Selected Essays on Pre- And Early Modern mathematics

Description

This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice. This book is of interest to, and provides methodological inspiration for, historians of science or mathematics and students of these disciplines. Front Matter ....Pages i-xiii Front Matter ....Pages 1-1 Introduction (Jens Høyrup)....Pages 3-30 (Article I.1.) On Parts of Parts and Ascending Continued Fractions: An Investigation of the Origins and Spread of a Peculiar System (Jens Høyrup)....Pages 31-57 (Article I.2.) A Note on Old Babylonian Computational Techniques (Jens Høyrup)....Pages 59-66 (Article I.3.) On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six “Algebras” (Jens Høyrup)....Pages 67-116 (Article I.4.) Mahāvīra’s Geometrical Problems Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages (Jens Høyrup)....Pages 117-129 (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 (Jens Høyrup)....Pages 131-156 (Article I.6.) Geometrical Patterns in the Pre-Classical Greek Area (Jens Høyrup)....Pages 157-205 (Article I.7.) Broad Lines – A Forgotten Geometrical Ambiguity (Jens Høyrup)....Pages 207-218 (Article I.8.) Concerning the Position of ‘‘Heron’s Formula’’ in the Metrica (With a Platonic Note) (Jens Høyrup)....Pages 219-228 (Article I.9.) Heron, Ps-Heron, and near Eastern Practical Geometry an Investigation of Metrica, Geometrica, and other Treatises (Jens Høyrup)....Pages 229-255 (Article I.10.) Which Kind of Mathematics was Known and Referred to by those who wanted to Integrate Mathematics in Wisdom – Neopythagoreans and Others? (Jens Høyrup)....Pages 257-278 (Article I.11.) The Rare Traces of Constructional Procedures in “Practical Geometries” (Jens Høyrup)....Pages 279-290 (Article I.12.) About the Italian Background to Rechenmeister Mathematics (Jens Høyrup)....Pages 291-345 (Article I.13.) The “Unknown Heritage” – Trace of a Forgotten Locus of Mathematical Sophistication (Jens Høyrup)....Pages 347-395 (Article I.14.) A Diluted Al-Karajī In Abbacus Mathematics (Jens Høyrup)....Pages 397-407 (Article I.15.) “Proportions” in and around the Italian Abbacus Tradition (Jens Høyrup)....Pages 409-457 (Article I.16.) Archimedes – Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance (Jens Høyrup)....Pages 459-477 Front Matter ....Pages 479-479 (Article II.1.) Existence, Substantiality, and Counterfactuality Observations on the Status of Mathematics according to Aristotle, Euclid, and Others (Jens Høyrup)....Pages 481-509 (Article II.2.) Conceptual Divergence – Canons and Taboos – And Critique (Jens Høyrup)....Pages 511-535 (Article II.3.) Tertium Non Datur, or, on Reasoning Styles in Early Mathematics (Jens Høyrup)....Pages 537-563 (Article II.4.) Embedding – Multi-purpose Device for Understanding Mathematics and its Development, or Empty Generalization? (Jens Høyrup)....Pages 565-590 (Article II.5.) What is “Geometric Algebra”, and what has it been in Historiography? (Jens Høyrup)....Pages 591-631 (Article II.6.) State, “Justice”, Scribal Culture and Mathematics in Ancient Mesopotamia. Sarton Lecture 2008 (Jens Høyrup)....Pages 633-660 (Article II.7.) How to Educate a KAPO Reflections on the Absence of a Culture of Mathematical Problems in Ur III (Jens Høyrup)....Pages 661-688 (Article II.8.) A Hypothetical History of Old Babylonian Mathematics − Places, Passages, Stages, Development (Jens Høyrup)....Pages 689-709 (Article II.9.) Written Mathematical Traditions in Ancient Mesopotamia Knowledge, Ignorance, and Reasonable Guesses (Jens Høyrup)....Pages 711-737 (Article II.10.) Mesopotamian Mathematics, Seen “From The Inside” (By Assyriologists) and “From The Outside” (By Historians of Mathematics) (Jens Høyrup)....Pages 739-769 (Article II.11.) Fibonacci - Protagonist or Witness? who Taught Catholic Christian Europe about Mediterranean Commercial Arithmetic? (Jens Høyrup)....Pages 771-794 (Article II.12.) What did the Abbacus Teachers Aim at when they (sometimes) Ended Up doing Mathematics? (Jens Høyrup)....Pages 795-822 (Article II.13.) Hesitating Progress–The Slow Development Toward Algebraic Symbolization in Abbacus - and Related Manuscripts, C. 1300 to C. 1550 (Jens Høyrup)....Pages 823-876 (Article II.14.) Embedding – Another Case of Stumbling Progress (Jens Høyrup)....Pages 877-910 (Article II.15.) Baroque Mind-set and New Science a Dialectic of 17th-Century High Culture Sarton Chair Lecture, Ghent University, 13 November 2008 (Jens Høyrup)....Pages 911-933 Back Matter ....Pages 935-969