Bøker i Science Networks. Historical Studies-serien

This book reconstructs, from both historical and theoretical points of view, Leibniz's geometrical studies, focusing in particular on the research Leibniz carried out in his final years. This is the first ever, comprehensive historical reconstruction of Leibniz's geometry.

»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time.The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.

In this book the author presents a comprehensive study of Diophantos' monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail.

This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi's original work on logarithms, Arithmetische und Geometrische Progreß Tabulen. It provides the first-ever English translation of Bürgi's text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority. High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies.The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions. The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 "Graz manuscript". A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the "Gdansk manuscript") is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two. The final chapter considers two important questions about Bürgi's work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions. Appendices are also included that contain a timeline of Bürgi's life, the underlying concept of Napier's construction of logarithms, and scans of all 58 sheets of the tables from Bürgi's text.Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work. It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching.

This book presents new insights into Leibniz's research on planetary theory and his system of pre-established harmony. It also provides an in-depth discussion of Kepler's influence on Leibniz's planetary theory and more generally, on Leibniz's concept of pre-established harmony.

This book presents a history of classical mechanics, documenting methods of study from Greece in the fourth century BC to late nineteenth-century Europe. The text assesses effectiveness of forces based on the virtual motion of their points of application.

The chief purpose of the book is to present, in detail, a compilation of proofs of the Cantor-Bernstein Theorem (CBT) published through the years since the 1870's. Over thirty such proofs are surveyed.The book comprises five parts. In the first part the discussion covers the role of CBT and related notions in the writings of Cantor and Dedekind. New views are presented, especially regarding the general proof of CBT obtained by Cantor, his proof of the Comparability Theorem, the ruptures in the Cantor-Dedekind correspondence and the origin of Dedekind's proof of CBT.The second part covers the first CBT proofs published (1896-1901). The works of the following mathematicians is considered in detail: Schroder, Bernstein, Bore, Schoenflies and Zermelo. Here a subtheme of the book is launched; it concerns the research project following Bernstein's Division Theorem (BDT).In its third part the book covers proofs that emerged during the period when the logicist movement was developed (1902-1912). It covers the works of Russell and Whitehead, Jourdain, Harward, Poincare, J. Konig, D. Konig (his results in graph theory), Peano, Zermelo, Korselt. Also Hausdorff's paradox is discussed linking it to BDT.In the fourth part of the book are discussed the developments of CBT and BDT (including the inequality-BDT) in the hands of the mathematicians of the Polish School of Logic, including Sierpinski, Banach, Tarski, Lindenbaum, Kuratowski, Sikorski, Knaster, the British Whittaker, and Reichbach.Finally, in the fifth part, the main discussion concentrates on the attempts to port CBT to intuitionist mathematics (with results by Brouwer, Myhill, van Dalen and Troelstra) and to Category Theory (by Trnkova and Koubek).The second purpose of the book is to develop a methodology for the comparison of proofs. The core idea of this methodology is that a proof can be described by two descriptors, called gestalt and metaphor. It is by comparison of their descriptors that the comparison of proofs is obtained. The process by which proof descriptors are extracted from a proof is named 'proof-processing', and it is conjectured that mathematicians perform proof-processing habitually, in the study of proofs.

This first of three volumes starts with a short introduction to historical metrology as a scientific discipline and goes on with an anthology of acient and modern measurement systems of all kind, scientific measures, units of time, weights, currencies etc.

Oliver Heaviside's electromagnetic investigations - from the publication of his first electrical paper in 1972 to the public recognition awarded to him by Lord Kelvin in 1889 - have consistently attracted attention over the years, and of late have become a major source for the study of the development of field theory after Maxwell.

The main focus of this book is on the interconnection of two unorthodox scientific ideas, the varying-gravity hypothesis and the expanding-earth hypothesis.

This book provides a scientific and intellectual biography of John von Neumann, who proposed a conception of the world as a mathematical game, one globally governed by a universal logic in which individual consciousness moved following different strategies.

Category theory is a general mathematical theory of structures and of structures of structures.

This third volume of Gyllenbok's encyclopaedia of historical metrology comprises the second part of the compendium of measurement systems and currencies of all sovereign states of the modern World (J-Z). Units of measurement are of vital importance in every civilization through history.

This second volume of Gyllenbok's encyclopaedia of historical metrology comprises the first part of the compendium of measurement systems and currencies of all sovereign states of the modern World (A-I). Units of measurement are of vital importance in every civilization through history.

While it is well known that the Delian problems are impossible to solve with a straightedge and compass - for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments - the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised?Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete.In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.

While it is well known that the Delian problems are impossible to solve with a straightedge and compass ¿ for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments ¿ the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised?Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete.In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.