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{{Short description|Indian mathematician and Jain scholar (750–825)}}
{{Use dmy dates|date=February 2016}}
{{Use dmy dates|date=February 2016}}
{{Use Indian English|date=February 2016}}
{{Use Indian English|date=February 2016}}
{{Infobox religious biography
{{Infobox religious biography
| honorific-prefix = [[Acharya (Jainism)|Acharya]] Shri
| honorific-prefix   = [[Acharya (Jainism)|Acharya]] Shri
| honorific-suffix = Ji Maharaj
| honorific-suffix   = Ji Maharaj
| image = Virsena Acharya.jpg
| image             = Virsena Acharya.jpg
| alt = Virasena
| alt               = Virasena
| caption = [[Acharya]] Virasena
| caption           = [[Acharya]] Virasena
| religion = [[Jainism]]
| religion           = [[Jainism]]
| sect = ''[[Digambara]]''
| sect               = ''[[Digambara]]''
| birth_date = 792 CE
| birth_date         = 750
| death_date = {{death year and age|853|792}}
| death_date         = 825
| works = ''[[Dhavala]]''
| teacher            = Aryanandi
| predecessor = [[Aryanandi]]
| disciples          = [[Jinasena]], Dasharayaguru, Vinayasena, Shripal, Padmasena, Devasena, [[Kumudendu Muni]]
| successor = [[Jinasena]]
| works             = ''[[Dhavala]]''
| predecessor       = [[Aryanandi (8th century)|Aryanandi]]
| successor         = [[Jinasena]]
}}
}}
{{Jainism}}
{{Jainism}}
'''Acharya Virasena''' (792-853 CE),{{sfn|Jaini|1991|p=111}} also known as '''Veerasena''', was a [[Digambara monk]] and belonged to the lineage of Acharya [[Kundakunda]].<ref name="Indranandi" /> He  was an [[Indian mathematician]] and Jain philosopher and scholar. He was also known as a famous orator and an accomplished poet.<ref name="Jinasena" /> His most reputed work is the Jain treatise ''[[Dhavala]]''.<ref>Satkhandagama : Dhavala (Jivasthana) Satparupana-I (Enunciation of Existence-I)
'''Acharya Virasena''' (750–825CE),{{sfn|Jaini|1991|p=111}} also spelt as '''Veerasena''', was a Jain monk and belonged to the lineage of Acharya [[Kundakunda]].<ref name="Indranandi" /> He  was an [[Indian mathematician]] and Jain philosopher and scholar of Digambar sect. He was also known as a famous orator and an accomplished poet.<ref name="Jinasena" /> He is renowned for his work on the monumental Jain commentary series on the <nowiki>''Shatkhandagama'', known as the ''</nowiki>''[[Dhavala]]''<nowiki>''</nowiki> texts.<ref>Satkhandagama : Dhavala (Jivasthana) Satparupana-I (Enunciation of Existence-I)
An English Translation of Part 1 of the Dhavala Commentary on the Satkhandagama of Acarya Pushpadanta & Bhutabali Dhavala commentary by Acarya Virasena English tr. by Prof. Nandlal Jain, Ed. by Prof. Ashok Jain {{ISBN|9788186957479}}</ref> The late Dr. Hiralal Jain places the completion of this treatise in 816 AD.<ref>{{cite book
An English Translation of Part 1 of the Dhavala Commentary on the Satkhandagama of Acarya Pushpadanta & Bhutabali Dhavala commentary by Acarya Virasena English tr. by Prof. Nandlal Jain, Ed. by Prof. Ashok Jain {{ISBN|9788186957479}}</ref> The late Dr. Hiralal Jain places the completion of this treatise in 816.<ref>{{cite book
   |last = Nagrajji
   |last = Nagrajji
   |first = Acharya Shri
   |first = Acharya Shri
Line 25: Line 28:
   |page = 530
   |page = 530
   |isbn = 9788170227311
   |isbn = 9788170227311
}}</ref>
}}</ref> He played a critical role in the development of Digambara scholasticism and is considered one of the greatest Jain scholars of early medieval India.


