other thirteenth-century mathematician. The Tractatus minutiarum on fractions seems to be a second part of the Communis et consuetus – they are often found together in the manuscripts. The Demonstratio de minutiius likewise is linked to the Demonstratio de algorismo, and contains and expands the propositions found in the Tractatus minutiarum – again a re-edition of the original text. The Algorismus demonstratus is a spurious attribution although for a long time this item was ascribed to Jordanus. Up until Eneström began to sort out the various treatises, the Algorismus demonstratus – since it was the only one published (ed. Johannes Schöner, Nuremberg, 1543) – was the heading under which all the treatises were grouped. Eneström thought it highly unlikely, however, that this version was the work of Jordanus since no manuscript ascribes it to him (if they give an author, it is generally a Magister Gernarus, or Gerhardus or Gernandus). The first part of this treatise (also known as the Algorismus de integris) contains definitions, axioms and 43 propositions. The second part (the Algorismus de minutiis) contains definitions and 42 propositions. Eneström shows that while different from the algorismi treatises of Jordanus, the Algorismus demonstratus is still closely related to them. Arithmetic: The De elementis arismetice artis This treatise on arithmetic contains over 400 propositions divided into ten books. There are three versions or editions in manuscript form, the second one with different or expanded proofs than found in the first, and a number of propositions added at the end; the third version inserts the added propositions into their logical position in the text, and again changed some of the proofs. Jordanus’ aim was to write a complete summary of arithmetic, similar to what Euclid had done for geometry. Jordanus collected and organized the whole field of arithmetic, based both on Euclid’s work and on that of Boethius. Definitions, axioms and postulates lead to propositions with proofs which are somewhat sketchy at times, leaving the reader to complete the argument. Here also Jordanus uses letters to represent numbers, but numerical examples, of the type found in the De numeris datis, are not given. Algebra: The De numeris datis The editor of this treatise on algebra, Barnabas Hughes, has found two sets of manuscripts for this text, one containing 95 propositions, the other, 113. As well some of the common propositions have different proofs. There are also 4 digests or revisions