Table Of ContentScience Networks . Historical Studies
Volume8
Edited by Erwin Hiebert and Hans Wussing
Editorial Board:
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Springer Basel AG
Hubert L.L. Busard
Menso Folkerts
Robert of Chester's (?)
Redaction of Euclid's Elements,
the so-called Adelard 11 Version
Volume I
Springer Basel AG
Authors' addresses
Dr. Hubert L. L. Busard Prof. Dr. Menso Folkerts
Herungerstraat 123 Institut für Geschichte der
NL-5911 AK Venlo Naturwissenschaften
Museumsinsel, Postfach
D-W-8000 München 26
Deutsche Bibliothek Cataloging-in-Publication Data
Busard, Hubert L. L.:
Robert of Chester's (?) redaction of Euclid's Elements, the
so-called Adelard 11 version / Hubert L. L. Busard ; Menso
Folkerts. - Basel ; Boston ; Berlin : Birkhäuser.
ISBN 978-3-0348-9708-2 ISBN 978-3-0348-8636-9 (eBook)
DOI 10.1007/978-3-0348-8636-9
NE: Folkerts, Menso:; Euklid: Elements
Vol. 1 (1992)
(Science networks; Vol. 8)
ISBN 978-3-0348-9708-2
NE:GT
This work is subject to copyright. All rights are reserved, whether the whole or part
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© 1992 Springer Basel AG
Originally published by Birkhäuser Verlag Basel in 1992
Softcover reprint ofthe hardcover 1st edition 1992
ISBN 978-3-0348-9708-2
Table of Contents
Volume I
Preface ............................................... 7
1 Introduction .......................................... 11
2 Description of the Manuscripts .............................. 33
3 Relationships between the Manuscripts . . . . . . . . . . . . . . . . . . . . . . . .. 83
4 Editorial Remarks ...................................... 91
Concordance Heiberg Text - Version II . . . . . . . . . . . . . . . . . . . . . . . . . .. 93
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 101
Euclides, Elementa
Liber I ....................... . . . . . . . . . . . . . . . . . . . . . . .. 113
Liber II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 131
Liber III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 137
Liber IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 153
Liber V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161
Liber VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 171
Liber VII ............................................. 187
Liber VIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 201
Liber IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 211
Liber X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 223
Liber XI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 265
Liber XII ............................................. 293
Liber XIII. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 311
Liber XIV 329
Liber XV ............................................. 341
Index of Latin Words ...................................... 345
Table of Contents
Volume II
Apparatus criticus
Conspectus siglorum 441
Liber I ..................................................... 445
Liber II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 487
Liber III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 499
Liber IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 527
Liber V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 539
Liber VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 563
Liber VII ................................................... 595
Liber VIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 623
Liber IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 641
Liber X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 663
Liber XI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 735
Liber XII 783
Liber XIII 807
Liber XIV 835
Liber XV 851
Addenda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 859
Preface
The Latin "Version II", till now attributed to Adelard of Bath, is edited here
for the first time. It was the most influential Euclid text in the Latin West
in the 12th and 13th centuries. As the large number of manuscripts and the
numerous quotations in other scientific and philosophical texts show, it was
far better known than the three Euclid translations made from the Arabic in
the 12th century (Adelard of Bath, version I; Hermann of Carinthia; Gerard
of Cremona). Version II became the basis of later reworkings, in which the
enunciations were taken over, but new proofs supplied; the most important
text of this kind is the redaction made by Campanus in the late 1250s, which
became the standard Latin "Euclid" in the later Middle Ages.
The introduction deals with the questions of when and by whom version II
was written. Since Marshall Clagett's fundamental article (1953) it has been
generally accepted that version II is one of three Euclid texts attributable to
Adelard of Bath. But a comparison of the text of version II with those of
versions I and III yields little or no reason to assume that Adelard was the
author of version II. Version II must have been written later than version I and
before version III; its author was acquainted with Euclid texts of the Boethius
tradition and with two of those transmitted from Arabic, version I (almost
certainly by Adelard) and the version by Hermann of Carinthia. It seems that in
the formation of version II the definitions, postulates, axioms, and enunciations
(with corollaries, if any) were collected first and the proofs added later. We are
able to give almost exact time limits for the first of these procedures: a terminus
post quem is Hermann's translation of Euclid's Elements, which seems to have
been made shortly before 1140, and a terminus ante quem is provided by the
oldest extant version II manuscript, Chartres 498, which was written by Thierry
of Chartres probably not later than 1141. Thus the enunciations must have been
compiled about 1140. There are good reasons to suppose that Robert of Chester
was the author of this compilation. Of these the most compelling are that he
was one of the very few who at this early stage could have been acquainted
with Hermann's translation, and that Hermann, Robert's friend and associate
in Spain, was a pupil of Thierry. The question of the authorship of the proofs is
more difficult. In manuscript Miinchen, Clm 13021, written between 1163 and
1168, the diagrams in some propositions of book X are lettered in the same
way as in our text; and therefore the proofs must have existed at that time.
From the style it is clear that they were written by only one person, and it is
possible that this person was Robert of Chester. He may have added the proofs
8 Preface
after the translation of the Qur'iin, finished in 1143.
There are 61 manuscripts which transmit the complete text of version II
or parts of it. We have given some account of the scientific parts of all of
them, identifying the mathematical items and giving their incipits, and have
described the general characteristics of the text of version II that it contains. It
seems impossible to construct a traditional stemm a of the manuscripts, but in
the chapter Relationships between the Manuscripts some groups and subgroups
within the manuscript tradition are noted and the more striking agreements
and differences among the manuscripts are listed. To facilitate further research
on the style of version II and its author, an Index of Latin Words is added. This
gives a reference to every instance of every word (and some terms consisting
of several words) except numerals and diagram-letters, though very common
words of no mathematical interest are listed with no references.
Because of the size of the critical apparatus, the variant readings are given
in a separate volume. This volume also contains an appendix (Addenda) in
which larger additions or alternative readings and alternative proofs found in
many manuscripts are given.
It is a great pleasure for us to acknowledge the assistance we have recei
ved from librarians and scholars. We thank all the libraries which provided
us with microfilms of their manuscripts. Professor Paul Kunitzsch gave valua
ble information about the Arabic terms, and Dr. Richard Lorch revised the
English text. Professor Bernhard Bischoff, Munich, kindly supplied informa
tion about the date and place of origin of the manuscripts from an inspection
of the microfilms. In solving the numerous software problems and preparing
the edition of the Latin text with ED MAC, Gerhard Brey gave us invaluable
help. Finally, we thank the editors of Science Networks, Professors Hiebert and
Wufiing, for accepting the edition for this series, and the Birkhauser Verlag,
especially Doris Worner and Benno Zimmermann, for help with the technical
details of publishing the book.
Venlo and Munich, August 1990
Hubert L. 1. Busard
Menso Folkerts
Volume I