Virasena was a noted mathematician. He gave the derivation of the [[volume]] of a [[frustum]] by a sort of infinite procedure. He worked with the concept of ''ardhaccheda'': the number of times a number could be divided by 2; effectively [[base-2 logarithm]]s. He also worked with logarithms in base 3 (trakacheda) and base 4 (caturthacheda).<ref>{{citation| contribution=History of Mathematics in India|title=Students' Britannica India: Select essays|editor1-first=Dale|editor1-last=Hoiberg|editor2-first=Indu|editor2-last=Ramchandani|first=R. C.|last=Gupta|page=329|publisher=Popular Prakashan|year=2000| contribution-url=https://books.google.com/books?id=-xzljvnQ1vAC&q=Virasena+logarithm&pg=PA329}}</ref>
==Life==
Virasena was a disciple of the Jain acharya [[Aryanandi (8th century)|Aryanandi]] and flourished during the [[Rashtrakuta]] King [[Dhruva Dharavarsha]] and [[Govinda III]].<ref name="jaini1979">Jaini, Padmanabh S. The Jaina Path of Purification. University of California Press, 1979, p. 118.</ref> He was based in the Deccan region and attracted several prominent disciples, including Jinasena I and Gunasena, later known as Jinasena II.<ref name="upadhye">Upadhye, A.N. “Virasena and the Dhavala Tradition.” In Studies in Jaina History and Culture, ed. P.S. Jaini, Motilal Banarsidass, 1999.</ref>
 
Virasena was proficient in astrology, grammar, logic, mathematics and prosody. He wrote ''[[Dhavala]]'', a commentary on Jain canon ''[[Shatakhandagama]]''. He also started the work on ''Jayadhavalaa'' which was completed by his disciples. He was among the jewels of [[Rashtrakuta]] Emperor Dhruva dharavarsha and Govinda III, it is also says that he also present at the time of [[Amoghavarsha]].{{sfn|Natubhai Shah|2004|p=31}}
 
His lineage started with Chandrasena who initiated Aryanandi.{{sfn|Pannalal Jain|1951|pp=30-31}} Aryanandi initiated Virasena and [[Jayasena (Jain monk)|Jayasena]].{{sfn|Pannalal Jain|1951|pp=30-31}} Virasena initiated six disciples who were Dasharayguru, [[Jinasena]], Vinayasena, Shripal, Padmasena and Devasena.{{sfn|Pannalal Jain|1951|pp=30-31}} Dasharayguru and Jinasena initiated Gunabhadra who later initiated Lokasena.{{sfn|Pannalal Jain|1951|pp=30-31}} Vinayasena initiated Kumarasena who started the [[Kashtha Sangha]].{{sfn|Pannalal Jain|1951|pp=30-31}}
 
== Works ==
 
=== Dhavala and Related Texts ===
Virasena is primarily known for initiating the commentary project on the ''Shatkhandagama'', one of the most revered canonical texts in Digambara [[Jainism]]. This massive commentary is collectively referred to as the ''[[Dhavala]]'' series, and it includes:
 
•⁠  ⁠''Dhavala''
 
•⁠  ⁠''Jayadhavala''
 
•⁠  ⁠''Mahadhavala''
 
While Virasena began the ''Dhavala'', he was unable to complete it in his lifetime. The work was carried forward by his disciples Jinasena II (Gunasena) and others.<ref name="cort2010">Cort, John E. Framing the Jina: Narratives of Icons and Idols in Jain History. Oxford University Press, 2010, pp. 115–116.</ref>
 
These texts are not only commentaries but also rich repositories of Jain philosophy, cosmology, and metaphysics.
 
