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Ganitasarakaumudi The Moonlight of the Essence of Mathematics by Thakkura Pheru
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Ganitasarakaumudi The Moonlight of the Essence of Mathematics by Thakkura Pheru
by Sakhya
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About the Book

The Ganitasarakaumudi was composed in the early fourteenth century at Delhi by the Jain Polymath thakkura Pheru who held a high position at the treasury of Ala al din Khalji, and contributed to the popularization of Science by producing six treatises in Apabhramsa verse on diverse scientific subjects.

The Ganitasarakaumudi extends the range of mathematics far beyond the traditional framework. The first three chapters are structured like the earlier Mathematical texts in Sanskrit and treat traditional topic like fundamental operations, fractions, series, proportion, plane and solid geometry and so on. The remaining two chapters contain supplementary material derived from diverse areas of contemporary life where numbers play a role such as mathematical riddles, conversion of dates from Vikrama era to Hijri era, magic squares, and most remarkably average yield per bigha of several kinds of grains and pulses – topics that were not touched upon in any mathematical text before.

The present volume offers, besides an introduction, a critically emended text, an English Translation, and a detailed mathematical commentary where efforts were made to interpret Pheru’s formulas and algorithms in modern notation. There are several appendices including a comprehensive glossary index.

Preface

Of the few scholars working on Sanskrit texts on astronomy and mathematics today, the largest group is concentrated in Japan in the ancient city of Kyoto. This group has the admirable habit of meeting once a week to study an original text. One of the valuable fruits of this joint study is the Studies in Indian Mathematics: Series, Pi and Trigonometry (Tokyo, 1997), which was awarded the Publication Prize by the Mathematical Society of Japan in 2005.

When I spent a semester at Kyoto University as Visiting Professor of Indian Science in 2002, I was invited to join the group, then consisting of Professors Michio Yano, Takao Hayashi and Takanori Kusuba. I had met Professor Yano for the first time in 1976 during the International Symposium on Aryabhata in New Delhi; since then we have been meeting often in India and elsewhere. Professor Kusuba and I were together at Brown University in the academic year 1992-93. I came to know Professor Hayashi in 1986 through his marvellous PhD thesis on the Bakhshali Manuscript.

For our weekly meetings, we chose the Ganitasara-kaumudi of Thakkura Pheru who held a high position in the treasury of Ala' aI-Din Khalji at Delhi. This work is not only the first mathematical work to be composed in Middle Indic, but it also extends the range of mathematics beyond the traditional frame- work. In those six months, we translated the text and drafted a mathematical commentary. It took, however, some time to prepare our work for publication, as all of us were busy with various academic and administrative duties in the intervening years. The work is now complete, thanks to the diligent efforts of Professor Hayashi who acted as the editor of the team, put together our individual inputs and prepared the press copy in LATEX. It is also he who suggested the name for our group.

The group name SaKHYa emphasizes the warm bond of friendship that developed among us during the past several years through the common interest in the history of science; it has an additional significance as well, for it was generated mathematically by the permutation of the initial letters of our names. Permutation and combination have been important elements in Indian mathematics; they also played a significant role in systems of classification in other sustras, Indeed, they were employed, for the very first time - in the classification of poetic metres - by Pingala Naga in his Chandahsutra, where he taught, among others, how to arrange the permutations in a tabular form called prastura. The initial letters of our four names produce a set of permutations (caturaksara-prastara) consisting of 24 terms. From the fourteenth term of this series is derived the group name SaKHYa.

SaKHYa is now pleased to offer to the historians of mathematics this edition, translation, mathematical commentary, and a detailed glossary-index of Thakkura Pheru's Ganitasara-kaumudi, 'The Moonlight of the Essence of Mathematics,' also known as Ganitasara, 'The Essence of Mathematics.'

As we complete this joint venture, we recall the memory of those scholars who inspired us in this task in various ways. Sri Bhanwar Lal Nahata of Kolkata discovered the writings of Thakkura Pheru in a single manuscript copy and published them in collaboration with Sri Agar Chand Nahata. When I brought out Thakkura Pheru's Rayanaparikkha with an English translation and commentary in 1984, Bhanwar Lal-ji sent me a warm letter of appreciation, which I greatly cherish, and shared with me his own notes on Pheru's other writings. The link between Bhanwar Lalji and me was Sri Hazari Mull Banthia of Kanpur from whom I learnt much about contemporary Jainism.

