Newly Discovered Mathematical Manuscripts from Jaina Bhandara

Newly Discovered Mathematical Manuscripts from Jaina Bhandara
Anupam Jain & S.C. Agrwal

 '''Abstract Jaina literature is very vast and varied. During last 6 Decades many Jaina texts are discovered and published with Hindi/English translation. Even then many are still lying unpublished & waiting the attention of scholars. During the survey made by authors in the M.P. region several new Manuscripts are discovered. Being the Mathematician we have special interest in the mathematical manuscripts hence we have collected all such information and submitting in the present paper.'''

Mathematics is an integral part of the Jaina literature. Apart from many philosophical texts which include Mathematical formulae, concepts. illustrations and applications, we get many exclusively mathematical texts written by ancient Jaina scholars.

Ganita-Sara-Samgraha (GSS) of Mahaviracarya is an Important Jaina Mathematical text which was published by Madras Govt. in 1912 with the English translation and notes by M. Rangacarya. So for Trisatika (Ganitasara) of Sridhara, Ganita Tilaka Commentary of Simhatilaka Suri and Ganisata Kaumudi of Thakkurupheru has been published. Recently Istankapancavisatika of ``Tejasingh has been published by Takao Hayashi in Ganita Bharati (2006) (Bulletin of (I.S.H.M). Still many important Mathematical texts are laying unpublished in different Jaina Grantha Bhandara (Libraries). They are reported first time or these unreported Manuscripts are discovered during the survey sponsored by National Mission for Manuscripts N. Delhi. Apart from many others following six are more Important Mathematical. Manuscmpts. Original Manuscripts are laying in the respective Bhandara and we have collected their Xerox copies.

1.Ganitasara of Sridhara (799 A.D.)

2.Jyotirjnavidhi of Sridhara (799 A.D.)

3.Lokanuyoga of Jinasena (850 A.D.)

4.Sattrinsika of Madhavacandra Traividya (11th C.A.D.)

5.Trailokya Dipaka of Pt. Vamadeo (16th C.A.D.)

6.Ganitasara of Hemaraja (17th C.A.D.)

Now we give some basic details of these manuscripts together with their Importance from the point of view of Indian Mathematics.

1. Ganita-Sara-Published copy of Ganita-Sara (Trisatika) contains only 180 verses while Usha Asthana and Mamta Agrawal reported1 more than 300 verses in their Doctoral Dissertations Submitted in Lucknow university & C.C.S. University Meerut. So for two editoons of Ganita Sara (Trisatika) have been published

१.त्रिशतिका—श्रीधराचार्य विरचिता, सं.—सुधाकर द्विवेदी, चंद्रप्रभा प्रेस, वाराणसी, १८९९ It has only original text, No. Translation is given. २.	त्रिशतिका (पाटीगणितसार), श्रीधराचार्य विरचिता सुक्षेमा अनुवाद तथा अनुशीलन सहित, डॉ. सुद्युम्न आचार्य, राष्ट्रीय संस्कृत संस्थान, नई दिल्ली, २००४

It has detailed explanation in Hindi too. But regarding original verses it totally depend on the Dvivedi edition which is obviously incomplete. A very important and oldest available copy is preserved in Jaina Math, Moodbidri. It is preserved on No 781 having 15 Folios. It is complete, correct and with the commentary of Ballabha. A more authentic version can be prepared and published with the help of the help of this copy2. A zerox copy of it is available with Ist author. The New edition must be produced keeping in mind that Sridhara was prior to Mahavira because in a MSS of Ganita-sara-samgraha. It is mentioned ‘कुमादित्युत्तंक श्रीधराचार्यरित भद्रं भूयात’

2. Jyotirjnanavidhi-In ancient India Jyotisa and Ganita are interrelated subjects. Infact in the beginning Mathematics was a part of Jyotisa as in Aryabhatiya of Aryabhata (476 A.D.). The mathematician Sridhara is also the author of Jyotirjnanavidhi. It is concluded by K.S. Shukla, L.C. Jain, R.C. Gupta and many other historians4. Jyotirjnanavidhi was a Jaina Text because its method for finding proper time (Muhurta) was quoted by later Jaina Scholars like vasunandi in his Pratistapathas which are very important texts regarding religious ceremonies. The Jaina value 20 and 3 (Rough) used in this text also. It has Jaina Mangla-carana.

There is a reference of Gatasakabda (Last Saka) 7205. Hence it is clear that is was written by Sridhara in 799 A.D. (721 saka) Therefore it has been conformed that mathematician Sridhara was alive tn 799 A.D. It is still unpublished and three copies are available in Modabidri, Arrah & Ujjain. It is a text of first rate importance and should be published. The arrah manuscript is incomplete but the manuscript recovered from Ujjain is complete. As per Ujjain manuscript, it has 10 chapters. The moodbidri MSS, written in kanari script, is also complete. The 10 chapters are following.

1.Samjnadhikara

2.Dhruvadhikara

3.Tithyadhikara

4.Samkranti-Rtuahoradhikara

5.Grahanilyadhikara

6.Grahayuddhadhikara

7.Grahanadhikara

8.Lagnaprakarana

9.Ganitadhikara

10.Muhurtadhikara

We are planning to publish the text Jyotirjnanavidhi shortly. 3. Lokanuyoga-It is a part of Harivamsa purana written by Acarya Jinasena in 9th C.A.D. but the copy available in Ailaka Pannalala Sarasvati Bhavan, Ujjain bears many illustrations and notes hence it is useful in understanding geometrical knowledge of Jaina tradition. It has thrre chapters and 73 folios.6 I — Adholoka

II — Madhyaloka

III — Urdhvaloka

4. Sattrisika — Many Manuscripts of it are available in the Bhandaras of Jaipur. Karanja, Udaipur and Ujjain under the name of Sattrinsika of Sattnisatika or-Chattisitika. It was written by Madhava Candra Traividya (11th C.A.D.) on the basis of Ganita Sara Samgraha (GSS) of Mahavitacarya6. In the puspika of Karanja Manuscripts it is mentioned.

