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.

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.

Exploring the Hindu concepts of good and bad deaths, this rich ethnography follows pilgrims who choose to travel to the holy city of Kashi to die.

A collection of triptychs by acclaimed photographer Ed Kashi, which plays on the visual appetite of a hectic world. The triptychs span eras and continents, challenging notions of perspective and the possibility of singularity for any image. Contained in a format dating back to the Middle Ages, Kashi's images examine current issues of social and political significance, bringing together the joy, sorrow, destruction and reconstruction of a world in flux.

A study of Hindu death rituals and the sacred specialists who perform them in the Indian city of Banaras.

Marathi, an Indo-Aryan language, is the official language of Maharashtra, including Mumbai. Father Thomas Stephens, the first English traveler to Goa, a pioneer linguist, wrote "Christa Puran" in Marathi (1616) and "Arte da Lingoa Canarim" in Portuguese, printed in (1640). The latter is a grammar of Konkani, a language closely related to Marathi. It is the first grammar of its kind marking a new grammatical tradition for modern Indo-Aryan languages. The present volume contains an extensive account of Marathi phonology, morphology, word formation and syntax. It succinctly describes the accentual system, special compound verb forms, unique pronominal anaphors, complex agreement due to split ergative system, and special pronominal marking. The book also contains a case study of a child s acquisition of Marathi and an essay on Women s Language, the two topics that are increasingly becoming relevant to the grammar."

Based on the revolutionary #1 New York Times bestseller that is changing the way America eats, this is the only supermarket guide that exposes the true cause of belly fat and disease: hidden sugar! Transforming your health, energy, and waistline is as easy as 1, 2, 3: 1. Unlock the secret to fat loss that food conglomerates don’t want you to know. 2. Follow the one simple menu that tells you exactly what to eat to melt up to 9 pounds this week. 3. Discover thousands of "Belly Good" items that make shedding pounds each week a snap. With a bonus dining-out section featuring menu items from some of your favorite restaurants, this comprehensive guide will help you look and feel your best in no time at all!