==Mathematics==
Virasena was a noted mathematician. He gave the derivation of the [[volume]] of a [[frustum]] by a sort of infinite procedure. He worked with the concept of ''ardhachheda'': the number of times a number can be divided by 2. This coincides with the [[binary logarithm]] when applied to [[powers of two]], but gives the [[p-adic order|2-adic order]] rather than the logarithm for other integers.<ref>See, e.g., {{citation|title=Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness|volume=22|series=Progress in Computer Science and Applied Logic|first=Igor|last=Shparlinski|publisher=Birkhäuser|year=2013|isbn=978-3-0348-8037-4|page=35|url=https://books.google.com/books?id=z635BwAAQBAJ&pg=PA35}}.</ref><ref>{{citation| contribution=History of Mathematics in India|title=Students' Britannica India: Select essays|editor1-first=Dale|editor1-last=Hoiberg|editor2-first=Indu|editor2-last=Ramchandani|first=R. C.|last=Gupta|page=329|publisher=Popular Prakashan|year=2000| contribution-url=https://books.google.com/books?id=-xzljvnQ1vAC&q=Virasena+logarithm&pg=PA329|language=en}}</ref>  


Virasena gave the approximate formula ''C''&nbsp;=&nbsp;3''d''&nbsp;+&nbsp;(16''d''+16)/113 to relate the circumference of a circle, ''C'', to its diameter, ''d''.  For large values of ''d'', this gives the approximation π&nbsp;≈&nbsp;355/113&nbsp;=&nbsp;3.14159292..., which is more accurate than the approximation π&nbsp;≈&nbsp;3.1416 given by [[Aryabhata]] in the ''[[Aryabhatiya]]''.<ref>{{Citation
Virasena gave the approximate formula ''C''&nbsp;=&nbsp;3''d''&nbsp;+&nbsp;(16''d''+16)/113 to relate the circumference of a circle, ''C'', to its diameter, ''d''.  For large values of ''d'', this gives the approximation π&nbsp;≈&nbsp;355/113&nbsp;=&nbsp;3.14159292..., which is more accurate than the approximation π&nbsp;≈&nbsp;3.1416 given by [[Aryabhata]] in the ''[[Aryabhatiya]]''.<ref>{{Citation
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   | first2 = S. L.
   | first2 = S. L.
   | title = First Degree Indeterminate Analysis in Ancient India and its Application by Virasena
   | title = First Degree Indeterminate Analysis in Ancient India and its Application by Virasena
|url=http://www.new1.dli.ernet.in/data1/upload/insa/INSA_1/20005b5d_127.pdf
  | url = http://www.new1.dli.ernet.in/data1/upload/insa/INSA_1/20005b5d_127.pdf
| journal = Indian Journal of History of Science
  | journal = Indian Journal of History of Science
   | volume = 32
   | volume = 32
   | issue = 2
   | issue = 2
   | pages = 127–133
   | pages = 127–133
   | date = February 1997
   | date = February 1997
  | access-date = 17 September 2014
  | archive-date = 29 November 2014
  | archive-url = https://web.archive.org/web/20141129100731/http://www.new1.dli.ernet.in/data1/upload/insa/INSA_1/20005b5d_127.pdf
  | url-status = dead
   }}</ref>
   }}</ref>
 


==Life==
== Disciples ==
Virasena was proficient in astrology, grammar, logic, mathematics and prosody. He wrote ''[[Dhavala]]'', a commentary on Jain canon ''[[Shatakhandagama]]''. He also started the work on ''Jayadhavalaa'' which was competed by his disciples. He was among the jewels of [[Rashtrakuta]] king [[Amoghavarsha]].{{sfn|Natubhai Shah|2004|p=31}}
Virasena mentored several disciples who carried forward his intellectual legacy:
•⁠  ⁠'''[[Jinasena]]''': Author of the ''Adi Purana'', an epic Jain text on Rishabhanatha and Bharata.
•⁠  ⁠'''Gunasena (Jinasena II)''': Successor of Jinasena I, and co-author of the ''Dhavala'' commentary series.


