Introduction.- On Parts of Parts and Ascending Continued Fractions: An Investigation of the Origins and Spread of a Peculiar System.- A Note on Old Babylonian Computational Techniques.- On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six "Algebras".- Mahavira's Geometrical Problems: Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages.- Sanskrit-Prakrit Interaction in Elementary Mathematics as Reflected in Arabic and Italian Formulations of the Rule of Three - and Something More on the Rule Elsewhere.- Geometrical Patterns in the Pre-classical Greek Area: Prospecting the Borderland between Decoration, Art, and Structural Inquiry.- Broad Lines - A Forgotten Geometrical Ambiguity.- Concerning the Position of "Heron's Formula" in the Metrica (with a Platonic note).- Mero, ps-Heron, and Near Eastern Practical Geometry: An Investigation of Metrica, Geometrica, and other Treatises.- Which Kindof Mathematics was Known and Referred to by Those Who Wanted to Integrate Mathemaitcs in «Wisdom» - Neopythagoreans and others?.- The Rare Traces of Constructional Procedures in "Practical Geometries".- About the Italian Background to Rechenmeister Mathematics.- The "Unknown Heritage" - Trace of a Forgotten Locus of Mathematical Sophistication.- A diluted al-Karaji in Abbacus Mathematics.- "Proportions" in and around the Italian Abbacus Tradition.- Archimedes - Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance.- Existence, Sustainability, and Counterfactuality: Observations on the Status of Mathematics According to Aristotle, Euclid, and Others.- Conceptual Divergence - Cannons and Taboos - and Critique.- Tertium non datur, or, On Reasoning Styles in Early Mathematics.- Embedding - Multi-purpose Device for Understanding Mathematics and Its Development, or Empty Generalization?.- What is "Geometric Algebra", and what has it been in Historiography?.- State, "Justice", Scribal Culture and Mathematics in Ancient Mesopotamia. Sarton Lecture 2008.- How to Educate a Kapo: Reflections on the Absence of a Culture of Mathematical Problems in Ur III.- A Hypothetical History of Old Babylonian Mathematics - Places, passages, Stages, Development.- Written Mathematical Traditions in Ancient Mesopotamia: Knowledge, ignorance, and reasonable guesses.- Mesopotamian Mathematics, Seen "From the Inside" (by Assyriologists) and "from the outside" (by Historians of Mathematics).- Fibonacci - Protagonist or Witness? Who Taught Catholic Christian Europe about Mediterranean Commercial Arithmetic?.- What did Abbacus Teachers Aim at When They (Sometimes) Ended up Doing Mathematics?.- Hesitating Progress - the Slow Development toward Algebraic Sybolization in Abbacus- and Related Manuscripts, c. 1300 To c. 1550.- Embedding - Another Case of Stumbling Progress.- Baroque Mindset and New Science: A Dialectic of 17th-Century High Culture. Sarton Chair Lecture, Ghent University, 13 November 2008.
