We have developed a software DRaFT which enables easy and accurate reproduction of mathematical diagrams which appear in manuscripts. The reproduction of the diagrams in major manuscripts of following works has been published: Euclid’s ElementsBooks VI, XI, XII, XIII (including those of Book XII in Bologna manuscript, which are considerably DIFFERENT from other traditions, and have been inedited), Arabic version of Menalaus’ Spherics by Al-Harawi. The reproduction as well as the software is available at http://www.greekmath.org. We have also made some suggestions concerning the principle of critical assessment of variants of diagrams in different manuscripts

In the period 2011/7/1-2012/3/31, we have made progress on a number of key issues of the project. (1) We have worked on the Arabic edition and English translation of the source text. (2) We have examined one of the key manuscripts (Leiden Or. 399) in person and taken photographs. (3) We have decided on the tools for constructing the website and built an example site (http://www.aoni.waseda.jp/sidoli/theodosius_spherics_constructions.html). We have now discovered that the two manuscripts Ahmet III 3464 (A) and Leiden Or. 399 (L) contain a significantly different version of the text than the Kraus manuscript (K), which is a copy of a related manuscript tradition. Hence, we are editing two different versions. The LA text will appear in the final monograph, accompanied with English translation and commentaries. Since we are also editing the K manuscript, we may publish this separately at a later date, as a critical Arabic edition, with no translation. We have edited, and translated more than three quarters of the text and we have written much of the introductory material. Sidoli was in Leiden 2012/3/30-2012/4/02 and visited the Leiden University Library to inspect the L manuscript. Photos were taken of many of the pages that contain material that is difficult to read in the microfilms. This will help in editing and proofreading. Along with a research assistant, Sidoli has compared the advantages of Cinderella(R) and the Geometry Applet(R) for producing Java-enabled diagrams of spherical geometry. By experimenting with a related text (Theodosius’Spherics, for which there is an unpublished English translation), we were able to determine that Geometry Applet(R) is suitable for our needs. We have made an example website to test out the features we will implement in the full site: http://www.aoni.waseda.jp/sidoli/theodosius_spherics_constructions.html

Report on the progress of the research on Menelaus's Spherics in medieval Arabic sources (メネラオス『球面論』の中世版の検討).In the first year of this project, we have acquired all of the necessary research materials, made a preliminary reading of the manuscripts and begun to edit and translate the text. The final product will be a monograph study of the text, including a critical edition of Menelaus' Spherics, English translation and mathematical and philological commentary. We have acquired microfilms of the following manuscripts: Ahmet III 3464 (A), Leiden Or. 399 (L), Kraus MB (K). These are the only known manuscripts that contain al-Harawi's verion of Menelaus' Spherics. We have also acquired a number of manuscripts of al-Tusi's later version of the Menelaus' Spherics (Princeton Garrett 105B, Copenhagen AC 27, Tehran Tabriz NL 3484). We have also had these images transferred to electronic files, to facilitate study. We have acquired the essential books and papers related to this project, so that we will have the secondary literature readily available as we proceed with our research. In the first year, we have made a preliminary reading of the three manuscripts which indicates that A and L are versions of the original al-Harawi edition of the text, whereas K is a heavily edited redaction, which appears to stem from the A tradition. Hence, we have begun an edition and translation of the text based on AL. The variations of K are indicated in the critical apparatus, but are generally not included in the edited text itself. Nathan SIDOLI has completed about 50 pages of edition and translation, and Takanori KUSUBA (Osaka University of Economics) has completed about the same number of pages. Kusuba is working on the first chapter of the text, while Sidoli is working on the second and third chapters. At this rate of progress, the edition and translation will be done in the next year, and it will take another six months to a year to produce a monograph for publication.