Śaṅkaranārāyaṇa: Difference between revisions

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{{Short description|Indian astronomer and mathematician}}
{{Short description|Indian astronomer and mathematician (840–900)}}
{{about|an Indian astronomer|the Diwan|Sankaranarayana Iyen}}
{{about|an Indian astronomer|the Travancore Diwan|Sankaranarayana Iyen}}
{{Use dmy dates|date=August 2019}}
{{Use dmy dates|date=August 2019}}
{{Use Indian English|date=August 2019}}
{{Use Indian English|date=August 2019}}
{{infobox person
{{infobox person
| name              = Sankara Narayana
| name              = Sankaranarayana
| image              =  
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| caption            =  
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| birth_name        =  
| birth_name        =  
| birth_date        = c. 840 CE
| birth_date        = c. 840  
| birth_place        =  
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| death_date        =  
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| resting_place_coordinates = <!-- {{coord|LAT|LONG|display=inline,title}} -->
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| nationality        = Indian
| citizenship        =  
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| alma_mater        =  
| alma_mater        =  
| employer          =  
| employer          = Sthanu Ravi Kulasekhara
| notable works      = ''Laghu Bhaskariya Vivarana''
| notable works      = ''Laghubhaskariyavivarana''
| occupation        = Astronomer-mathematician
| occupation        = Astronomer-mathematician
| years_active      =  
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'''Sankaranarayana''' (c. 840 – c. 900) was an Indian astronomer-mathematician in the court of [[Sthāṇu Ravi Kulaśekhara|Sthanu Ravi Kulasekhara]] (c. 844 – c. 870<ref name=":28">{{Cite book |last=Devadevan |first=Manu V. |url=https://books.google.com/books?id=exzhDwAAQBAJ&q=The+%E2%80%98Early+Medieval%27+Origins+of+India |title=The 'Early Medieval' Origins of India |publisher=Cambridge University Press |year=2020 |isbn=9781108494571 |location= |pages=150 |chapter=Changes in Land Relations and the Changing Fortunes of the Cēra State}}</ref>) of the early medieval [[Cēra/Perumāl̥ kingdom|Chera kingdom]] in [[Kerala]].<ref name="Joseph">{{cite book |author=Joseph |first=George Gheverghese |title=[[A Passage to Infinity]] |date=2009 |publisher=SAGE Publications Pvt. Ltd. |isbn=978-81-321-0168-0 |location=New Delhi |pages=13}}</ref><ref name=":02">{{Cite book |last=Veluthat |first=Kesavan |url=https://publications.efeo.fr/en/livres/628_south-indian-horizons-felicitation-volume-for-francois-gros-on-the-occasion-of-his-70th-birthday |title=South Indian Horizon: Felicitation Volume for François Gros |publisher=École Française D'Extrême-Orient |year=2004 |pages=471–85 |chapter=Mahodayapuram-Kotunnallur: a Capital City as a Sacred Centre}}</ref> He is celebrated as the author of ''Laghubhaskariyavivarana'' or ''Laghubhaskariyavyakha'', a detailed commentary on astronomical treatise ''Laghubhaskariya'' by 7th century mathematician [[Bhaskara I]] (which in turn was based on the works of the 5th century polymath [[Aryabhata I|Aryabhata]]).<ref>{{cite book |title=Laghubhaskariyavivarana |date=1949 |publisher=TSS |editor=Iyar |editor-first=S. Venkitasubramonia |volume=162 |location=Trivandrum |editor2=Asari |editor-first2=S. Kochukunju}}</ref><ref name=":0">{{Cite web |last=O'Connor |first=J. J. |last2=Robertson |first2=E. F. |date=2000 |title=Sankara Narayana |url=https://mathshistory.st-andrews.ac.uk/Biographies/Sankara/ |website=University of St. Andrews}}</ref>