We also remember fondly our mentor and friend Professor David Pingree; the four of us had the privilege of spending some time with him at Brown University; it is his monumental Census of the Exact Sciences in Sanskrit which first introduced us to Thakkura Pheru's scientific writings. We dedicate our book to the memory of Professor David Pingree.

We are highly indebted to Professor Irfan Habib who took a keen interest in our work and very kindly translated for us relevant passages from lndo-Persian sources, especially from the Dostur al-Albab fi ilm al-Hisab by Hajji Abd al- Hamid Muharrir Ghaznavi.

Our sincere thanks are due to Mr Ramesh Jain of the Manohar Publishers & Distributors for agreeing to bring out this work; he and his staff deserve all praise for the fine production of the volume. Thakkura Pheru composed the Ganitasura-kaumudi in Delhi; we are happy that our study of this work also is being published from Delhi.





Contents

Abbreviationsvi
Prefacevii
Part I Introduction
Section 1thakkura Pheru: Life and Worksxi
Section2Mathematics of the Ganitasarakaumudixviii
Part II Text
Chapter 0Introduction3
Chapter1Prathamo 'Dhyayah9
Chapter 2Dvitiyo'dhyayah17
Chapter 3Trtiyo 'Dhyayah19
Chapter 4Caturtho 'Dhyayah27
Chapter 5Pancamo 'Dhyayah35
Chapter 6Sutranukramanika39
Part III English Translation
Chapter 1Twenty-five Fundamental Operations45
Chapter 2Eight Classes of Reduction of Fractionsq57
Chapter 3Eight Types of Procedures61
Chapter 4Four Special Topics75
Chapter 5Quintet of Topic85
Chapter 6List of rules91
Part IV Mathematical
Chapter 1Twenty -five Fundamental Operations97
Chapter 2Eight Classes of Reduction on Fractions125
Chapter 3Eight Types of Procedures133
Chapter 4Four Special Topics163
Chapter 5Quintet of Topic183
Appendices
AConcordance of the Ganitasarakaumudi and Other Works195
BThe Type Problems207
CIndex to the Number in the Text215
DGlossary Index to the Text223
Bibliography
Index of Mathematical Terms267
Index of Things in the Text273
Index of Sanskrit/Prakrit authors and titles277












Ganitasarakaumudi The Moonlight of the Essence of Mathematics by Thakkura Pheru

Item Code:
NAM904
Cover:
Hardcover
Edition:
2009
ISBN:
9788173048098
Language:
English
Size:
11.5 inch X 9.0 inch
Pages:
325
Other Details:
Weight of the Book: 1.1 kg
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$50.00   Shipping Free - 4 to 6 days
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About the Book

The Ganitasarakaumudi was composed in the early fourteenth century at Delhi by the Jain Polymath thakkura Pheru who held a high position at the treasury of Ala al din Khalji, and contributed to the popularization of Science by producing six treatises in Apabhramsa verse on diverse scientific subjects.

The Ganitasarakaumudi extends the range of mathematics far beyond the traditional framework. The first three chapters are structured like the earlier Mathematical texts in Sanskrit and treat traditional topic like fundamental operations, fractions, series, proportion, plane and solid geometry and so on. The remaining two chapters contain supplementary material derived from diverse areas of contemporary life where numbers play a role such as mathematical riddles, conversion of dates from Vikrama era to Hijri era, magic squares, and most remarkably average yield per bigha of several kinds of grains and pulses – topics that were not touched upon in any mathematical text before.

The present volume offers, besides an introduction, a critically emended text, an English Translation, and a detailed mathematical commentary where efforts were made to interpret Pheru’s formulas and algorithms in modern notation. There are several appendices including a comprehensive glossary index.

Preface

Of the few scholars working on Sanskrit texts on astronomy and mathematics today, the largest group is concentrated in Japan in the ancient city of Kyoto. This group has the admirable habit of meeting once a week to study an original text. One of the valuable fruits of this joint study is the Studies in Indian Mathematics: Series, Pi and Trigonometry (Tokyo, 1997), which was awarded the Publication Prize by the Mathematical Society of Japan in 2005.

When I spent a semester at Kyoto University as Visiting Professor of Indian Science in 2002, I was invited to join the group, then consisting of Professors Michio Yano, Takao Hayashi and Takanori Kusuba. I had met Professor Yano for the first time in 1976 during the International Symposium on Aryabhata in New Delhi; since then we have been meeting often in India and elsewhere. Professor Kusuba and I were together at Brown University in the academic year 1992-93. I came to know Professor Hayashi in 1986 through his marvellous PhD thesis on the Bakhshali Manuscript.