श्री वीतरागय नम:।६। छत्तीसमेतेन सकल ८, भिन्न ८, भिन्न जाति ६, प्रकीर्णक १०, त्रेराशिक ४, इंता छत्तीस मे बुदु वीराचार्यरू पेल्हगणितवनु माधवचन्द्र त्रैविद्याचार्यरू शोध सिदरागि शोध्यसार संग्रहमेनिसकोंबुदु। This clearly shows that it is a work of Madhava Candra Traividya. Previously there is a lot of confusion about it. Many manuscripts of it are reported or catalouged as incomplete manuscript of GSS and some scholars mentioned it as another book of Mahaviracarya. M.B. Lal Agrawal Writes इसमें बीज गणित की ही चर्चा है’but there is no such material is available in it. More details of its content are given in the following article of authors. Anupam Jain and Suresh Chandra Agrawal माधवचंद्र और उनकी षटत्रिंशिका, अर्हत् वचन (इन्दौर), १ (१) सितम्बर १९८८, ६५-७४ It has following 13 sutaras and magic squares of 34 and 15 apart from first four chapters of GSS ie. Parikarm Vyavahara Kalasavarna Vyavahara Prakiranaka Vyavahara Trairasika Vyavahara There is an additional chapter varga saamkalitanayana sutra. It contains 13 sutra. 1.Varga saamkalitanayana sutra.

2.Ghana saamkalitanayana sutra.

3.Ekvaradisamkalitaghananayan Sutra.

4.Sarva dhananayanae Sutradvayam

5.Uttarottarcayabha vasamkalitaghananayana Sutra.

6.Ubhayantadagata Pursadvasasamyoganayam Sutra.

7.Vanikkarasthita ghananayana sutram

8.Samudra Madhye 1-2-3

9.Chedoasase Jato karana sutram

10.Karana Sutra Trayam

11.Gunaguna Sutram

12.Bahukarananayan Sutram

13.Vyasadyanayan Sutram

Hence this book is important for the study of Mahaviracarya too.

5. Trailokya Dipaka of Pt. Vamadeo—
Two copies are discovered so for and they are preserved in Amar Granthalaya, Indore and Jain Vidya Samsthan, Shri Mahavirji. Indore Copy has 62 Folios7. The Period of Pt. Vamadeo is prior to 1379 A.D. because the MSS collected from Shri Mahavirji written in Delhi in the period of Firoj Shah Tugalak. It is Pictorial Manuscript having many important geometrical illustrations. It should be published with translation.

6. Ganita-sara of Hemaraja
—We have two manuscripts of Ganita-sara written by Hemaraja (Godika) 1673 A.D. One mss was recovered from Adinatha Dig. Jain Mandir, Bundi (Raj.) & another from Digambar Jain mandir, Ganjbasoda (M.P.). This small book of 89 verses in Hindi seems to be of first Mathematical text written in Hindi poetry. The Hindi Tranlation has been published in Jnana Desana8. It is important from the point of view that it contains Jaina system of classification of numbers. It has only 7 Folios. Some more mathematical texts are reported but we do not have their zerox copies or we are not in position to confirm it. some of them are. Ganita Sathsau-Mahimodaya (1665 A.D.) Copy reported in Abhai Granthagara, Bikaner Ganita Sara-Ananda Kavi Copy reported in Sethia library, Bikaner Ganita Vilasa-Candrama Jain Math, Moodbidri No-169 & Jain Bhavana, Moodbidri No-89 Some books of Rajaditya and several ksetrasamasa, vrhat ksetrasamasa are still unpublished. One copy of Triloka Darpana by khadagasena is also collected recently. We suggest to establish a centre for Mathematical Manuscripts lying in different Bhandars of our country. Necessary facilities for the translation and critical study of such manuscripts can be arranged there.

References :
1.Usha Asthana, Acarya Sridhara and his Trisatika, Lucknow University. Lucknow, 1960 Mamta (Singhal) Agrawal, DeeÛeeÙe& ßeerOej SJeb Gvekeâe ieefCeleerÙe DeJeoeve, Ph.D Thesis C.C.S. University, Meerut 2002.

2.Ganita Sara (Trisatika), Acarya Sridhara with the Commentary of Ballabha, Folio-15, Lines per folio-6, Latter perline-45, Script-Kanari, Complete.Zerox copy of it is a available in Kunda Kunda Jnanapitha library, Indore.

3.Royal Asiatic Society, Kolkata, MSS No-230

4.Mamta Agrawal Ph. D. Thesis, CCS Univ., Meerut, 2002

5.Arrah Manuscript, P-5

6.Lokanuyoga, Acarya Jinasena, Folio-73, Script-Devanagari, Language-Samsakrta, Subject-Jainagama/Mathematics, Complete, Ailak Pannalala Saraswati Bhandara, Ujjain, No.-543, Zerox is in kundakunda Jnanapitha Library.

7.Trailokya Dipaka (Sarani Kala Sahita), Vamdeo Pandita, Script-Devnagari, Language. Samsakrta, Subject-Jainagama, Scribing period-V.S. 1980, Complete, Amar Granthalaya, Indore.

8.Jnana Desna (Meerut), 1 (1), January-June 2008, 77-78

'''अर्हत् वचन जुलाई—सितम्बर—२०१२, पेज. न. ६५—७०'''