'''Sankara Narayana''' (c. 840 – c. 900 AD) was an Indian astronomer-mathematician in the court of [[Sthāṇu Ravi Kulaśekhara|Ravi Kulasekhara]] (c. 844 – c. 883 AD) of the [[Cēra/Perumāl̥ kingdom|Chera Perumal kingdom]] of [[Kerala]].<ref name=":6">Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79 and 390-91.</ref><ref name="Joseph">{{cite book|author=George Gheverghese Joseph|title=[[A Passage to Infinity]]|publisher=SAGE Publications Pvt. Ltd.|location=New Delhi|date=2009|pages=13|isbn=978-81-321-0168-0}}</ref> He is best known as the author of ''Laghu Bhaskariya Vivarana'' or ''Vyakha'' (869/870 AD), a detailed commentary on treatise ''Laghu Bhaskariya'' by 7th century mathematician [[Bhaskara I]] (which in turn was based on the works of the 5th century polymath [[Aryabhata I|Aryabhata]]).<ref>{{cite book|title=Laghubhaskariyavivarana|date=1949|publisher=TSS|editor=S. Venkitasubramonia Iyar|volume=162|location=Trivandrun|editor2=S.Kochukunju Asari}}</ref><ref name="MacTutor">{{MacTutor|id=Sankara|title=Sankara Narayana}}</ref> Sankara Narayana is known to have established an astronomical observatory at the port of [[Koṭuṅṅallūr|Kodungallur]] in central Kerala.<ref name="Joseph" /><ref>{{cite book|author=Virendra Nath Sharma|title=Sawai Jai Singh and His Astronomy|date=1995|publisher=Motilal Banarsidass Publishers|location=Delhi|id={{Listed Invalid ISBN|81-208-1256-X}}}}</ref>  
Sankaranarayana is known to have established an astronomical observatory at the port of Mahodayapuram, present-day [[Koṭuṅṅallūr|Kodungallur]], in central Kerala.<ref name="Joseph" /><ref name=":1">{{cite book |author=Sharma |first=Virendra Nath |url=https://archive.org/details/sawai-jai-singh-and-his-astronomy-virendra-nath-sharma/page/n3/mode/1up |title=Sawai Jai Singh and His Astronomy |date=1995 |publisher=Motilal Banarsidass Publishers |location=Delhi |id={{Listed Invalid ISBN|81-208-1256-X}}}}</ref> ''Laghubhaskariyavivarana'' (Chapter VII) explicitly states that it was composed in [[Saka Year]] 791 (corresponding to 869/70 AD).<ref name=":0" /><ref name=":6">{{Cite book |last=Narayanan |first=M. G. S. |url=https://books.google.com/books?id=0YDCngEACAAJ |title=Perumals of Kerala |publisher=CosmoBooks |year=2013 |isbn=9788188765072 |location=Thrissur (Kerala) |pages=78–79 and 390–91 |orig-date=1972}}</ref> In the second verse of the commentary Sankaranarayana remembers five major predecessors in the field of mathematics (Aryabhata, Varahamihira, Bhaskara I, Govinda and Haridatta), including his possible master [[Govindasvami|Govinda]] (c. 800 – c. 860 AD).<ref name=":0" />


''Laghu Bhaskariya Vivarana'' (Chapter VII), produced in the court of king Ravi Kulasekhara at Kodungallur, explicitly states that it was composed in [[Saka Year]] 791 (=869/70 AD).<ref name="MacTutor" /><ref name=":6" /> It is also mentions that the year was the 25th regnal year of king Ravi Kulasekhara.<ref name=":63">Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79.</ref> In the second verse of the ''vivarana'' Narayana remembers five major precessors in the field of mathematics (Aryabhata, Varahamihira, Bhaskara I, Govinda and Haridatta), including his possible master [[Govindasvami|Govinda]] (c. 800 – c. 860 AD).<ref name=":63" />
The commentary notably mentions an expert astronomer who had travelled to the [[mleccha]] country.<ref name=":6s2" />


