This kind of modification illustrates el-Bizri’s
unfamiliarity with standards in history of mathematics and the widely agreed
upon rule that translations should preserve the kind and level of mathematical
knowledge and practice of the original and avoid transforming them into something
that belongs to a different period and different mathematical culture. Finally
there are several elementary technical mistakes in the translation of the
mathematical content.

4.
Historical
mistakes and omissions

These items consist
of incomplete or false historical information provided by the editor.

Numerous of
el-Bizri’s mistakes could have been avoided, if he had checked the English
translation of Nikomachos’ Introduction to Arithmetic and the German and
English translations of the two epistles presented in this book. The problems
with the editorial decisions as well as the inappropriate additions to the
translated text could have been avoided in most cases, if he had consulted
contemporary editions and translations of Arabic or Latin mathematical and
philosophical texts by other colleagues.

Sonja Brentjes

MPIWG, Berlin

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