Ganitasarakaumudi: The Moonlight of the Essence of Mathematics, by Thakkura Pheru.

• Author: Plofker, Kim
• Position: Book review

Ganitasarakaumudi: The Moonlight of the Essence of Mathematics, by Thakkura Pheru. Edited with Introduction, Translation, and Mathematical Commentary by SAKHYA (SREERAMULA RAJESWARA SARMA, TAKANORI KUSUBA, TAKAO HAYASHI, AND MICHIO YANO). NEW Delhi: MANOHAR, 2009. pp. xlvi 278. rs. 995.

One of the first significant Indian texts on pOtigonito (arithmetic) to follow the magisterial Lilavati composed by BhAskara II in the mid-twelfth century, the Gunitaseirakaumudi (ca. 1300) is unique or groundbreaking in many ways. It is the first treatise in this genre composed in Middle Indic (that is. in one of the Indo-Aryan vernaculars collectively known as Prakrits, more specifically late Middle Indic Apabhramga). Its author, Thakkura Pherii, was one of the first Jain merchant-officials to synthesize the traditional Indic versified textbook with technical knowledge relevant to the functioning of the newly established Indo-Muslim regimes. In this work Pherii combines standard topics from the Sanskrit "pre-algebra" mathematical canon (algorithms for basic arithmetic and its applications to commercial problems, rules in plane and solid geometry, etc.) with innovative features including the geometry of typical Muslim architectural elements such as the dome and true arch, Indic/Muslim calendar conversion rules, and various mathematical puzzles.

This admirably competent and comprehensive reedition of the 1961 editio prineeps by A. and B. Mahal& with accompanying bio-bibliographic introduction, translation, commentary, various technical appendices and indexes, and a detailed bibliography, was produced by a group of four scholars who began analyzing Sanskrit and hybrid-Sanskrit mathematical texts as students and colleagues of the late David Pingree at Brown University (to whose memory the book is dedicated). Together, the collaborators (whose nom de plume means "friendship" in Sanskrit) have amassed over a century of experience in working with such texts, and their expertise is evident in the breadth, depth, and precision of the published result.

As in many similar publications by the same authors, the structure of the book is rather complicated but systematically organized, making good use of LaTeX typesetting to represent both modern mathematical notation and graphical characteristics of the Prakrit text. Following a list of abbreviations and a preface by the first editor, part I in two sections discusses available information on Thakkura Pheru and surveys...