This book brings together a new edition of both Victorius of Aquitaine's Calculus (henceforward Calculus) and Abbo of Fleury's Commentary (henceforward Commentary). The presence of the edited text of the Calculus is of great benefit in reading Abbo's Commentary. This edition is based on one manuscript, F (Berlin, Staatsbibliothek zu Berlin--Preussicher Kulturbesitz, MS. Phill. 1833) which contains both the Calculus and the Commentary, and was copied in the late tenth or early eleventh century. This is the manuscript closest to Abbo and may have been compiled under Abbo's own direction. One of the particular strengths of this edition is that it makes use of all the seven extant manuscripts of the Commentary (something which no previous edition has done), and it gives a clear indication of all the variants and emendations. The editorial procedure is clearly established and the fact that the same principles have been applied to both texts edited here can only be a benefit.
The introduction to the edition provides a clear summary of the life and works of Abbo of Fleury in addition to a more detailed outline of the Calculus itself and the impact which this text may have had on late tenth-century mathematical scholarship. Following an explanation of the contents of each table which features in the subsequent edition of the Calculus, the author gives a summation of the content of the Commentary, using the section and paragraph numbers given in the edition. This summary is clear and easy to use and enables an easy navigation of the Commentary for the reader who wishes to locate specific parts of the text rather than study it in its entirety. The glossary of unusual words, usages and technical terms included after the text of the Commentary is useful for the scholar or student who is unfamiliar with the material; indeed it is useful for anyone who is familiar with Abbo and his Latin, which is firmly rooted in the hermeneutic style of the late tenth-century. The three indices (index nominum, index auctorum and index verborum potorium) again ensure easy navigation of complex texts.
The chief criticism to be made about this work is the brevity of some aspects of the introduction. For example, there is no clear statement as to why a new edition of this text is needed. It becomes apparent from reading the bibliography that this is the first edition to take into consideration all the available manuscripts and to present the edited text in its entirety, but no such assertions are made by the author herself. The descriptions of the manuscripts themselves are a little short; this reviewer would have liked more detail of the contents of the manuscripts in question in order to see how and where the Calculus and Commentary are placed in them, which could give an indication of use and potential audience for these texts.
More detail could be provided on Abbo's life and works and in particular on his association with Ramsey. Given the title of the work: Abbo of Fleury and Ramsey: Commentary on the Calculus of Victorius of Aquitaine remarkably little mention is made of Ramsey Abbey. In the brief biography of Abbo presented in the introduction, the author states that Abbo was a teacher at Ramsey abbey during the period 985 to autumn 987. In the following section, however, when listing Abbo's works, she states "Abbo's Commentary on the Calculus probably dates from this period, the early 980s, written at the request of his brothers (presumably the monks of Fleury)" (xiv). This seems to present something of a conundrum: if the work was potentially composed before Abbo went to Ramsey and at the request of the Fleury monks, why the association of the work with Ramsey in the title? One explanation for the use of the phrase "Abbo of Fleury and Ramsey" in the title of the book may be that it was an allusion to one of Abbo's pupils at Ramsey, Byrhtferth; Abbo's influence can be seen in a number of Byrhtferth's works, particularly the computistical texts copied into Oxford, St John's College, MS.17 and attributed to Byrhtferth and also Byrhtferth's commentary on computus known as the Enchiridion. Byrhtferth is briefly mentioned as a pupil of Abbo's a number of times in the introduction, but a clear connection between the Commentary and Ramsey is never firmly established.
Another minor criticism is the statement made in the Introduction that "Monastic reform in England, including the drafting of the Regularis Concordia, was influenced by Fleury observance" (xii). This statement fails to take into account much of the recent scholarship on both monastic reform in tenth-century England and the Regularis Concordia itself. Whilst not denying that Fleury and its observance had a role in influencing English monastic practice at this time, there are important questions which need to be addressed relating to the nature of 'the reform,' how widespread it was and the degree of unity it possessed. If the author is wanting (as appears to be the case from the title of the book) to make a connection between Abbo, his Commentary and Ramsey--and thereby Oswald and one element of English monasticism--then some acknowledgement of the current scholarship on English monasticism is necessary; a footnote citing Catherine Cubitt's review article discussing the three collections of essays on Dunstan, Aethelwold and Oswald, is all that would be needed [[1]].
More detail of the manuscripts and more discussion of Abbo's relationship with Ramsey would also enable scholars to refine our understanding of the role of both Abbo and his Commentary in Continental and English monasticism of the late tenth and early eleventh centuries. Overall, however, this is a welcome addition to the material available to the scholar of Early Medieval mathematics and philosophy and the criticisms made are, in effect, minor quibbles.
NOTES
[[1]] Catherine Cubitt, "Review Article: the tenth-century Benedictine Reform in England," Early Medieval Europe 6 (1997): 77-94.