==Observatory==
== Scientific contributions ==


* The ''vivarana'' mentions a royal observatory (under the charge of Sankara Narayana) at Mahodayapura (Kodungallur).<ref name="Joseph" />
=== Astronomical Observatory ===
* There are references to an instrument called "Rashi Chakra" marked by a "Yanthra Valaya" in the ''vivarana''. This instrument might be the same as the Gola Yanthra/Chakra Yanthra mentioned by famous polymath [[Aryabhata]]. The Chakra Yanthra was developed further and called Phalaka Yanthra by Bhaskara I.<ref>Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 390-391 and 408-409.</ref>
According to the commentary, Sankaranarayana installed an astronomical observatory at the Chera capital Mahodayapuram (on the Malabar Coast).<ref name="Joseph" /><ref name=":1" />
{{cquote|
* There are references to an instrument called "Rasichakra" marked by a "Yantravalaya" in the ''vivarana''. This instrument might be the same as the Golayantra/Chakrayantra mentioned by polymath [[Aryabhata]].<ref name=":2" /> The Chakrayantra was developed further and called Phalakayantra by Bhaskara I.<ref name=":2">{{Cite book |last=Narayanan |first=M. G. S. |url=https://books.google.com/books?id=0YDCngEACAAJ |title=Perumals of Kerala |publisher=CosmoBooks |year=2013 |isbn=9788188765072 |location=Thrissur (Kerala) |pages=390–391 and 408–409|orig-date=1972}}</ref>
 
{{cquote|''"Oh [king] Ravivarmadeva, now deign to tell us quickly, reading off from the [[armillary sphere]] installed [at the observatory] in Mahodayapura, duly fitted with all the relevant circles and with the sign ([[Degree (angle)|degree]]-[[Minute of arc|minute]]) markings, the time of the rising point of the [[ecliptic]] (''lagna'') when the [[Sun]] is at 10° in the sign of [[Capricornus|Capricorn]], and also when the [[Sun]] is at the end of the sign [[Libra (constellation)|Libra]], which I have noted."''<ref name="University of Chicago Press">{{cite book |url=https://press.uchicago.edu/books/hoc/HOC_V2_B1/Volume2_Book1.html |title=Cartography in the Traditional Islamic and South Asian Societies |date=1992 |publisher=[[University of Chicago Press]] |isbn=0-226-31635-1 |editor=Harley |editor-first=J. B. |series=The History of Cartography |volume=2 (1) |pages=360–61 |editor2=Woodward |editor-first2=David}}</ref>
''"Oh [king] Ravi Varma Deva, now deign to tell us quickly, reading off from the [[armillary sphere]] installed [at the observatory] in Mahodayapura, duly fitted with all the relevant circles and with the sign ([[Degree (angle)|degree]]-[[Minute of arc|minute]]) markings, the time of the rising point of the [[ecliptic]] (''lagna'') when the [[Sun]] is at 10° in the sign of [[Capricornus|Capricorn]], and also when the [[Sun]] is at the end of the sign [[Libra (constellation)|Libra]], which I have noted."''<ref>{{cite book|title=The history of cartography : Volume 2 Book 1 : Cartography in the traditional Islamic and South Asian societies|date=1992|publisher=[[University of Chicago Press]]|isbn=0-226-31635-1|editor=J.B. harley|pages=360|editor2=David Woodward}}</ref>
}}
}}
* At the directions of Sankara Narayana, in every 'katikai' (= 34 minutes), bells were sounded at different important centres of Mahodayapura to announce correct time.


==Mathematical contributions==
{{cquote|''"Oh, Ravi, deign to tell us immediately, reading off from the armillary sphere, by means of the reverse vilagna method, the time for offering the daily oblations, when the Sun, shrouded under thick clouds, is 10° in the Sign Leo and also when it is the middle (i.e. 15°) in the Sign Sagittarius."''<ref name="University of Chicago Press">{{cite book |url=https://press.uchicago.edu/books/hoc/HOC_V2_B1/Volume2_Book1.html |title=Cartography in the Traditional Islamic and South Asian Societies |date=1992 |publisher=[[University of Chicago Press]] |isbn=0-226-31635-1 |editor=Harley |editor-first=J. B. |series=The History of Cartography |volume=2 (1) |pages=360–61 |editor2=Woodward |editor-first2=David}}</ref>}}


