Selected Essays on Pre- And Early Modern mathematics

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