The Fourth Treatise: On Measurements
It contains an introduction and nine chapters that are divided into sections. The introduction contains the definition of area and the terminology used in it.
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Al-Kashı's Miftah. al-H.isab, Volume II: Geometry Translation and Commentary
Nuh Aydin • Lakhdar Hammoudi • Ghada Bakbouk
Al-Kāshī’s Miftāḥ al-Ḥisab, Volume II: Geometry Translation and Commentary
Nuh Aydin Department of Mathematics Kenyon College Gambier, OH, USA
Lakhdar Hammoudi Department of Mathematics Ohio University – Chillicothe Chillicothe, OH, USA
Ghada Bakbouk Department of Mathematics Kenyon College Gambier, OH, USA
ISBN 978-3-030-61329-7 ISBN 978-3-030-61330-3 (eBook) https://doi.org/10.1007/978-3-030-61330-3 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
ah.) is considered ah. al-H Written in 1427 in Arabic by al-K¯ash¯ı, Mift¯ . isab (Key to Arithmetic, henceforth Mift¯ as the synthesis and culmination of Islamic1 progress in mathematics at the time (see [15], p. 22 and [37], p. 66). Luckey’s seminal work [26] on this monumental book has mended the course of research in history of mathematics generally and that of Islamic mathematics in particular [29], rectifying long standing misconceptions regarding important discoveries such as decimal fractions [33], for example. This has profound impact on the study of the evolution of ideas and a fortiori contributes to the edifice of a more inclusive universal history of mathematics. Indeed, due to a chronic lack of study of primary sources in Chinese, Indian 2 , and Islamic civilizations, a Eurocentric narrative of history of science, called “classical narrative” by George Saliba [34] who refutes it through a critical analysis and evidence from primary sources, became dominant. Due to this common narrative, it has been believed for a
