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Al-Kashi's Miftah al-Hisab, Volume II: Geometry

Translation and Commentary

  • Book
  • © 2020

Overview

Authors:
  1. Nuh Aydin

    1. Department of Mathematics, Kenyon College, Gambier, USA

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  2. Lakhdar Hammoudi

    1. Department of Mathematics, Ohio University – Chillicothe, Chillicothe, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Ghada Bakbouk

    1. Department of Mathematics, Kenyon College, Gambier, USA

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    You can also search for this author in PubMed   Google Scholar

  • Offers English readers the very first complete translation of Jamshid al-Kashi’s historic book on arithmetic

  • Provides new insights into the history of mathematics

  • Contains scans of the source manuscript next to the translation, which serve to highlight the meticulousness of the translation

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Table of contents (2 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • Nuh Aydin, Lakhdar Hammoudi, Ghada Bakbouk
    Pages 1-12

  3. The Fourth Treatise: On Measurements

    • Nuh Aydin, Lakhdar Hammoudi, Ghada Bakbouk
    Pages 13-189

  4. Back Matter

    Pages 191-195
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Keywords

About this book

Jamshīd al-Kāshī’s Miftāḥ al-Ḥisab (Key to Arithmetic) was largely unknown to researchers until the mid-20th century, and has not been translated to English until now. This is the second book in a multi-volume set that finally brings al-Kāshī’s groundbreaking textbook to English audiences in its entirety. As soon as it was studied by modern researchers, it changed some false assumptions about the history of certain topics in mathematics. Written as a textbook for students of mathematics, astronomy, accounting, engineering, and architecture, Miftah covers a wide range of topics in arithmetic, geometry, and algebra. By sharing al-Kāshī’s most comprehensive work with a wider audience, this book will help establish a more complete history of mathematics, and extend al-Kāshī’s influence into the 21st century and beyond. 
The book opens by briefly recounting al-Kāshī’s biography, so as to situate readers in the work’s rich historical context. His impressive status in the kingdom of Ulugh Beg is detailed, as well as his contributions to both mathematics and astronomy. As a master calculator and astronomer, al-Kāshī’s calculations of 2π and sin(1⁰) were by far the most accurate for almost two centuries. His law of cosines is still studied in schools today. This translation contributes to the understanding and appreciation of al-Kāshī’s esteemed place in the scientific world. A side-by-side presentation of the source manuscript—one of the oldest known copies—and the English translation is provided on each page. Detailed footnotes are also provided throughout, which will offer readers an even deeper look at the text’s mathematical and historical basis.
 
Researchers and students of the history of mathematics will find this volume indispensable in filling in a frequently overlooked time period and region. This volume will also provide anybody interested in the history of Islamic culture with an insightful look at one of the mathematical world’s most neglected figures.

Reviews

“It is especially useful for people that need arithmetic and elementary mathematics to solve practical problems in their everyday life or in their professions. … The facsimile is reproduced in a high-quality coloured version that makes it easy for readers to read the main text as well as the marginal notes. Thanks to the side-by-side presentation of the manuscript … . this study remains invaluable for all those who would like to discover the most important text of al-Kāshī.” (Marc Moyon, zbMATH 1471.01002, 2021)

Authors and Affiliations

  • Department of Mathematics, Kenyon College, Gambier, USA

    Nuh Aydin, Ghada Bakbouk

  • Department of Mathematics, Ohio University – Chillicothe, Chillicothe, USA

    Lakhdar Hammoudi

Bibliographic Information

  • Book Title: Al-Kashi's Miftah al-Hisab, Volume II: Geometry

  • Book Subtitle: Translation and Commentary

  • Authors: Nuh Aydin, Lakhdar Hammoudi, Ghada Bakbouk

  • DOI: https://doi.org/10.1007/978-3-030-61330-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-61329-7Published: 03 December 2020

  • Softcover ISBN: 978-3-030-61332-7Published: 04 December 2021

  • eBook ISBN: 978-3-030-61330-3Published: 02 December 2020

  • Edition Number: 1

  • Number of Pages: VIII, 195

  • Number of Illustrations: 31 b/w illustrations, 89 illustrations in colour

  • Topics: History of Mathematical Sciences

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