His lineage started with Chandrasena who initiated Aryanandi.{{sfn|Pannalal Jain|1951|pp=30-31}} Aryanandi initiated Virasena and Jayasena.{{sfn|Pannalal Jain|1951|pp=30-31}} Virasena initiated six disciples who were Dasharayguru, [[Jinasena]], Vinayasena, Shripal, Padmasena and Devasena.{{sfn|Pannalal Jain|1951|pp=30-31}} Dasharayguru and Jinasena initiated [[Gunabhadra (Jain monk)|Gunabhadra]] who later initiated Lokasena.{{sfn|Pannalal Jain|1951|pp=30-31}} Vinayasena initiated Kumarasena who started the [[Kashtha Sangha]].{{sfn|Pannalal Jain|1951|pp=30-31}}
== Legacy ==
Acharya Virasena is revered as a pioneering figure in the Digambara tradition for his scholarship and rigorous analysis of Jain doctrine. His contributions to Jain literature and mathematics mark him as a significant figure in early medieval Indian intellectual history. The ''Dhavala'' series continues to be studied by Jain scholars and remains a cornerstone of Digambara exegesis.


==See also==
==See also==
*[[Indian mathematics]]
*[[Indian mathematics]]
*[[Umaswami]]
*[[Umaswami]]
*[[Hemachandra]]
*[[Shatkhandagama]]
*[[Jainism in Karnataka]]
*[[Rashtrakuta literature]]


==References==
==References==
===Citations===
===Citations===
{{reflist|refs=
<references>
<ref name="Jinasena">Jinasena. ''Ādi Purāņa''</ref>
<ref name="Jinasena">Jinasena. ''Ādi Purāņa''</ref>
<ref name="Indranandi">Indranandi. ''Shrutāvatāra''</ref>}}
<ref name="Indranandi">Indranandi. ''Shrutāvatāra''</ref>
</references>


===Sources===
==Bibliography==
* {{citation |editor-last=Jain |editor-first=Pannalal |editor-link=Pannalal Jain |title=Mahapurana Adipurana of Bhagavata Jinasenacharya |url=https://archive.org/details/in.ernet.dli.2015.327048 |year=1951 |publisher=[[Bharatiya Jnanapitha]] |ref={{sfnref|Pannalal Jain|1951}} }}
* {{citation |editor-last=Jain |editor-first=Pannalal |editor-link=Pannalal Jain |title=Mahapurana Adipurana of Bhagavata Jinasenacharya |url=https://archive.org/details/in.ernet.dli.2015.327048 |year=1951 |publisher=[[Bharatiya Jnanapitha]] |ref={{sfnref|Pannalal Jain|1951}} }}
* {{citation |last=Jaini |first=Padmanabh S. |author-link=Padmanabh Jaini |title=Gender and Salvation: Jaina Debates on the Spiritual Liberation of Women |url=https://books.google.com/books?id=GRA-uoUFz3MC |date=1991 |isbn=0-520-06820-3 |publisher=[[University of California Press]] }}
* {{citation |last=Jaini |first=Padmanabh S. |author-link=Padmanabh Jaini |title=Gender and Salvation: Jaina Debates on the Spiritual Liberation of Women |url=https://books.google.com/books?id=GRA-uoUFz3MC |date=1991 |isbn=0-520-06820-3 |publisher=[[University of California Press]] }}
* {{citation |last=Shah |first=Natubhai |author-link=Natubhai Shah |title=Jainism: The World of Conquerors |url=https://books.google.com/books?id=qLNQKGcDIhsC |volume=I |date=2004 |orig-year=First published in 1998 |publisher=[[Motilal Banarsidass]] |isbn=81-208-1938-1 |ref={{sfnref|Natubhai Shah|2004}} }}
* {{citation |last=Shah |first=Natubhai |author-link=Natubhai Shah |title=Jainism: The World of Conquerors |url=https://books.google.com/books?id=qLNQKGcDIhsC |volume=I |date=2004 |orig-year=First published in 1998 |publisher=[[Motilal Banarsidass]] |isbn=81-208-1938-1 |ref={{sfnref|Natubhai Shah|2004}} }}
* ⁠Cort, John E. Framing the Jina: Narratives of Icons and Idols in Jain History. Oxford University Press, 2010. ISBN 9780195385021.
*⁠ Dundas, Paul. The Jains. 2nd ed., Routledge, 2002. ISBN 9780415305940.
* ⁠Jaini, Padmanabh S. The Jaina Path of Purification. University of California Press, 1979. ISBN 9780520039944.
* ⁠Upadhye, A.N. “Virasena and the Dhavala Tradition.” In Studies in Jaina History and Culture, ed. P.S. Jaini, Motilal Banarsidass, 1999.


