Adelard: Euclid

In 1992 an edited edition of Adelard's Euclid was published. However, although the work had long been believed to be due to Adelard of Bath, it is now believed to be due to Robert of Chester. The work Robert of Chester's (?) redaction of Euclid's Elements, the so-called Adelard II version. Vol. I, II. (Latin), was edited by Hubert L L Busard and Menso Folkerts and published by Birkhäuser Verlag, Basel. We quote from the 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; Gherard 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 München, 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 after the translation of the Quran, finished in 1143.

There are 61 manuscripts which transmit the complete text of version II or parts of it. We give some account of the scientific parts of all of them, identifying the mathematical items and giving their incipits, and describe the general characteristics of the text of version II that it contains. It seems impossible to construct a traditional stemma 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.


JOC/EFR March 2006

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