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Al-Kashi on Root Extraction

This is a detailed examination of Chapter Five of the Third Treatise of Jamshīd Ghiyāth al-Dīn al-Kāshī (al-Kāshānī, d. 1429) from his book, The Key to Arithmetic (Miftāḥ al-Ḥisāb), also known as The Computers' Key (Miftāḥ al-Ḥussāb). A facsimile of the original manuscript is reproduced in Chapter Three of the text, along with an opposite-page translation and commentary. A sexagesimal multiplication table, useful to those engaged in computations from Babylonian, Greek, Arabic, and Byzantine scientific writings, is included in a back pocket of the book.