"...
Ungleich wichtiger als die Vorgaengerschaft auf dem Gebiete des
Figurendrucks ist seit 1482 erst ermoeglichte Verbreitung
geometrischen Wissens an der Hand des im Drucke nunmehr kaeuflichen
Elementarwerkes. Wie sehr es einem Beduerfnisse entgegenkam, ist
aus der Haeufigkeit der Nachdrucke zu ermessen. Gleich im ersten
Jahre 1482 sind zweierlei Ausgaben vorhanden beide bei Ratdolt in
Venedig gedruckt, unterschieden in dem ersten Bogen, spaeterhin
uebereinstimmend. Es ist natuerlich ganz unmoeglich, zu entscheiden,
ob man hier wirklich von zwei Ausgaben zu reden hat, oder ob nur
die erste Lage noch einmal gedruck worden ist, wofuer wir allerdings
einen Grund nicht abzusehen vermoegen. Eine weitere Druckgebung hat
1486 bei Reger in Ulm stattgefunden, eine weitere 1491 bei einem
Magister Leonardo von Basel, aber ohne die Widmung an den inzwischen
1485 verstorbenen Fuersten Mocenigo. [Seite 291]
..."
This passage may be roughly rendered (in English) as follows:
"...
Much more important than the pioneering on that areas of figure
printing, was that after 1482 the knowledge of geometry could so
easily spread through the availability of a printed edition of
the Elements. How far this need was fulfilled can be measured by
the frequency of new editions. Even in the first year, 1482, two
different editions were available, both printed by Ratdolt in
Venice, which differed only with respect to the first 'Bogen'.
Naturally, it is rather impossible to decide whether one should
really speak here of a new edition, or merely of a reprinting, for
which we are unable to foresee, however, a reason. A further
printing occurred in 1486 in Ulm by Reger, and again in 1491 by a
Magister Leonardo of Basel, but without the dedication to the
prince Mocenigo - who, in the meantime, had died. [page 291]
..."
We may endlessly discuss what IS the meaning (sense) of "edition". At any
rate, I (mildly) disagree with those that state that the SECOND edition
of Euclid "Elements" was published in 1491. I agree with Cantor when he
explicitly acknowledges "Es ist natuerlich ganz unmoeglich, zu entscheiden,
ob man hier wirklich von zwei Ausgaben zu reden hat, oder ob nur die erste
Lage noch einmal gedruck worden ist, wofuer wir allerdings einen Grund nicht
abzusehen vermoegen".
Now... what ever happened to the other reference (Ulm, 1486)?
(B) Helpful references (and a few reviews!):
[1] Clagett, Marshall:
"The Medieval Latin Translations from the Arabic of the Elements of Euclid,
with Special Emphasis on the Versions of Adelard of Bath", _Isis_ vol 44,
pp 16-42, 1953.
[2] Busard, H.L.L.:
"The Translation of the Elements of Euclid from the Arabic into Latin by
Hermann of Carinthia (?), Books VII, VIII and IX.", _Janus_ vol 59,
pp 125-187, 1972.
[3] Busard, H.L.L.:
"The Translation of the Elements of Euclid from the Arabic into Latin by
Hermann of Carinthia (?). Books VII-XII.", Mathematical Centre Tracts. 84.
Amsterdam: Mathematisch Centrum, 198 pages, 1977.
[4] Busard, H.L.L.(ed.):
"The First Latin Translation of Euclid's Elements Commonly Ascribed to
Adelard of Bath. Book I-VIII and books X.36-XV.2.", Studies and Texts,
64. Toronto: Pontifical Intitute of Mediaeval Studies. VI, 425 p. 1983.
[5] Busard, H.L.L.:
"The Mediaeval Latin Translation of Euclid's Elements - Made Directly from
the Greek", Boethius, Texte und Abhandlungen zur Geschichte der Exakten
Wissenschaften, Bd. XV, Stuttgart: Franz Steiner Verlag Wiesbaden GmbH,
v+411 pages, 1987.
[6] Busard, Hubert L.L.:
"Some Early adaptations of Euclid's Elements and the Use of its Latin
Translations" in "Mathemata, Festschr. H. Gericke", Boethius 12, pp 129-164,
1985.
George A. Saliba reviewed this essay for ZfM
[ online text at http://www.emis.de/cgi-bin/MATH-item?574.01007 ]
as follows:
"This detailed article is devoted to notes taken in connection
with the two Latin editions of Euclid's Elements already published
by the author. Their interest for the general reader who is not
concerned with the variants in the edition is very limited.
For the general reader, however, the lesson to be drawn from this
study and from the one by P. Kunitzsch [ibid, 115-128 (1985;
see the review above)] is that the process of editing the Elements
of Euclid, whether in Latin or in Arabic is very difficult indeed,
for every time one thinks that he has established the stemma of one
version, a new manuscript appears to disrupt the earlier arrangements.
