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 third and final 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, Miftah 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.
Author(s): Nuh Aydin, Lakhdar Hammoudi, Ghada Bakbouk
Edition: 1
Publisher: Birkhäuser
Year: 2022
Language: English
Pages: 287
Tags: Mathematics' History; Mathematics; Algebra
Preface
Contents
Introduction
A Biography of al-Kashı and a Brief History
Al-Kashı's Letters: Invaluable Source
Ulugh Beg in al-Kashı’s Letters
Samarkand in al-Kashı's letters: Center of Knowledge
List of al-Kashı's Known Works
Manuscript Copies of Miftah
Pedagogical Aspects of Miftah
Possible Future Projects
Notes on Translation and the Purpose of This Work
Original Table of Contents of The Fifth Treatise
The Fifth Treatise
First Chapter: On Algebra
First Section: On Definitions and Terminology
Second Section: On the Addition of Monomials
Third Section: On Subtraction
Fourth Section: On Multiplication of Polynomials
Fifth Section: On the division of terms by each other
Sixth Section: On the extraction of the roots of these expressions and the square root of any power
Seventh Section: On Algebraic Problems
Eight Section: On How to Find the Unknown in the Mentioned Six Known Problems
Ninth Section: On How to Extract the Unknown
Tenth Section: On What We Promised to Mention
Second Chapter: On Finding the Unknown using the Rule of Double False Position
Third Chapter: On Including some Arithmetic Rules that are much Needed for Finding the Unknowns
The First Rule
The Second Rule
The Third Rule
The Fourth Rule
The Fifth Rule
The Sixth Rule
The Seventh Rule
The Eighth Rule
The Ninth Rule
The Tenth-Twelfth Rules
The Thirteenth-Fifteenth Rules
The Sixteenth Rule
The Seventeenth-Twenty-First Rules
The Twenty-Second-Twenty-Sixth Rules
The Twenty-Seventh-Twenty-Ninth Rules
The Thirtieth-Thirty-Third Rules
The Thirty-Fourth-Thirty-Seventh Rules
The Thirty-Eighth-Thirty-Ninth Rules
The Fortieth-Forty-First Rules
The Forty-Second-Forty-Fifth Rules
The Forty-Sixth-Forty-Ninth Rules
The Fiftieth Rule
Fourth Chapter: On Examples
First Section: Twenty-Five Examples
Second Section: Eight Examples on Wills
Third Section: Eight Examples in Which the Unknown is Found Using Geometric Rules
Glossary
Bibliography
