Ibn al-Haytham's Theory of Conics, Geometrical Constructions and Practical Geometry


Book Description

Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3, provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The present text is complemented by two preceding volumes of A History of Arabic Sciences and Mathematics, which focused on founding figures and commentators in the ninth and tenth centuries, and the historical and epistemological development of ‘infinitesimal mathematics’ as it became clearly articulated in the oeuvre of Ibn al-Haytham. This volume examines the increasing tendency, after the ninth century, to explain mathematical problems inherited from Greek times using the theory of conics. Roshdi Rashed argues that Ibn al-Haytham completes the transformation of this ‘area of activity,’ into a part of geometry concerned with geometrical constructions, dealing not only with the metrical properties of conic sections but with ways of drawing them and properties of their position and shape. Including extensive commentary from one of world’s foremost authorities on the subject, this book contributes a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context. This fundamental text will appeal to historians of ideas, epistemologists and mathematicians at the most advanced levels of research.




Ibn Al-Haytham's Theory of Conics, Geometrical Constructions and Practical Geometry


Book Description

Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3, provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The present text is complemented by two preceding volumes of A History of Arabic Sciences and Mathematics , which focused on founding figures and commentators in the ninth and tenth centuries, and the historical and epistemological development of 'infinitesimal mathematics' as it became clearly articulated in the oeuvre of Ibn al-Haytham. This volume examines the increasing tendency, after the ninth century, to explain mathematical problems inherited from Greek times using the theory of conics. Roshdi Rashed argues that Ibn al-Haytham completes the transformation of this 'area of activity,' into a part of geometry concerned with geometrical constructions, dealing not only with the metrical properties of conic sections but with ways of drawing them and properties of their position and shape. Including extensive commentary from one of world's foremost authorities on the subject, this book contributes a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context. This fundamental text will appeal to historians of ideas, epistemologists and mathematicians at the most advanced levels of research.







Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics


Book Description

This fifth volume of A History of Arabic Sciences and Mathematics is complemented by four preceding volumes which focused on the main chapters of classical mathematics: infinitesimal geometry, theory of conics and its applications, spherical geometry, mathematical astronomy, etc. This book includes seven main works of Ibn al-Haytham (Alhazen) and of two of his predecessors, Thābit ibn Qurra and al-Sijzī: The circle, its transformations and its properties; Analysis and synthesis: the founding of analytical art; A new mathematical discipline: the Knowns; The geometrisation of place; Analysis and synthesis: examples of the geometry of triangles; Axiomatic method and invention: Thābit ibn Qurra; The idea of an Ars Inveniendi: al-Sijzī. Including extensive commentary from one of the world’s foremost authorities on the subject, this fundamental text is essential reading for historians and mathematicians at the most advanced levels of research.




Ibn al-Haytham, New Astronomy and Spherical Geometry


Book Description

This volume provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The fourth volume of A History of Arabic Sciences and Mathematics is complemented by three preceding volumes which focused on infinitesimal determinations and other chapters of classical mathematics. This book includes five main works of the polymath Ibn al-Haytham (Alhazen) on astronomy, spherical geometry and trigonometry, plane trigonometry and studies of astronomical instruments on hour lines, horizontal sundials and compasses for great circles. In particular, volume four examines: the increasing tendency to mathematize the inherited astronomy from Greek sources, namely Ptolemy's Almagest; the development of celestial kinematics; new research in spherical geometry and trigonometry required by the new kinematical theory; the study on astronomical instruments and its impact on mathematical research. These new historical materials and their mathematical and historical commentaries contribute to rewriting the history of mathematical astronomy and mathematics from the 11th century on. Including extensive commentary from one of the world’s foremost authorities on the subject, this fundamental text is essential reading for historians and mathematicians at the most advanced levels of research.




The Arts of Ornamental Geometry


Book Description

This collective study focuses on a unique anonymous medieval document on ornamental geometry featuring geometrical constructions and textual instructions in Persian. Selections from the unpublished work of Alpay Özdural (d. 2003) on this subject have been updated with original contributions by Jan P. Hogendijk, Elaheh Kheirandish, Gülru Necipoğlu, and Wheeler M. Thackston. The chapters interpreting this fascinating document are followed, for the first time, by a facsimile, transcription, and translation, as well as drawings of incised construction lines invisible in the photographed facsimile. This publication intersects with the current interest in Islamic geometrical patterning as an inspiration for tessellation and parametrically derived forms in contemporary architecture and the arts. It aims to make this celebrated source more accessible, given its multifaceted relevance to historians of art, architecture, and science, as well as mathematicians, physicists, artists, and architects. For those who wish to obtain a copy of the full, unedited original book manuscript of Alpay Özdural, where he discusses the mathematical properties of all geometrical constructions in the Anonymous Compendium as well as the step-by-step method for drawing each one, his work is available online at https://doi.org/10.6084/m9.figshare.5255416