From a historical point of view, the interesting results reached by
P. Kunitzsch [loc. cit.] and the author point to the fact that
medieval translators, readers, and commentators were much more freer
with the text than we are, and were probably after the contents of
the texts rather than the word. As a result it would not be uncommon
that in the same manuscript certain lacunae of one version would be
filled by the corresponding segments from another, or certain comment
on a theorem or a proof would be incorporated as if it belonged to
the original text. The editorial skill required in sorting out this
material is immense. Students of history of mathematics will be
forever indebted for the works of the author in that regard.
* Busard, Hubert L.L.; Folkerts, Menso:
[7] "Robert of Chester's (?) Redaction of Euclid's Elements: The So-called
Adelard II Version. Vol. I." Science Networks. Historical Studies. 8.
Basel: Birkhaeuser, 430 pages, 1992.
[8] "Robert of Chester's (?) Redaction of Euclid's Elements: The So-called
Adelard II version. Vol. II.", Science Networks. Historical Studies. 9.
Basel: Birkhaeuser. pages 442-959, 1992. [ISBN: 3-ISSN 7643-2727]
George A. Saliba reviewed both volumes for ZfM
[ online text at http://www.emis.de/cgi-bin/MATH-item?823.01012 ]
as follows:
"The two volumes under review include the first Latin critical edition
of Euclid's Elements, usually attributed to Adelard of Bath. The first
volume (pp. 1-430) has a historical analytical introduction, description
of the manuscripts as well as the other scholarly apparatus like
editorial policy, concordance, bibliography, the text itself, and an
index, while the second volume (pp. 431-959) contains the actual
critical apparatus. When we remember that the number of manuscripts
consulted for that purpose is more than sixty, then we should not be
surprised to find the critical apparatus taking a whole volume just to
record the variant readings.
"The text itself, also dubbed as 'version II' of the Latin translation
of Euclid's Elements from Arabic, was apparently the most popular in
the Latin west, as the number of manuscripts clearly attests. It was
certainly much more frequently used than the other translations
attributed to Adelard of Bath (version I), Hermann of Corinthia, and
Gerard of Cremona. Marshall Clagett was the first to identify this
text as being a second version executed by Adelard of Bath. The present
editors subject this identification to very close analysis, and conclude
by arguing very convincingly that the text was most likely completed by
Robert of Chester, sometime around the year 1140. The oldest extant
manuscript dates to the year 1141.
"The contents of the text seem to have combined the Boethian tradition
with the Arabic one as preserved in the translations of Hermann and
Adelard. Clagett had argued in the fifties that this versions II is
only an 'abridgement' of the other version completed by Adelard. In
fact the language of the text does not offer formal proofs as one would
have expected, rather it presents schemes for proofs that one could
carry out if s/he pleases. As a result, the present editors were
forced to raise the question as to whether version II was a translation
or a compilation, and had to conclude that it was the latter. In the
following section (pp. 18-22), and after comparative analysis of the
contents with the known versions of Adelard and Hermann, they conclude
that Adelard could not have been the compiler. That leaves Robert of
Chester as the most likely candidate. But the question mark following
his name in the title reflects the belief of the editors that they
could not be certain about that.
"One of the most interesting features of this text is the heavy use
of Arabic in the 'proofs'. This does not only reveal that the
translator, whoever he might have been, was quite familiar with
Arabic, but that he also expected his readers as well to understand
such expressions as elfadhel (al-fadl) 'remainder', burrahunnu
(burhanuhu) 'its proof', alamud (al-'amud) 'perpendicular', etc.
The peculiarity of these terms is that they were not necessarily
technical in nature, and could have been translated into Latin
rather than transliterated. But for some unknown reason the
compiler did not think that he needed to do that. This situation
begs the question of the competence of the readers to understand
such terms in their transliterated forms, a question never raised
by the present editors. Instead they use this evidence to support
their argument for the authorship of Robert of Chester, and
conclude their introduction with a very short biographical sketch
of the same author.
"In sum, the question of authorship, the heavy use of transliterations
of Arabic terms in this version to the exclusion of the others, and
the detailed variants and critical apparatus assembled by the present
editors should only be considered as opening the doors for much more
serious research on the subject. The editors are to be thanked for
preparing a solid foundation for such a research."