* ''Laghu Bhaskariya Vivarana'' covers the standard mathematical methods of [[Aryabhata I]] such as the solution of the [[indeterminate equation]] by = ax ± c (a, b, c integers) in integers which is then applied to astronomical problems. The Indian method involves using the [[Euclidean algorithm]]. It is called [[Kuṭṭaka|kuttakara]] ("pulveriser").<ref name="MacTutor" />
* At the expiry of every ''ghatika'' (= 24 minutes), drums were sounded by the soldiers (at different corners of the city of Mahodayapuram, such as certain "Balakridesvara") to announce time.<ref name=":6s2">{{Cite book |last= |first= |url=https://archive.org/details/laghubhaskariyabhaskaracharyavivarnashankarnaraynaed.narayanapillaip.k.universit_123_/page/n1/mode/1up |title=Laghubhaskariya Vivarana |date= |publisher=University of Kerala |year=1974 |isbn= |editor-last=Pillai |editor-first=P. K. Narayana |location=Trivandrum (Kerala) |pages=XX and XXI-XII |orig-date= |orig-year=1949}}</ref>


* The most unusual feature of the Laghubhāskarīyavivaraṇa is the use of [[katapayadi system]] of [[numeration]] as well as the [[place-value]] [[Sanskrit]] numerals which Laghubhāskarīyavivaraṇa frequently uses.<ref name="MacTutor" />
=== Mathematical contributions ===
* ''Laghubhaskariyavivarana'' covers several the standard mathematical methods of [[Aryabhata I]] such as the solution of the [[indeterminate equation]] [by = ax ± c] (where a, b, and c are [[integer]]s) in integers (which is then applied to astronomical problems by the author).<ref name=":0" /> The standard Indian method involves the use of [[Euclidean algorithm]] called [[Kuṭṭaka|kuttakara]] ("pulveriser").<ref name=":0" />
* The most unusual features of the ''Laghubhaskariyavivarana'' are the uses of [[katapayadi system]] of [[numeration]] and the [[place-value]] [[Sanskrit]] numerals.<ref name=":0" />
* Sankaranarayana is the earliest author known to use katapayadi numeration with the specific name.<ref name=":0" />


== Identification of king Ravi Kulasekhara with Sthanu ==
== Historiographical significance ==
''Laghubhaskariyavivarana'' describes "great mansions" in the city of the Mahodayapuram.<ref name=":6s2" /> He marks out the city of Mahodayapuram as a "senamukha".<ref name=":02" /> King Ravi Varma had planned to construct an assembly hall in his capital (he had asked the astronomers to fix the purvapararekha and enjoined craftsmen for the construction). A number of specific locations in the capital were also mentioned (such as "Gotramallesvara" — where the royal residence was located — and the "Balakridesvara Ganapati Temple" near to it).<ref name=":6s2" /><ref name=":02" /> Gotramallesvara is identifiable with present-day Lokamallesvaram in [[Koṭuṅṅallūr|Kodungallur]].<ref name=":02" />


* The opening verse of ''Laghu Bhaskariya Vyakha'' gives an indirect invocation to the lord called "Sthanu" (carefully composed to be applicable to god [[Shiva|Siva]] and the ruling king).<ref name=":64">Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79.</ref>
=== Identification of king Ravi Kulasekhara with Sthanu ===
 
