Fwd: Fw: new book on Rajaditya
Balachandra Rao
VYAVAHARA GANITA and LILAVATI
WITH
New Kannada and English Translation
By
Dr.(Mrs).Padmavathamm
Krishnaveni
Śri.K.G.Prakash
ABOUT THE BOOK
Rājāditya was a Jainā poet. Probably he was the first person who wrote mathematical works in Kannada. He is the author of the following works on mathematics.
1. Vyavahāragaṇita
2. Kṣetragaṇita
3. Vyavahāraratna
4. Līlāvati
5. Chitrahasuge
6. Jainagaṇita Sūtrodāharaṇa
Out of the above six works of Rājāditya, only Vyavahāragaṇita
has been published by the Madras (now Chennai) Government in the year 1955. This was critically edited by Prof.Mariappa Bhat who was the Head of the Kannada Department in the University of Madras. This edition of Vyavahāragaṇita is based on three palm-leaf manuscripts and one paper manuscript which were preserved in the Madras Government. This is written in Kanda , Vtta and Shloka metres.
Rājāditya was known by many other names such as Rājā, Rājavarma, Bhāskara, Bāchayya. Many titles like, Vōjeveḍanga, Padyavidyādhara, Uttamabhavyabhūsaṇa, Jinapadakamalamadhukara were conferred on him. It is evident from his compositions of verses that he is not only a mathematician but also a good poet.
In the Introduction to Vyavahāragaṇita he has beautifully described his native place Poovinabāge. This is mostly located in North-Karnataka and resembles very much Hoovinahaḍagali and Bāgevāḍi.
In Vyavahāragaṇita, Rājāditya states that his master was Shubhachandra, father was Shripathi, mother was Vasantha and patrons were Bāhubali-Bharatha. Being handsome, honest, helpful to others and a great scholar, Rājāditya was flourishing very well in some royal court. He was also a devotee of Nemitīrthaṁkara.
The Introductory Chapter of Vyavahāragaṇita ends beautifully thus –
“ Idu Shubha Chandradeva yogīndra pādāravinda Madhukarāyamāṇa Mānasānaṁdita Sakalagaṇita tattvavilāsa vinēyajana vinuta śri Rājāditya viracitamappa Vyavahāragaṇitado pīṭhīkā prakaraṇaṁ samāptaṁ “.
Rājādityā’s mathematical works are mainly in the form of verses which is a rare combination of poetic genius and scientific knowledge.
The published work Vyavahāragaṇita is concerned with commercial arithmetic of olden times. It consists of the following eight sections – Technical terms, Proportion- both direct and inverse, Proportionate Division, Mixture, Interest, Profit and Loss, Discount and Miscellaneous.
In almost every topic, the principle is first stated which is followed by illustration of examples. At the end of every problem we find labdha which is a brief analysis with the answer to that problem. This labdha is followed by ṭīkā which gives a clear explanation. Hundreds of problems in this book are taken from real life which enable us to have an idea of the socio-economic conditions which prevailed in Karnataka during the 12th century A.D.
It is surprising to note that in many parts of Karnataka, copies of Vyavahāragaṇita were made and were used to teach mathematics for children during 12th century A.D. From the manuscript (No.D.1445) available at Madras Oriental Research Library, it is clear that Vyavahāragaṇita was used not only by Jains but also by Brahmins and others.
Regarding the time of Rājāditya there is a controversy between historians and Dr.Venkatasubbiah. But after a long debate later historians Shri Narasimhacharya and others have accepted the period 1190 A.D of Rājāditya given by Dr.Venkatasubbiah.
From the chapter on terminology in Vyavahāragaṇita we find names upto 40 unit places. They are – ekkaṁ, dāhaṁ, śataṁ, sāvira, dāsāvīra, lakṣa, daśalakṣa, kōṭi, dākōṭi, śatakōṭi, arbuda, nyarbuda, kharva, mahākharva, padma, mahāpadma, kṣoṇi, mahākṣoṇi, śaṁkha, mahāśaṁkha, kṣiti, mahākṣiti, kṣōbha, mahākṣōbha, naḍi, mahānaḍi, naga, mahānaga, ratha, mahāratha, hari, mahāhari, phaṇi, mahāphaṇi, kratu, mahākratu, sāgara, mahāsāgara, parimita, mahāparimita.
There are many synonyms for the numbers 0 upto 9 in Vyavahāragaṇita. Example for “0” :
0 – divi, kaika, śūnya, agra, aṁbara, gagana, meghamārga, ākāśa, jaladharamārga, baṁdhayōga, viyat, ayanapatha, abhra, khaṁ, vattaṁ, āgasa, jaladharapatha, vyadvite.
Many names are also there for addition, subtraction, multiplication and division.
Regarding Vyavahāragaṇita, Rājāditya says thus –
Dhāruṇiyo sakala budhā
Dhāramenal svalpa māgiyaṁ vyavahāra
Dhāramenal sāramenal
Śri Rājādityanatiyiṁ viracisidaṁ ||
From the above it follows that his work is brief and is useful for many practical purposes.
He says that to know mathematics, ancient mathematical works are sufficient. But for easy transactions and quick references, Vyavahāragaṇita is written.
From Vyavahāragaṇita it appears that instead of using money, exchange system was in practice. Problems related to arecanut indicate that arecanuts were sold not by weighing but by actual counting.
Rājāditya occupies a unique place in the History of Kannada literature as he was the first person to write mathematics in Kannada.
Published work Vyavahāragaṇita is in old Kannada. The authors have translated all the Sutrās in Vyavahāragaṇita into New Kannada. They also have given solutions to all the problems. With a view to reach the readers outside Karnataka they have translated this work into English.
The new edition includes Līlāvati which is another work of Rājāditya. Līlavati is so far not published. The original palm-leaf manuscript was obtained from Kannada Adhyayana Kendra , Jnānabhārati, Bangalore University, Bangalore. The length of this manuscript is 13.5 cms and its breadth is 5 cms. There are 12 lines in each leaf generally. Some pages contain less than 12 lines also. We hope that this new edition will be a valuable contribution to the History of Mathematics and in particular to the Indian History of Mathematics.
With regards,
Blachandra Rao