==External links==
==External links==
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{{Authority control}}
{{Authority control}}


[[Category:792 births]]
[[Category:750 births]]
[[Category:853 deaths]]
[[Category:825 deaths]]
[[Category:Digambara Acharyas]]
[[Category:Digambara Acharyas]]
[[Category:Indian Jain monks]]
[[Category:Indian Jain monks]]
[[Category: Rashtrakuta people]]
[[Category:9th-century Indian Jains]]
[[Category:9th-century Indian Jains]]
[[Category:9th-century Jain monks]]
[[Category:9th-century Jain monks]]
[[Category:9th-century Indian monks]]
[[Category:9th-century Indian monks]]
[[Category:9th-century philosophers]]
[[Category:9th-century Indian philosophers]]
[[Category:9th-century Indian mathematicians]]
[[Category:9th-century Indian mathematicians]]
[[Category:Indian mathematicians]]
[[Category:Indian mathematicians]]
 
[[Category:Digambara monks]]
[[Category:8th-century Indian Jains]]
[[Category:Jain acharyas]]
[[Category:Jain writers]]
[[Category:Rashtrakuta dynasty]]


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{{India-scientist-stub}}
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{{Jainism-stub}}

Latest revision as of 16:43, 29 March 2026


Acharya Shri

Virasena

Ji Maharaj
Virasena
Acharya Virasena
Personal
Born750
Died825
ReligionJainism
SectDigambara
Notable work(s)Dhavala
Religious career
TeacherAryanandi
PredecessorAryanandi
SuccessorJinasena
Part of a series on
Jainism
Jain prayers
Philosophy
Ethics
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Major sects
Jain Literature
Other
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Tirth

Acharya Virasena (750–825CE),[1] also spelt as Veerasena, was a Jain monk and belonged to the lineage of Acharya Kundakunda.[2] He was an Indian mathematician and Jain philosopher and scholar of Digambar sect. He was also known as a famous orator and an accomplished poet.[3] He is renowned for his work on the monumental Jain commentary series on the ''Shatkhandagama'', known as the ''Dhavala'' texts.[4] The late Dr. Hiralal Jain places the completion of this treatise in 816.[5] He played a critical role in the development of Digambara scholasticism and is considered one of the greatest Jain scholars of early medieval India.

Life[edit | edit source]

Virasena was a disciple of the Jain acharya Aryanandi and flourished during the Rashtrakuta King Dhruva Dharavarsha and Govinda III.[6] He was based in the Deccan region and attracted several prominent disciples, including Jinasena I and Gunasena, later known as Jinasena II.[7]

Virasena was proficient in astrology, grammar, logic, mathematics and prosody. He wrote Dhavala, a commentary on Jain canon Shatakhandagama. He also started the work on Jayadhavalaa which was completed by his disciples. He was among the jewels of Rashtrakuta Emperor Dhruva dharavarsha and Govinda III, it is also says that he also present at the time of Amoghavarsha.[8]

His lineage started with Chandrasena who initiated Aryanandi.[9] Aryanandi initiated Virasena and Jayasena.[9] Virasena initiated six disciples who were Dasharayguru, Jinasena, Vinayasena, Shripal, Padmasena and Devasena.[9] Dasharayguru and Jinasena initiated Gunabhadra who later initiated Lokasena.[9] Vinayasena initiated Kumarasena who started the Kashtha Sangha.[9]

Works[edit | edit source]

Dhavala and Related Texts[edit | edit source]

Virasena is primarily known for initiating the commentary project on the Shatkhandagama, one of the most revered canonical texts in Digambara Jainism. This massive commentary is collectively referred to as the Dhavala series, and it includes:

•⁠ ⁠Dhavala

•⁠ ⁠Jayadhavala

•⁠ ⁠Mahadhavala

While Virasena began the Dhavala, he was unable to complete it in his lifetime. The work was carried forward by his disciples Jinasena II (Gunasena) and others.[10]

These texts are not only commentaries but also rich repositories of Jain philosophy, cosmology, and metaphysics.