Sankaranarayana says that he was patronized by king Ravi, who had the title Kulasekhara (and thus helps in the identification of Chera ruler Sthanu Ravi with Kulasekhara). The opening verse of the commentary gives an indirect invocation or praise to the lord called "Sthanu" (carefully composed to be applicable to god [[Shiva|Siva]] and the ruling king).<ref name=":62">{{Cite book |last=Narayanan |first=M. G. S. |url=https://books.google.com/books?id=0YDCngEACAAJ |title=Perumals of Kerala |publisher=CosmoBooks |year=2013 |isbn=9788188765072 |location=Thrissur (Kerala) |pages=78–79 |orig-date=1972}}</ref><ref name=":6s2" />{{cquote
<br />{{cquote
| quote = ''"Sa Sthanurjayati trirupasahito lingepi lokarcitah."''
| quote = ''"Sa Sthanurjayati trirupasahito lingepi lokarcitah".''
| author = Sankaranarayana
| author = Sankara Narayana
| source = ''Laghubhaskariyavyakha,'' Chapter I
| source = ''Laghu Bhaskariya Vyakha,'' Chapter I (c. 870 AD)
| width = 50%
| width = 50%
| align = center
| align = center
}}
}}


*Sankara Narayana also mentions that the full name of his king as "Ravi Varma Kulasekhara".<ref name=":62">Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79.</ref>
''Laghubhaskariyavivarana,'' according to the commentary itself, was composed in the 25th regnal year of king Ravi Kulasekhara.<ref name=":62" />
*''Laghu Bhaskariya Vivarana'' was composed in the 25th regnal year of king Kulasekhara.<ref name=":62" />


== Date of ''Laghu Bhaskariya Vivarana'' ==
=== Date of ''Laghubhaskariyavivarana'' ===
''Laghubhaskariyavivarana'' is dated by the author in three methods.<ref name=":62" />


==== As a Kali Date (when the ruler made enquiries regarding solar eclipse) ====
{{cquote
| quote = ''"Angartvambara nanda devamanubhir yate dinanam gane<br>Graste tigma mayukhamalinitamobhute parahne divi<br>Prsta praggrahanad dvitiyaghatika grasa pramanam raver<br>Bharta sri Kulasekharena vilasad velavrtaya bhuva."''
| author = Sankaranarayana
| source = ''Laghubhaskariyavyakha,'' Chapter IV
| width = 50%
| align = center
}}
* "Angartvambara nanda devamanubhir yate dinanam gane"
* "Angartvambara nanda devamanubhir yate dinanam gane"
** Anga = 6, Rtu = 6, Ambara = 0, Nanda = 9, Veda = 4, and Manu = 14
** Anga = 6, Rtu = 6, Ambara = 0, Nanda = 9, Veda = 4, and Manu = 14
** Order - 6609414
** Order - 6609414
** Reverse Order - 1449066
** Reverse Order - 1449066
* Kali Date - 3967 years and 86 days = 25 Mithuna, [[Malayalam calendar|Kollam Era]] 41<ref name=":62" /> = 866 AD


* Kali Date - 3967 years and 86 days = 25 Mithuna, [[Malayalam calendar|Kollam Era]] 41 = 870 AD
==== In the Saka Era ====
 
{{cquote
* "Evam Sakabdah punariha candra randhramuni sankhyaya asambhiravagatah"
| quote = ''"Evam Sakabdah punariha candra randhramuni sankhyaya asambhiravagatah."''
| author = Sankaranarayana
| source = ''Laghubhaskariyavyakha,'' Chapter I
| width = 50%
| align = center
}}
* "Sakabdah punariha candra randhramuni sankhyaya"
** Candra = 1, Randhra = 9, and Muni = 7
** Candra = 1, Randhra = 9, and Muni = 7
** Order - 197
** Order - 197
** Reverse Order - 791 ([[Shaka era|Saka Year]]) = 870 AD
** Reverse Order - 791 ([[Shaka era|Saka Year]]) = 870 AD<ref name=":62" />
 