For our weekly meetings, we chose the Ganitasara-kaumudi of Thakkura Pheru who held a high position in the treasury of Ala' aI-Din Khalji at Delhi. This work is not only the first mathematical work to be composed in Middle Indic, but it also extends the range of mathematics beyond the traditional frame- work. In those six months, we translated the text and drafted a mathematical commentary. It took, however, some time to prepare our work for publication, as all of us were busy with various academic and administrative duties in the intervening years. The work is now complete, thanks to the diligent efforts of Professor Hayashi who acted as the editor of the team, put together our individual inputs and prepared the press copy in LATEX. It is also he who suggested the name for our group.

The group name SaKHYa emphasizes the warm bond of friendship that developed among us during the past several years through the common interest in the history of science; it has an additional significance as well, for it was generated mathematically by the permutation of the initial letters of our names. Permutation and combination have been important elements in Indian mathematics; they also played a significant role in systems of classification in other sustras, Indeed, they were employed, for the very first time - in the classification of poetic metres - by Pingala Naga in his Chandahsutra, where he taught, among others, how to arrange the permutations in a tabular form called prastura. The initial letters of our four names produce a set of permutations (caturaksara-prastara) consisting of 24 terms. From the fourteenth term of this series is derived the group name SaKHYa.

SaKHYa is now pleased to offer to the historians of mathematics this edition, translation, mathematical commentary, and a detailed glossary-index of Thakkura Pheru's Ganitasara-kaumudi, 'The Moonlight of the Essence of Mathematics,' also known as Ganitasara, 'The Essence of Mathematics.'

As we complete this joint venture, we recall the memory of those scholars who inspired us in this task in various ways. Sri Bhanwar Lal Nahata of Kolkata discovered the writings of Thakkura Pheru in a single manuscript copy and published them in collaboration with Sri Agar Chand Nahata. When I brought out Thakkura Pheru's Rayanaparikkha with an English translation and commentary in 1984, Bhanwar Lal-ji sent me a warm letter of appreciation, which I greatly cherish, and shared with me his own notes on Pheru's other writings. The link between Bhanwar Lalji and me was Sri Hazari Mull Banthia of Kanpur from whom I learnt much about contemporary Jainism.

We also remember fondly our mentor and friend Professor David Pingree; the four of us had the privilege of spending some time with him at Brown University; it is his monumental Census of the Exact Sciences in Sanskrit which first introduced us to Thakkura Pheru's scientific writings. We dedicate our book to the memory of Professor David Pingree.

We are highly indebted to Professor Irfan Habib who took a keen interest in our work and very kindly translated for us relevant passages from lndo-Persian sources, especially from the Dostur al-Albab fi ilm al-Hisab by Hajji Abd al- Hamid Muharrir Ghaznavi.

Our sincere thanks are due to Mr Ramesh Jain of the Manohar Publishers & Distributors for agreeing to bring out this work; he and his staff deserve all praise for the fine production of the volume. Thakkura Pheru composed the Ganitasura-kaumudi in Delhi; we are happy that our study of this work also is being published from Delhi.





Contents

Abbreviationsvi
Prefacevii
Part I Introduction
Section 1thakkura Pheru: Life and Worksxi
Section2Mathematics of the Ganitasarakaumudixviii
Part II Text
Chapter 0Introduction3
Chapter1Prathamo 'Dhyayah9
Chapter 2Dvitiyo'dhyayah17
Chapter 3Trtiyo 'Dhyayah19
Chapter 4Caturtho 'Dhyayah27
Chapter 5Pancamo 'Dhyayah35
Chapter 6Sutranukramanika39
Part III English Translation
Chapter 1Twenty-five Fundamental Operations45
Chapter 2Eight Classes of Reduction of Fractionsq57
Chapter 3Eight Types of Procedures61
Chapter 4Four Special Topics75
Chapter 5Quintet of Topic85
Chapter 6List of rules91
Part IV Mathematical
Chapter 1Twenty -five Fundamental Operations97
Chapter 2Eight Classes of Reduction on Fractions125
Chapter 3Eight Types of Procedures133
Chapter 4Four Special Topics163
Chapter 5Quintet of Topic183
Appendices
AConcordance of the Ganitasarakaumudi and Other Works195
BThe Type Problems207
CIndex to the Number in the Text215
DGlossary Index to the Text223
Bibliography
Index of Mathematical Terms267
Index of Things in the Text273
Index of Sanskrit/Prakrit authors and titles277












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