Bücher der Reihe Sources and Studies in the History of Mathematics and Physical Sciences

In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus' "Collection" (1588, in Latin translation) and Descartes' death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. Hethen analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry's proper subject and procedures in such a way as to incorporate the use of algebraic methods without destroying the true nature of geometry. Although mathematicians later essentially discarded Descartes' methodological convictions, his influence was profound and pervasive. Bos' insistence on the foundational aspects of the "Géométrie" provides new insights both in the genesis of Descartes' masterpiece and in its significance for the development of the conceptions of mathematical exactness.

This book identifies three of the exceptionally fruitful periods of the millennia-long history of the mathematical tradition of India: the very beginning of that tradition in the construction of the now-universal system of decimal numeration and of a framework for planar geometry;

Deals with the development of the terms of analysis in the 18th and 19th centuries, the two main concepts being negative numbers and infinitesimals. Looking at German and French textbooks, this work reveals the history and throws light on major figures, such as Cauchy.

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work.

This is a history of the use of Bayes theoremfrom its discovery by Thomas Bayes to the rise of the statistical competitors in the first part of the twentieth century.

In 1821, Augustin-Louis Cauchy published a textbook to accompany his course in analysis at the Ecole Polytechnique. It is still regarded as one of the most influential mathematics book ever written, and this is the first English translation of that book.

This book presents a detailed and rigorous account of the work of Tobias Mayer, a mathematician and astronomer of the middle 18th century. Mayer's most famous contribution is his set of lunar tables, which were the best available in their time.

China's most sophisticated system of computational astronomy was created for a Mongol emperor to celebrate victory over China after forty years of war. This book explains how and why, and reconstructs the observatory and the science that made it possible.

In this examination of the Babylonian cuneiform "algebra" texts, based on a detailed investigation of the terminology and discursive organization of the texts, Jens Hoyrup proposes that the traditional interpretation must be rejected.

A new translation makes this classic and important text more generally accessible. The text is placed in its contemporary context, but also related to the interests of practising mathematicians today. This book will be of interest to mathematical historians, researchers, and numerical analysts.

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Robert Simson is recognised as the first person to achieve an insight into the nature of the subject - Porisms. In this book, Ian Tweddle presents a translation of Simson's work. Supplemented by historical and mathematical notes and comments, this book is useful to those with an interest in mathematical history or geometry.

The discovery of a gradual acceleration in the moon's mean motion by Edmond Halley in the last decade of the seventeenth century led to a revival of interest in reports of astronomical observations from antiquity.

This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science.

Based on a modern approach incorporating recent insights, this book offers new translations and a new analysis of the procedure texts of Babylonian mathematical astronomy, the earliest known form of mathematical astronomy of the ancient world.

The book analyzes the mathematical tablets from the private collection of Martin Schoyen. This provides new insight into Babylonian understanding of sophisticated mathematical objects. The tablets are classified according to mathematical content and purpose, while drawings and pictures are provided for the most interesting tablets.

This fascinating insight into the minds of two great twentieth-century mathematicians affords an insider's view of the birth of modern probability theory as well as a revealing epistolary portrait spanning five decades of Levy and Frechet's academic careers.

Here is a selection of more than 400 letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz, covering the period from 1883 until just before his death. The letters have been selected primarily according to scientific interest.

Finally, the authors survey the major categories of individual tables compiled in these texts, complete with brief analyses of some of the methods for constructing and using them, and then chronicle the evolution of the table-text genre and the impacts of its changing role on the discipline of Sanskrit jyotisa.

"The Almagest", by the Greek astronomer and mathematician Ptolemy, is the most important surviving treatise on early mathematical astronomy, offering historians valuable insight into the astronomy and mathematics of the ancient world. This title provides students of the history of astronomy with a self-contained introduction to the "Almagest".

This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. The book clearly shows how long it took to recognize the seminal importance of Noether's results.

This book provides a critical edition, translation, and study of the version of Euclid's treatise made by Thabit ibn Qurra, which is the earliest Arabic version that we have in its entirety.

The book will be of particular interest to scholars engaged in the study of Islamic theoretical astronomy, but is accessible to a general readership interested in learning what constituted an introduction to Ptolemaic astronomy in Islamic lands.

This book details the history of complex function theory. It examines the rise of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables.

First published in 1202, Fibonacci's Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe.

Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today.

This is the second and final volume of Dutch physicist Hendrik Antoon Lorentz's scientific correspondence with Dutch colleagues, including Pieter Zeeman and Paul Ehrenfest.

This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich.

This book provides a critical edition, translation, and study of the version of Euclid's treatise made by Thabit ibn Qurra, which is the earliest Arabic version that we have in its entirety.