==== In regnal years ====
{{cquote
{{cquote
| quote = ''"Angartvambara nanda devamanubhir yate dinanam gane<br>Graste tigma mayukhamalinitamobhute parahne divi<br>Prsta praggrahanad dvitiyaghatika grasa pramanam raver<br>Bharta sri Kulasekharena vilasad velavrtaya bhuva".''
| quote = ''"Capapravista guru sauri samatva kalam<br>Yamyottaram gamanamantaratah pramanam<br>Acaksvya sarvamavagamya bhatoktamargad<br>Ityuktavan ravirasena nrpabhivandya."<br><br>"Tada pancavimsati Varsanyatitani devasya."''
| author = Sankara Narayana
| author = Sankaranarayana
| source = ''Laghu Bhaskariya Vyakha,'' Chapter IV (c. 870 AD)
| source = ''Laghubhaskariyavyakha,'' Chapter VII
| width = 50%
| align = center
}} {{cquote
| quote = ''"Evam Sakabdah punariha candra randhramuni sankhyaya asambhiravagatah".''
| author = Sankara Narayana
| source = ''Laghu Bhaskariya Vyakha,'' Chapter 1 (c. 870 AD)
| width = 50%
| align = center
}} {{cquote
| quote = ''"Capapravista guru sauri samatva kalam<br>Yamyottaram gamanamantaratah pramanam<br>Acaksvya sarvamavagamya bhatoktamargad<br>Ityuktavan ravirasena nrpabhivandya".<br>"Tada pancavimsati Varsanyatitani devasya".''
| author = Sankara Narayana
| source = ''Laghu Bhaskariya Vyakha,'' Chapter VII (c. 870 AD)
| width = 50%
| width = 50%
| align = center
| align = center
}}
}}
 
* Meeting of Guru (=Jupiter) and Sauri (=Saturn) in Capa (Dhanu) = 25th regnal year of the king. In the 9th century, these two planets came to Dhanu Rasi simultaneously only in 869 AD.<ref name=":62" />
* Meeting of Guru (=Jupiter) and Sauri (=Saturn) in Capa (Dhanu) = 25th regnal year of the king = 870 AD


==See also==
==See also==
*[[Indian mathematics]]
*[[Indian mathematics]]
*[[History of mathematics]]
*[[History of mathematics]]
*[[List of astronomers and mathematicians of the Kerala school]]


==References==
==References==
{{reflist}}
{{reflist}}
 
{{Kerala School}}
{{Indian astronomy}}
{{Indian astronomy}}
{{Indian mathematics}}
{{Indian mathematics}}
{{Scientific Research in Kerala |state=collapsed}}
{{Scientific Research in Kerala |state=collapsed}}
{{authority control}}
{{authority control}}


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[[Category:Hindu astronomy]]
[[Category:Hindu astronomy]]
[[Category:People from Thrissur district]]
[[Category:People from Thrissur district]]
[[Category:Kerala school of astronomy and mathematics]]
[[Category:Scientists from Kerala]]
[[Category:Year of birth uncertain]]
[[Category:Year of birth uncertain]]
[[Category:9th-century Indian mathematicians]]
[[Category:9th-century Indian mathematicians]]
[[Category:10th-century Indian mathematicians]]
[[Category:10th-century Indian mathematicians]]
[[Category:Scientists from Kerala]]
[[Category:9th-century Indian astronomers]]
[[Category:9th-century Indian astronomers]]
[[Category:10th-century Indian astronomers]]
[[Category:10th-century Indian astronomers]]
[[Category:Scholars from Kerala]]
[[Category:People from the Kodungallur Chera kingdom]]
[[Category:Chera dynasty]]

Latest revision as of 03:49, 4 March 2026


This article is about an Indian astronomer. For the Travancore Diwan, see Sankaranarayana Iyen.

Sankaranarayana
Bornc. 840
OccupationAstronomer-mathematician
EmployerSthanu Ravi Kulasekhara
Notable work
Laghubhaskariyavivarana

Sankaranarayana (c. 840 – c. 900) was an Indian astronomer-mathematician in the court of Sthanu Ravi Kulasekhara (c. 844 – c. 870[1]) of the early medieval Chera kingdom in Kerala.[2][3] He is celebrated as the author of Laghubhaskariyavivarana or Laghubhaskariyavyakha, a detailed commentary on astronomical treatise Laghubhaskariya by 7th century mathematician Bhaskara I (which in turn was based on the works of the 5th century polymath Aryabhata).[4][5]

