BUCHBESPRECHUNGEN
Paul Kunitzsch and Richard Lorch, Theodosius' Sphaerica: Arabic
and Medieval Latin translations. Stuttgart: Franz Steiner Verlag,
2010.431pp. (Boethius Band 62.) ISBN 978-3-515-09288-3.
The book under review is concerned with the Arabic and Latin traditions
of the Spherics of Theodosius of Bythinia (ca. 100 BC). This ancient Greek
mathematical work consists of three "books" or big chapters, containing (in
the Greek version) a total of 70 propositions on the sphere with figures and
proofs. Book I deals with great and small circles on the sphere, poles of these
circles, and tangent planes to the sphere. In Book II Theodosius continues
with theorems on parallel, intersecting and tangent circles on one and the
same sphere. Book III is about arcs of great circles cut off by a series of other
circles on the same sphere. Although the material in the Spherics is presented
in an abstract way, there are immediate astronomical applications and thus
the Spherics belonged to the standard astronomical curriculum in late Greek
antiquity. The Greek text was translated into Arabic at least two times, and at
least two medieval Latin translations were made from the Arabic. Lorch's
articler can be consulted for a general overview of the Arabic and Latin
tradition of the Spherics. It turns out that one of the extant Latin versions is a
literal translation of one of the extant Arabic versions. This Arabic version is
a revision by Thabit ibn Qurra of an Arabic translation made by one or more
translators. Kunitzsch and Lorch have identified the Latin translator of Thabit's
Arabic revision as Gerard of Cremona. Thabit's Arabic text and Gerard's
Latin translation are presented in the book under review on facing pages, so
readers of both Arabic and Latin can have the fascinating experience of
reading the Arabic text and Gerard's translation side by side, almost as if one
is seeing through Gerard's eyes.
Kunitzsch and Lorch have edited the Arabic version from three manuscripts.
The Latin translation is extant, in full or in part, in around 20 manuscripts, of
which l0 have been collated in the present edition. Kunitzsch and Lorch have
attempted to reconstruct Gerard's original translation. They add a critical
apparatus, concise mathematical paraphrases of the propositions in English,
and some lemmas to the Arabic text in one of the manuscripts (Istanbul,
Seray, AhmetIIl3464).
I The Transmission of Theodosius Sphaerica, in: Mathematische Probleme
im
Mittelalter. Der lateinische und arabische Sprachbereich,hrsg. von Menso Folkerts,
Wiesbaden (Harrassowitz in Komm.) 1996, pp. 159-183.
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Buchbesprechungen
Kunitzsch and Lorch state that
"[i]t is our intention to provide future
scholars with reliable information rather than to draw conclusions ourselves."
The quality of the editions is indeed excellent, but a lot of interesting information
is contained only implicitly in the book. For example, the reader who wants
to investigate the relationship between the Latin manuscripts has to do this by
himself on the basis of the critical apparatus which the authors have printed.
One may also regret the absence of an index of technical terms (Arabic-Latin).
It is hoped that such an index will be published because it will facilitate the
analysis of Gerard's translation techniques. Gerard used interesting variations;
for example he translated bu'd (distance) as elongatio in I:1 and longitudo in
I:6. In I:9 he translated the Arabic ma ("what") insightfully as spacium,
"space". In a similar way. one may investigate Thabit ibn Qurra's translation
techniques and mathematical understanding using the book under review.
As a further example, I now quote the first sentence of proposition 10 of
Book III in a literal translation. The Arabic and Latin texts are on pp. 278-81
and my translation is adapted from the English paraphrase on pp. 412-3.
Words and passages that I have added to the paraphrase are in angular brackets
< >, and words that I have deleted are in square brackets [ ]; italics are mine.
Theodosius enunciates the following theorem inThabit's and Gerard's versions:
"When the pole of the parallel circles is on the circumference of a great
circle, and two great circles cut this circle at right angles, one of them being
from the parallel circles and the other inclined to the parallel circles, and two
points are marked on the inclining circle, however they fall, on the same side
<of> [as] the great circle from among the parallel circles, and great circles
are drawn passing through the resulting points and through the pole, then the
ratio of the arc of the greatest circle of the parallel circles that falls between
the first great circle and the great circle drawn afterwards [and] so <it (i.e.,
the circle drawn afterward)> passes through the poles, to the arc of the
inclining circle that falls between these two circles, is as the ratio of the arc of
the greatest of the parallel circles that <falls between the great circles that>
pass through the pole of the parallel circles and through the marked points to
some arc which is less than the arc of the inclining circle between the points
that are marked."
This long and abstruse sentence shows Thabit's and Gerard's perfect
understanding of the subject. The Arabic and Latin versions do not contain
the slight imperfections in the paraphrase of Lorch and Kunitzsch that have
been corrected above.
The word inclined / inclining (Arabic'. ma'il , Greek: /oxos) reveals something
interesting about the Greek source that was translated into Arabic. The word
is used but never defined in the extant Greek version ofthe Spherics.The
meaning is explained in a definition in Book I of the Arabic version (pp.
14-15,345), to the effect that two planes are inclined if two straight lines in
the planes perpendicular to the line of intersection make an acute angle. We
note that the definition is not found in Book XI of Euclid' s Elements, and that
P.
KuNrrzscu & R. Loncu: Theodosius
399
the two "planes" in the definition should be understood in modern terms as
half-planes on one side ofthe line ofintersection. once this has been clarified,
an otherwise opaque proof of Proposirion III:2 (pp. zz\-z2i ,398-400) becomes
transparent. Thus the Arabic definition of inclined may well have been extant
in the Greek source. Nevertheless, the Arabic definition was dismissed as
"inutile" in the standard French translation of the spherics by paul ver Eecke2
[p. xL]. Here is what Ver Eecke has to say concerning the way in which he
believed that "les Arabes" dealt with Theodosius' work in general [p. xl-i]:
"on ne peut que regretter les alterations profondes qu'ils firent subir aux
textes originaux et en conclure que ... leurs savants ont 6t6 plus anim6s du
ddsir de s'assimiler des connaissances acquises avant eux, que p6n6tr6s de
respect pour les oeuvres dans lesquelles ces connaissances avaient 6t6
divulgu6es" [one can only regret the fundamental changes which they (the
Arabic scholars) made in the original (Greek) texts, and conclude that the
(Arabic) scholars were more motivated by the wish to assimilate knowledge
than by respect for the (Greek) works in which this knowledge was communicatedl. The present book contains ample material to refute ver Eecke's
thesis. In some cases Theodosius' thought may have been preserved more
faithfully by the Arabic and Latin versions than by the extant Greek version
that was translated by Ver Eecke.
Researchers of the ancient and medieval scientific traditions will be grateful
to Kunitzsch and Lorch for producing this excellent volume.
JeN P.
Hocslorrx*