This book began with my edition of the anonymous treatise. A translation and notes seemed essential if the material of the treatise was to be understood. It then seemed that Chapter 5 of Heytesbury's Rules for Solving Sophismata, on which the treatise was based, should also be included. My translation of the Heytesbury treatise is based on a fifteenth-century edition, supplemented by readings from a few of the better manuscripts. (A critical edition from all the manuscripts, of which Chapter 5 will be mine, is now in progress under the supervision of Paul Spade, but only a few insignificant changes in the translation should be necessitated by the completed edition. ) An examination of related materials seemed reasonable, and these included Heytesbury's commentator Gaetano, as well as a chapter from a treatise by Johannes Venator (in an edition in progress provided by Francesco del Punta). It seemed unnecessary to publish Gaetano's and Venator's related works in this volume, but all their departures from Heytesbury and the anonymous treatise are noted here. I have not examined other works in the tradition in any detail. I owe a great deal to my teacher, Norman Kretzmann, not only as regards the edition and translations, but also as regards the notes, study and introduction. The referees of the typescript (to me unknown) made unusually thorough criticisms and suggestions to which I have paid close attention. The book is far better for my having done so.

Notes.- Rules for Solving Sophisms, Chapter 5: On Maxima and Minima.- 1: Introduction and basic notions.- 2: Conditions under which limits exist.- 3: Rules for the choice of limit in each case..- 4: Objections and replies concerning the general program.- 5: Objections and replies concerning the conditions under which limits exist.- 6: Objections and replies concerning the choice of limits.- Notes.- Treatise Concerning Maxima and Minima.- 1: The four-fold distinction.- 2: Exposition of the members of the distinction.- 3: Requirements for correct application of the division.- 4: Rules for choosing the correct part of the division.- 5: Doubts concerning what has been said.- Notes.- Tractatus de Maximo et Minimo.- Study.- 1. The nature of Heytesbury's "De maximo et minimo" and his theory.- 2. The tradition behind the theory.- 3. The fundamentals of the theory.- 4. Conditions for the existence of a limit.- 5. The choice of limit.- 6. Conclusion.- Notes.- Indices.- Index of names and topics.- Index of sophismata.- Scholars cited.