Sankaranarayana is known to have established an astronomical observatory at the port of Mahodayapuram, present-day Kodungallur, in central Kerala.[2][6] Laghubhaskariyavivarana (Chapter VII) explicitly states that it was composed in Saka Year 791 (corresponding to 869/70 AD).[5][7] In the second verse of the commentary Sankaranarayana remembers five major predecessors in the field of mathematics (Aryabhata, Varahamihira, Bhaskara I, Govinda and Haridatta), including his possible master Govinda (c. 800 – c. 860 AD).[5]

The commentary notably mentions an expert astronomer who had travelled to the mleccha country.[8]

Scientific contributions[edit | edit source]

Astronomical Observatory[edit | edit source]

According to the commentary, Sankaranarayana installed an astronomical observatory at the Chera capital Mahodayapuram (on the Malabar Coast).[2][6]

  • There are references to an instrument called "Rasichakra" marked by a "Yantravalaya" in the vivarana. This instrument might be the same as the Golayantra/Chakrayantra mentioned by polymath Aryabhata.[9] The Chakrayantra was developed further and called Phalakayantra by Bhaskara I.[9]

"Oh [king] Ravivarmadeva, now deign to tell us quickly, reading off from the armillary sphere installed [at the observatory] in Mahodayapura, duly fitted with all the relevant circles and with the sign (degree-minute) markings, the time of the rising point of the ecliptic (lagna) when the Sun is at 10° in the sign of Capricorn, and also when the Sun is at the end of the sign Libra, which I have noted."[10]

"Oh, Ravi, deign to tell us immediately, reading off from the armillary sphere, by means of the reverse vilagna method, the time for offering the daily oblations, when the Sun, shrouded under thick clouds, is 10° in the Sign Leo and also when it is the middle (i.e. 15°) in the Sign Sagittarius."[10]

  • At the expiry of every ghatika (= 24 minutes), drums were sounded by the soldiers (at different corners of the city of Mahodayapuram, such as certain "Balakridesvara") to announce time.[8]

Mathematical contributions[edit | edit source]

Historiographical significance[edit | edit source]

Laghubhaskariyavivarana describes "great mansions" in the city of the Mahodayapuram.[8] He marks out the city of Mahodayapuram as a "senamukha".[3] King Ravi Varma had planned to construct an assembly hall in his capital (he had asked the astronomers to fix the purvapararekha and enjoined craftsmen for the construction). A number of specific locations in the capital were also mentioned (such as "Gotramallesvara" — where the royal residence was located — and the "Balakridesvara Ganapati Temple" near to it).[8][3] Gotramallesvara is identifiable with present-day Lokamallesvaram in Kodungallur.[3]

Identification of king Ravi Kulasekhara with Sthanu[edit | edit source]

Sankaranarayana says that he was patronized by king Ravi, who had the title Kulasekhara (and thus helps in the identification of Chera ruler Sthanu Ravi with Kulasekhara). The opening verse of the commentary gives an indirect invocation or praise to the lord called "Sthanu" (carefully composed to be applicable to god Siva and the ruling king).[11][8]

"Sa Sthanurjayati trirupasahito lingepi lokarcitah."

— Sankaranarayana, Laghubhaskariyavyakha, Chapter I

Laghubhaskariyavivarana, according to the commentary itself, was composed in the 25th regnal year of king Ravi Kulasekhara.[11]

Date of Laghubhaskariyavivarana[edit | edit source]

Laghubhaskariyavivarana is dated by the author in three methods.[11]

As a Kali Date (when the ruler made enquiries regarding solar eclipse)[edit | edit source]

"Angartvambara nanda devamanubhir yate dinanam gane
Graste tigma mayukhamalinitamobhute parahne divi
Prsta praggrahanad dvitiyaghatika grasa pramanam raver
Bharta sri Kulasekharena vilasad velavrtaya bhuva."

