Vararuchi and Madhavas Chandravakya

How to cite this paper: Dinesh Mohan Joshi | Girishbhatta. B "Vararuchi and Madhava's Chandravakya" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456 6470, Volume 6 | Issue 6, October 2022, pp.1781 1792, URL: www.ijtsrd.com/papers/ijtsrd52171.pdf

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जिों प्राज्ञाय

शशी िन्द्यः स्याि्

गोरितप्रयः

िनातन यत्र

अन्नों गोत्रश्री: रुष्टास्ते नागाः

सधगन्धः तकि पुरोगा अभीः

मान्यः ि कति: अररष्टनाशम्

बािो मे केश: कुशधाररण: इतष्टतिभद्यिे ि राजा प्रीि: िुगुप्रायोऽिौ सधगस्तु ह्रािः अङ्गातन यदा

कतिकण्ठिा कथा शीििम्पद्यानन्दः श्रीतिभना न मुकुन्दाि् तनराधारोऽतहराजः

तिकटधीः

2 वेण्वारोह एवं स्फटचन्द्राप्ति में “धनननकरो ननर्यर्ौ” दिर्ा गर्ा है प्िसका मान

8r 01o 17′ 35′′

8r 15o 00′ 42′′

8r 28o 29′ 20′′

9r 11o 42′ 31′′

9r 24o 40′ 06′′

10r 07o 22′ 48′′

10r 19o 52′ 04′′

11r 02o 10′ 04′′

11r 14o 19′ 32′′

11r 26o 23′ 37′′

8o 25′ 46′′ 20o 29′ 29′′ 1r 02o 38′ 12′′ 1r 14o 55′ 07′′ 1r 27o 23′ 03′′

2r 10o 04′ 11′′ 2r 23o 00′ 06′′

3r 06o 11′ 35′′ 3r 19o 38′ 33′′ 4r 03o 20′ 09′′ 4r 17o 14′ 47′′ 5r 01o 20′ 06′′ 5r 15o 33′ 17′′ 5r 29o 51′ 05′′ 6r 14o 10′ 03′′ 6r 28o 26′ 41′′

11r 02o 10′ 09

16o 52′ 28o 28′ 1r 11o 10′ 1r 23o 31′ 2r 06o 05′ 2r 18o 52′ 3r01o 55′ 3r 15o 14′ 3r 28o 47′ 4r 12o 35′ 4r 26o 34′ 5r 10o 44′ 5r 24o 59′ 6r 09o 18′ 6r 23o 36′ 7r 07o 51′ 7r 21o 58′ 8r 05o 55′ 8r 19o 40′ 9r 03o 10′ 9r 16o 25′ 9r 29o 24′ 10r 12o 08′ 10r24o 39′ 11r 06o 58′ 11r 19o 08′ 1o 13′ 13o 15′ 25o 19′ 1r 07o 27/ 1r 19o 43′ 2r 02o 10′ 2r 14o 49′ 2r 27o 43′ 3r 10o 53′ 3r 24o 18′ 4r 07o 58′ 4r 21o 52′ 5r 05o 56′ 5r 20o 08′ 6r 04o 26′

51′′ 28o 57′ 33′′ 1r 11o 09′ 23′′ 1r 23o 30′ 53′′ 2r 06o 04′ 27′′ 2r 18o 52′ 02′′ 3r 01o 54′ 50′′ 3r 15o 13′ 16′′ 3r 28o 46′ 54′′ 4r 12o 34′ 33′′ 4r 26o 34′ 16′′ 5r 10o 43′ 28′′ 5r 24o 59′ 07′′ 6r 09o 17′ 53′′ 6r 23o 36′ 14′′ 7r 07o 50′ 43′′ 7r21o 58′ 00′′ 8r 05o 55′ 11′′ 8r 19o 39′ 48′′ 9r 03o 10′ 03′′ 9r 16o 24′ 56′′ 9r 29o 24′ 14′′ 10r 12o 08′ 29′′ 10r 24o 39′ 08′′ 11r 06o 58′ 15′′ 11r 19o 08′ 30′′ 1o 13′ 00′′ 13o 15′ 11′′ 25o 18′ 33′′ 1r 07o 26′ 34′′ 1r 19o 42′ 27′′ 2r 02o 09′ 03′′ 2r 14o 48′ 39′′ 2r 27o 42′ 55′′ 3r 10o 52′ 40′′ 3r 24o 17′ 59′′ 4r 07o 58′ 04′′ 4r 21o 51′ 22′′ 5r 05o 55′ 39′′ 5r 20o 08′ 08′′ 6r 04o 25′ 35′′