Mathematics[edit | edit source]

Virasena was a noted mathematician. He gave the derivation of the volume of a frustum by a sort of infinite procedure. He worked with the concept of ardhachheda: the number of times a number can be divided by 2. This coincides with the binary logarithm when applied to powers of two, but gives the 2-adic order rather than the logarithm for other integers.[11][12]

Virasena gave the approximate formula C = 3d + (16d+16)/113 to relate the circumference of a circle, C, to its diameter, d. For large values of d, this gives the approximation π ≈ 355/113 = 3.14159292..., which is more accurate than the approximation π ≈ 3.1416 given by Aryabhata in the Aryabhatiya.[13]


Disciples[edit | edit source]

Virasena mentored several disciples who carried forward his intellectual legacy: •⁠ ⁠Jinasena: Author of the Adi Purana, an epic Jain text on Rishabhanatha and Bharata. •⁠ ⁠Gunasena (Jinasena II): Successor of Jinasena I, and co-author of the Dhavala commentary series.

Legacy[edit | edit source]

Acharya Virasena is revered as a pioneering figure in the Digambara tradition for his scholarship and rigorous analysis of Jain doctrine. His contributions to Jain literature and mathematics mark him as a significant figure in early medieval Indian intellectual history. The Dhavala series continues to be studied by Jain scholars and remains a cornerstone of Digambara exegesis.

See also[edit | edit source]

References[edit | edit source]

Citations[edit | edit source]

  1. ↑ Jaini 1991, p. 111.
  2. ↑ Indranandi. Shrutāvatāra
  3. ↑ Jinasena. Ādi Purāņa
  4. ↑ Satkhandagama : Dhavala (Jivasthana) Satparupana-I (Enunciation of Existence-I) An English Translation of Part 1 of the Dhavala Commentary on the Satkhandagama of Acarya Pushpadanta & Bhutabali Dhavala commentary by Acarya Virasena English tr. by Prof. Nandlal Jain, Ed. by Prof. Ashok Jain ISBN 9788186957479
  5. ↑ Nagrajji, Acharya Shri (2003). Agama and Tripitaka: Language and Literature. Concept Publishing Company. p. 530. ISBN 9788170227311.
  6. ↑ Jaini, Padmanabh S. The Jaina Path of Purification. University of California Press, 1979, p. 118.
  7. ↑ Upadhye, A.N. “Virasena and the Dhavala Tradition.” In Studies in Jaina History and Culture, ed. P.S. Jaini, Motilal Banarsidass, 1999.
  8. ↑ Natubhai Shah 2004, p. 31.
  9. ↑ 9.0 9.1 9.2 9.3 9.4 Pannalal Jain 1951, pp. 30-31.
  10. ↑ Cort, John E. Framing the Jina: Narratives of Icons and Idols in Jain History. Oxford University Press, 2010, pp. 115–116.
  11. ↑ See, e.g., Shparlinski, Igor (2013), Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness, Progress in Computer Science and Applied Logic, vol. 22, Birkhäuser, p. 35, ISBN 978-3-0348-8037-4.
  12. ↑ Gupta, R. C. (2000), "History of Mathematics in India", in Hoiberg, Dale; Ramchandani, Indu (eds.), Students' Britannica India: Select essays, Popular Prakashan, p. 329
  13. ↑ Mishra, V.; Singh, S. L. (February 1997), "First Degree Indeterminate Analysis in Ancient India and its Application by Virasena" (PDF), Indian Journal of History of Science, 32 (2): 127–133, archived from the original (PDF) on 29 November 2014, retrieved 17 September 2014

Bibliography[edit | edit source]

External links[edit | edit source]

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