— Sankaranarayana, Laghubhaskariyavyakha, Chapter IV
  • "Angartvambara nanda devamanubhir yate dinanam gane"
    • Anga = 6, Rtu = 6, Ambara = 0, Nanda = 9, Veda = 4, and Manu = 14
    • Order - 6609414
    • Reverse Order - 1449066
  • Kali Date - 3967 years and 86 days = 25 Mithuna, Kollam Era 41[11] = 866 AD

In the Saka Era[edit | edit source]

"Evam Sakabdah punariha candra randhramuni sankhyaya asambhiravagatah."

— Sankaranarayana, Laghubhaskariyavyakha, Chapter I
  • "Sakabdah punariha candra randhramuni sankhyaya"
    • Candra = 1, Randhra = 9, and Muni = 7
    • Order - 197
    • Reverse Order - 791 (Saka Year) = 870 AD[11]

In regnal years[edit | edit source]

"Capapravista guru sauri samatva kalam
Yamyottaram gamanamantaratah pramanam
Acaksvya sarvamavagamya bhatoktamargad
Ityuktavan ravirasena nrpabhivandya."

"Tada pancavimsati Varsanyatitani devasya."

— Sankaranarayana, Laghubhaskariyavyakha, Chapter VII
  • Meeting of Guru (=Jupiter) and Sauri (=Saturn) in Capa (Dhanu) = 25th regnal year of the king. In the 9th century, these two planets came to Dhanu Rasi simultaneously only in 869 AD.[11]

See also[edit | edit source]

References[edit | edit source]

  1. ↑ Devadevan, Manu V. (2020). "Changes in Land Relations and the Changing Fortunes of the Cēra State". The 'Early Medieval' Origins of India. Cambridge University Press. p. 150. ISBN 9781108494571.
  2. ↑ 2.0 2.1 2.2 Joseph, George Gheverghese (2009). A Passage to Infinity. New Delhi: SAGE Publications Pvt. Ltd. p. 13. ISBN 978-81-321-0168-0.
  3. ↑ 3.0 3.1 3.2 3.3 Veluthat, Kesavan (2004). "Mahodayapuram-Kotunnallur: a Capital City as a Sacred Centre". South Indian Horizon: Felicitation Volume for François Gros. École Française D'Extrême-Orient. pp. 471–85.
  4. ↑ Iyar, S. Venkitasubramonia; Asari, S. Kochukunju, eds. (1949). Laghubhaskariyavivarana. Vol. 162. Trivandrum: TSS.
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 5.6 O'Connor, J. J.; Robertson, E. F. (2000). "Sankara Narayana". University of St. Andrews.
  6. ↑ 6.0 6.1 Sharma, Virendra Nath (1995). Sawai Jai Singh and His Astronomy. Delhi: Motilal Banarsidass Publishers. ISBN 81-208-1256-X.
  7. ↑ Narayanan, M. G. S. (2013) [1972]. Perumals of Kerala. Thrissur (Kerala): CosmoBooks. pp. 78–79 and 390–91. ISBN 9788188765072.
  8. ↑ 8.0 8.1 8.2 8.3 8.4 Pillai, P. K. Narayana, ed. (1974) [1949]. Laghubhaskariya Vivarana. Trivandrum (Kerala): University of Kerala. pp. XX and XXI-XII.
  9. ↑ 9.0 9.1 Narayanan, M. G. S. (2013) [1972]. Perumals of Kerala. Thrissur (Kerala): CosmoBooks. pp. 390–391 and 408–409. ISBN 9788188765072.
  10. ↑ 10.0 10.1 Harley, J. B.; Woodward, David, eds. (1992). Cartography in the Traditional Islamic and South Asian Societies. The History of Cartography. Vol. 2 (1). University of Chicago Press. pp. 360–61. ISBN 0-226-31635-1.
  11. ↑ 11.0 11.1 11.2 11.3 11.4 11.5 Narayanan, M. G. S. (2013) [1972]. Perumals of Kerala. Thrissur (Kerala): CosmoBooks. pp. 78–79. ISBN 9788188765072.

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