Synopsis Palmariorum Matheseos Or A New Introduction To The Mathematics Containing The Principles Of Arithmetic And Geometry Demonstrated In A Short And Easie Method
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The Rise and Fall of the German Combinatorial Analysis
This text presents the ideas of a particular group of mathematicians of the late 18th century known as “the German combinatorial school” and its influence. The book tackles several questions concerning the emergence and historical development of the German combinatorial analysis, which was the unfinished scientific research project of that group of mathematicians. The historical survey covers the three main episodes in the evolution of that research project: its theoretical antecedents (which go back to the innovative ideas on mathematical analysis of the late 17th century) and first formulation, its consolidation as a foundationalist project of mathematical analysis, and its dissolution at the beginning of the 19th century. In addition, the book analyzes the influence of the ideas of the combinatorial school on German mathematics throughout the 19th century.
Mathematical Book Histories
This book both articulates and responds to increasing scholarly interest in the materiality of the book. Taking as its base the unique collection of mathematical books in the Russell Library at Maynooth, it addresses questions related to printing techniques and print culture, book production, provenance, and reading practices. It considers the histories of individual items of the Russell Collection, their previous locations and owners, and explores ways in which annotations, underlinings, hand-drawn diagrams, and the like reveal patterns of reading and usage. Finally, it seeks to elicit more information on a previously under-researched topic: the historical role of mathematics in the extensive network of Irish colleges that once covered Catholic Europe, located in places such as Salamanca, Rome, Douai, and Prague. Alongside delivering important new insights into print culture as a medium for transmitting scientific ideas, Mathematical Book Histories is thus also intended to contribute to a broader understanding of the role and significance of mathematics in the context of clerical instruction and more broadly in the academic tradition of Ireland up to the beginning of the twentieth century. Many of the volumes in the Russell Library reflect the remarkably rich book-trade that flourished in seventeenth and early eighteenth century Dublin and which was quite distinct from that in London. Booksellers often bought in their wares directly from abroad, with the result that publications could enter collections that did not enter the purview of contemporary English or Scottish scholars in Britain.
Irrationality, Transcendence and the Circle-Squaring Problem
Author: Eduardo Dorrego López
language: en
Publisher: Springer Nature
Release Date: 2024-05-02
This publication, now in its second edition, includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728–1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations, as in the first edition, are accompanied by a contextualised study of each of these works and provide an overview of Lambert’s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.