[9] Busard, H.L.L.:
A Thirteenth-century Adaptation of Robert of Chester's Version of Euclid's
Elements", 2 vols. Algorismus. 17. Muenchen: Institut f. Geschichte der Naturwissenschaften, 559 pages, 1996. [ISBN: 3-89241-018-6/pbk]
Fellow listmember, Jens Hoeyrup, reviewed these volumes for ZfM
[ online text at http://www.emis.de/cgi-bin/MATH-item?863.01026 ]
as follows:
"With this double volume, H. L. L. Busard has given us the sixth
version of the medieval Elements, edited with his usual care. The
first part of the introduction recapitulates, as nobody without
the author's unequalled knowledge of the manuscript sources could
do it, the essentials of the history of the medieval Elements,
with particular focus on the so-called Adelard tradition; the parts
of the story that concern the Gerard version and the translation
made directly from the Greek are largely left out, as relatively
irrelevant with regard to the version that follows. The best known
pre-Campanus members of the 'Adelard family' were baptized Adelard I,
Adelard II, and Adelard III by Marshall Clagett. Adelard I, published
by H. L. L. Busard (ed.) in 1983 [4] seems really to be Adelard's
work. Version II, published by H.L.L. Busard (ed.) and I.M. Folkerts
(ed.) in 1992 [Robert of Chester's (?) redaction of Euclid's Elements,
the so-called Adelard II version (1992; Zbl 834.01002)] was by far
the most widely spread. The introduction summarizes the arguments
that its enunciations were made first and the proofs (in books I--VI,
proof sketches) later, but that everything is likely to come from the
same hand, which with high plausibility is identified as that of
Robert of Chester. Two 12th-century versions exist that were derived
from or interacted with version II but also used the Boethius tradition.
One was published by M. Folkerts (ed.) in 1970 ['Boethius' Geometrie II.
Ein mathematisches Lehrbuch des Mittelalters. (1970; Zbl 223.01007)].
The other, identified during the work on Version II, is described in
the present introduction.
"The introduction further describes the characteristics of the late
12th-century 'Adelard III' version (rebaptized Adelard IIIA) as
well as the version Adelard IIIB, no older than Jordanus's Liber
philotegni, and shows that IIIB does not descend from IIIA. Both
instead are reworkings of Version II, provided with full and formal
proofs. IIIB has certain features in common with the version 'Bonn
et al.' (from Bonn, Universitaetsbibliothek 573, the oldest
representative of the manuscript family). This is the version
published in the volumes under review. This version is shown to have
been fairly well-known in the 13th century, and to have served
together with the Anaritius commentary as fundament for the so-called
Albertus commentary (the ascription of which to Albertus Magnus, as
it is argued, seems doubtful). 'Bonn et al.' derives its definitions
and enunciations from Version II, sometimes with additional commentary
or minor changes. The proofs are new and full, in the early books very
detailed. When several cases are possible, all are proved; at times,
an aliter introduces an alternative proof. There are thus affinities
with Version IIIA, as also the Campanus version, the former probably
to be explained from a common setting and shared didactical/meta-
theoretical aims, the second from shared sources. Three propositions
on the relation between cords and arcs are inserted between books IX
and X in some of the manuscripts. The second has affinities both with
the pseudo-Jordanian De triangulis (the proof) and Jordanus's Liber
philotegni (the enunciation). If the reviewer is right in considering
De triangulis a student reportatio from lectures held over a preliminary
version of Liber philotegni (thus probably by Jordanus himself), this
might mean that the author of the insertion made use of a similar
preliminary version -- and thus, probably but not certainly, that he
was in contact with the 'Jordanian circle'. The character of 'Bonn
et al.' can be illustrated by the beginning of the proof of prop. I.
1, the construction of the equilateral triangle with a given side
[trans. JH]: For this proposition, the third postulate is needed, and
the first and the last [this proof sketch is fully unrelated to that
of Version II; a similar sketch is found in I.2, but not further on/JH].
The third is that over any point a circle may be drawn occupying any
amount of space. In agreement with this postulate, over one of the end
points of the given line you draw a circle according to the quantity of
the line. In the same way you draw a circle over he other end of the
same line according to the quantity of that line. But the point over
which a circle is drawn is called its centre. When this is done you will
see the circles cutting each other. Then in agreement with the first
postulate, which is: from any point to any to draw a line, is drawn a
line from the centre of each circle to the contact point of the
circumferences. Thus the first line will be equal to each of the others
in agreement with the last postulate [actually, with the definition of
the circle/JH], which is: all lines going from the centre to the
circumference are equal [etc.]. Volume II (= pp. 397-559) contains the
critical apparatus. No commentary is given, apart from what is found in
the introduction. The edition is thus a most welcome gift to the
community of historians of medieval mathematics, and at the same time
an invitation to further work."
(C) Now, sailing other waters, let me friendly remind you all that:
It is usually *unnecessary* to include the full text of a
previous post when replying to it. Do not quote irrelevant
segments; this will save downloading time, and disc space.
However, you may include the *relevant* TEXT that sets the
conTEXT.
The omission of accents is strongly recommended. If you do
believe that a specific reference requires accents, then a
code would be advisable.
Pertinent queries, replies, comments ... should be written
with the same standards of *thoughtfulness* and care that
apply to other *scholarly* activities.
At all times, subscribers should strive to submit posts in
a supreme and conscious effort to keep the signal-to-noise
ratio as high as possible.
Greetings from rainy Montevideo,
Julio Gonzalez Cabillon