Selected Essays on Pre- and Early Modern Mathematical Practice

Chapter 1 Introduction

Chapter 2 (Article I.1.) On Parts of Parts and Ascending Continued Fractions: An Investigation of the Origins and Spread of a Peculiar System

Chapter 3 (Article I.2.) A Note on Old Babylonian Computational Techniques

Chapter 4 (Article I.3.) On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six “Algebras”

Chapter 5 (Article I.4.) Mahāvīra’s Geometrical Problems Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages

Chapter 6 (Article I.5.) 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

Chapter 7 (Article I.6.) Geometrical Patterns in the Pre-Classical Greek Area

Chapter 8 (Article I.7.) Broad Lines – A Forgotten Geometrical Ambiguity

Chapter 9 (Article I.8.) Concerning the Position of ‘‘Heron’s Formula’’ in the Metrica (With a Platonic Note)

Chapter 10 (Article I.9.) Heron, Ps-Heron, and near Eastern Practical Geometry an Investigation of Metrica, Geometrica, and other Treatises

Chapter 11 (Article I.10.) Which Kind of Mathematics was Known and Referred to by those who wanted to Integrate Mathematics in Wisdom – Neopythagoreans and Others?

Chapter 12 (Article I.11.) The Rare Traces of Constructional Procedures in “Practical Geometries”

Chapter 13 (Article I.12.) About the Italian Background to Rechenmeister Mathematics

Chapter 14 (Article I.13.) The “Unknown Heritage” – Trace of a Forgotten Locus of Mathematical Sophistication

Chapter 15 (Article I.14.) A Diluted Al-Karajī In Abbacus Mathematics

Chapter 16 (Article I.15.) “Proportions” in and around the Italian Abbacus Tradition

Chapter 17 (Article I.16.) Archimedes – Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance

Chapter 18 (Article II.1.) Existence, Substantiality, and Counterfactuality Observations on the Status of Mathematics according to Aristotle, Euclid, and Others

Chapter 19 (Article II.2.) Conceptual Divergence – Canons and Taboos – And Critique

Chapter 20 (Article II.3.) Tertium Non Datur, or, on Reasoning Styles in Early Mathematics

Chapter 21 (Article II.4.) Embedding – Multi-purpose Device for Understanding Mathematics and its Development, or Empty Generalization?

Chapter 22 (Article II.5.) What is “Geometric Algebra”, and what has it been in Historiography?

Chapter 23 (Article II.6.) State, “Justice”, Scribal Culture and Mathematics in Ancient Mesopotamia. Sarton Lecture 2008

Chapter 24 (Article II.7.) How to Educate a KAPO Reflections on the Absence of a Culture of Mathematical Problems in Ur III

Chapter 25 (Article II.8.) A Hypothetical History of Old Babylonian Mathematics − Places, Passages, Stages, Development

Chapter 26 (Article II.9.) Written Mathematical Traditions in Ancient Mesopotamia Knowledge, Ignorance, and Reasonable Guesses

Chapter 27 (Article II.10.) Mesopotamian Mathematics, Seen “From The Inside” (By Assyriologists) and “From The Outside” (By Historians of Mathematics)

Chapter 28 (Article II.11.) Fibonacci - Protagonist or Witness? who Taught Catholic Christian Europe about Mediterranean Commercial Arithmetic?

Chapter 29 (Article II.12.) What did the Abbacus Teachers Aim at when they (sometimes) Ended Up doing Mathematics?

Chapter 30 (Article II.13.) Hesitating Progress–The Slow Development Toward Algebraic Symbolization in Abbacus - and Related Manuscripts, C. 1300 to C. 1550

Chapter 31 (Article II.14.) Embedding – Another Case of Stumbling Progress

Chapter 32 (Article II.15.) Baroque Mind-set and New Science a Dialectic of 17th-Century High Culture Sarton Chair Lecture, Ghent University, 13 November 2008