Classical Mathematics from Al-Khwarizmi to Descartes


Book Description

This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat. ‘Early modern,’ mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from ‘classical mathematics,’ to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Rashed demonstrates that ‘early modern,’ mathematics is actually far more composite than previously assumed, with each branch having different traceable origins which span the millennium. Going back to the beginning of these parts, the aim of this book is to identify the concepts and practices of key figures in their development, thereby presenting a fuller reality of these mathematics. This book will be of interest to students and scholars specialising in Islamic science and mathematics, as well as to those with an interest in the more general history of science and mathematics and the transmission of ideas and culture.




Legal Authority in Premodern Islam


Book Description

Offering a detailed analysis of the structure of authority in Islamic law, this book focuses on the figure of Yahyā b. Sharaf al-Nawawī, who is regarded as the chief contributor to the legal tradition known as the Shāfi'ī madhhab in traditional Muslim sources, named after Muhammad b. Idrīs al-Shāfi'ī (d. 204/820), the supposed founder of the school of law. Al-Nawawī’s legal authority is situated in a context where Muslims demanded to stabilize legal disposition that is consistent with the authority of the madhhab, since in premodern Islamic society, the ruling powers did not produce or promulgate law, as was the case in other, monarchic civilizations. Al-Nawawī’s place in the long-term formation of the madhhab is significant for many reasons but for one in particular: his effort in reconciling the two major interpretive communities among the Shāfi'ites, i.e., the tarīqas of the Iraqians and Khurasanians. This book revisits the history of the Shāfi'ī school in the pre-Nawawic era and explores its later development in the post-Nawawic period. Presenting a comprehensive picture of the structure of authority in Islamic law, specifically within the Shafi’ite legal tradition, this book is an essential resource for students and scholars of Islamic Studies, History and Law.




The Philosophers and Mathematics


Book Description

This book explores the unique relationship between two different approaches to understand the nature of knowledge, reality, and existence. It collects essays that examine the distinctive historical relationship between mathematics and philosophy. Readers learn what key philosophers throughout the ages thought about mathematics. This includes both thinkers who recognized the relevance of mathematics to their own work as well as those who chose to completely ignore its many achievements. The essays offer insight into the role that mathematics played in the formation of each included philosopher’s doctrine as well as the impact its remarkable expansion had on the philosophical systems each erected. Conversely, the authors also highlight the ways that philosophy contributed to the growth and transformation of mathematics. Throughout, significant historical examples help to illustrate these points in a vivid way. Mathematics has often been a favored interlocutor of philosophers and a major source of inspiration. This book is the outcome of an international conference held in honor of Roshdi Rashed, a renowned historian of mathematics. It provides researchers, students, and interested readers with remarkable insights into the history of an important relationship throughout the ages.




Literature and the Islamic Court


Book Description

Courts were the most important frameworks for the production, performance, and evaluation of literature in medieval Islamic civilization. Patrons vying for prestige attracted to their courts literary people who sought their financial support. The most successful courts assembled outstanding literary people from across the region. The court of the vizier and literary person al-Sahib Ibn ʿAbbad (326-385/938-995) in western Iran is one of the most remarkable examples of a medieval Islamic court, with a sophisticated literary activity in Arabic (and, to a lesser extent, in Persian). Literature and the Islamic Court examines the literary activity at the court of al-Sahib and sheds light on its functional logic. It is an inquiry into the nature of a great medieval court, where various genres of poetry and prose were produced, performed, and evaluated regularly. Major aspects examined in the book are the patterns of patronage, selection, and auditioning; the cultural codes and norms governing performance, production, and criticism; the interaction between the patron and courtiers and among the courtiers themselves; competition; genres as productive molds; the hegemonic literary taste; and the courtly habitus. This book reveals the significance these courts held as institutions that were at the heart of literary production in Arabic. Using primary medieval Arabic sources, this book offers a comprehensive analysis of Islamic courts and as such is of key interest to students and scholars of Arabic literature, Islamic history and medieval studies.