Ganitavali

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It gives me immense pleasure in presenting to the scholars of mathematics engaged in fundamental research this volume of "Ganitavali" as compiled by Sri Bibhuti Bhusan Bhattacharya, an eminent Nyaya-Vaisesika scholar and edited by Dr. Manabendu Banerjee and Dr. Pradip Kumar Majumdar. This volume is based on this manuscript 'Ganitavali' in Devanagari script preserved at the Asiatic Society, Kolkata. Ganitavali mainly deals with Arithmetic and Astronomy and gives a glimpse of the high standard of mathematical and astronomical knowledge.

The golden age of the study of mathematics in India began from the time of Aryabhata I. He wrote Aryabhatiya in 499 A.D. which dealt with astronomy, geometry, algebra, mensuration etc. Varahamihira (505-587 A.D.) wrote Pancasiddhantika which is the collection of five Siddhantas like Paulisa-Siddhanta, Romaka-Siddhanta, Vasista- Siddhanta, Saura-Siddhanta and Pitamaha-Siddhanta of earlier dates. In the history of mathematics, the work has a high place for its amount of trigonometrical information. Bhaskara I (fl c. 600 A.D.) wrote three books on mathematics and astronomy. These books are (i) Mahabhaskariya (in eight chapters), (ii) Aryabhatiya-bhasya, a commentary on Aryabhatiya of Aryabhata I and (iii) Laghubhaskariya, an abridged and simplified version of Mahabhaskariya (in eight chapters). The most prominent Indian mathematician was Brahmagupta (fl c. 628 A.D) who wrote (i) Brahmasphuta Siddhanta and (ii) Khandakhadyaka. Brahmasphuta Siddhanta contains twenty-four chapters which include two chapters on mathematics viz. (i) Ganitadhyaya and (ii) Kuttakadhyaya. These two chapters are highly valuable. In these two chapters there is a great deal of discussion on arithmetic and algebra. Besides, there is also discussion on the formula of trigonometry. Lalla (c. 768 A.D.) wrote Sisyadhivrddhida which is an astronomical book. (c. 800-850 A.D.) wrote commentaries on two books-Mahabhaskariya and Laghubhaskariya of Bhaskara I. Besides these two commentaries he wrote "Govindakrti" but this book is lost. Quotations from this work are found to appear in the commentaries of the Indian astronomers Sankaranarayana (869 A.D.) and Udayadivakara (1073 A.D.). Prthudaka Svami (c. 850 A.D.) wrote a commentary on Brahmasphutasiddhanta. Mahaviracarya (850 A.D.), a Jaina mathematician wrote Ganita Sarasamgraha. This book is supposed to be regarded as a complete text book on mathematics. Sridharacarya's (c. 850-950) Pătiganita is a work on arithmetic and mensuration. He dealt with multiplication, division, square, square root, cube, cube root, fraction, summation of series (both A.P. and G.P) and he is the first mathematician who gave a rule to extract the roots of the equation ax² + bx = c. Aryabhata II wrote Mahasiddhanta, which contains Pati, kuttaka and bija. Sripati, another Jaina mathematician (c. 1039) wrote (i) Ganitatilaka (ii) Siddhantasekhara and (iii) Bijaganita. He also wrote five astronomical and astrologi- cal books. They are (i) Dhikotikarana (ii) Jyotisaratnamala, (iii) Dhruvamanasa (v) Jatakapaddhati, and (v) Daivajnavallabha. Bhaskara II (c. 1114 to 1200 A.D.) wrote three books viz (i) Lilavati (ii) Bijaganita, (iii) Siddhanta Siromani. He is also author of two works namely Vasanabhasya, his own commentary on Siddhanta-Siromoni and Karanakutuhala. Lilavati is based on Brahmagupta's Brahmasphuta-Siddhanta, Sridhara's Patiganita and Aryabhata II's Mahasiddhanta. It contains many useful propositions in Geometry and arithmetic. Narayana Pandit (c. 1356 A.D.) was the author of two books (i) GanitaKaumudi (ii) Bijaganitavatamsa. Madhava (c. 1400 A.D), a well known Keralian mathematician, wrote Venvaroha which is a book on spherical astronomy and mathematics. Paramesvara (c. 1430 A.D.) was the founder of drgganita system of astronomy who wrote commentaries on some popular classical books on astronomy and mathematics. His commentaries are: (i) Bhatadipika on Aryabhatiya, (ii) Paramesvari on Laghubhaskariya of Bhaskara I (iii) Siddhantadipika (or Karmadipika) on Mahabhaskariya (iv) Paramesvara on Munjala's Laghumanasa (v) the Vivarana on Suryasiddhanta and (vi) Vyakhya on Lilavati and others. Nilakantha Somasutvan (c. 1443 to 1543 A.D) wrote Aryabhatiyabhasya and Tantrasamgraha. Jnanaraja (1503 A.D.) wrote Siddhantasundara and Siddhantasundarabija. Citrabhanu (c. 1475 to 1550 A.D) wrote Karanampta. There are several mathematicians who wrote books on mathematics and astronomy but among these mathematicians we can mention the names of (i) Munisvara, a court astronomer of king Sajahan, who wrote Siddhanta Sarvabhauma, (ii) Kamalakar (1616 to 1700 A.D.) who wrote Siddhanta tattva viveka and (iii) Pandit Jagannath (c. 1657 to 1750 A.D.) who wrote Siddhantasamrat and Rekhaganita.