6r 18o 45′ 7r 03o 02′ 7r 17o 13′ 8r 01o 17′ 8r 15o 08′ 8r 28o 47′ 9r 12o 10′ 9r 25o 18′ 10r 08o 11′ 10r 20o 48′ 11r 03o 14′ 11r 15o 28′ 11r 27o 36′ 9o 39′ 21o 41′ 1r 03o 46′ 1r 15o 58′ 1r 28o 18′ 2r 10o 50′ 2r 23o 36′ 3r 06o 37′ 3r 19o 54′ 4r 03o 26′ 4r 17o 12′ 5r 01o 11′ 5r 15o 19′ 5r 29o 34′ 6r 13o 52′ 6r 28o 10′ 7r 12o 25′ 7r 26o 33′ 8r 10o 32′ 8r 24o 18′ 9r 07o 50′ 9r 21o 07′ 10r 04o 08′ 10r 16o 54′ 10r 29o 26′ 11r 11o 46′

चण्डो िै भोजपतिः

धीगम्योऽनङ्ग आिीि्3

6r 18o 44′ 36′′

7r 03o 01′ 39′′

7r 17o 13′ 19′′

8r 01o 16′ 26′′

8r 15o 08′ 17′′

8r 28o 46′ 40′′

9r 12o 10′ 11′′

9r 25o 18′ 05′′ 10r 08o 10′ 34′′ 10r 20o 48′ 32′′ 11r 03o 13′ 44′′ 11r 15o 28′ 32′′ 11r 27o 35′ 49′′ 9o 38′ 53′′ 21o 41′ 09′′ 1r 03o 46′ 10′′

1r 15o 57′ 19′′ 1r 28o 17′ 39′′ 2r 10o 49′ 48′′ 2r 23o 35′ 46′′ 3r 06o 36′ 53′′ 3r 19o 53′ 36′′ 4r 03o 25′ 39′′ 4r 17o 11′ 51′′ 5r 01o 10′ 21′′ 5r 15o 18′ 39′′ 5r 29o 33′ 46′′ 6r 13o 52′ 21′′ 6r 28o 10′ 56′′ 7r 12o 25′ 59′′ 7r 26o 34′ 13′′ 8r 10o 32′ 37′′ 8r 24o 18′ 42′′ 9r 07o 50′ 37′′ 9r 21o 07′ 12′′ 10r 04o 08′ 10′′ 10r 16o 54′ 00′′ 10r 29o 26′ 02′′ 11r 11o 46′ 17′′

11r 23o 58′ 6o 03′ 18o 05′ 1r 00o 08′ 1r 12o 16′ 1r 24o 30′ 2r 06o 56′ 2r 19o 33′ 3r 02o 26′ 3r 15o 34′ 3r 28o 57′ 4r 12o 36′ 4r 26o 17′ 5r 10o 31′ 5r 24o 42′ 6r 08o 59′ 6r 23o 18′ 7r 07o 36′ 7r 21o 48′ 8r 05o 52′ 8r 19o 46′ 9r03o 26′ 9r 16o 51′ 10r 00o 01′ 10r 12o 55′ 10r 25o 34′ 11r 08o 01′ 11r 20o 17′ 2o 25′ 14o 29′ 0r 26o 31′ 1r 08o36′ 1r 20o 46′ 2r 03o 05′ 2r 15o 36′ 2r 28o 20′ 3r 11o 19′ 3r 24o 34′ 4r 08o 04′

काष्ठिमा गात्रयतष्टः

अरररनाप्तः चण्डभानुजभयी

व्यिस्थच्छन्नोऽनुनयः

11r 23o 57′ 21

6o 02′ 20′′ 18o 04′ 36′′ 1r 00o 07′ 41′′ 7r 12o 15′ 01′′ 1r 24o 29′ 54′′ 2r 06o 55′ 12′′ 2r 19o 33′ 18′′ 3r 02o 25′ 54′′ 3r 15o 33′ 57′′

3r 28o 57′ 36′′

4r 2o 36′ 07′′ 4r 26o 28′ 04′′

5r 10o 31′ 17′′

5r 24o 43′ 01′′ 6r 09o 00′ 06′′

6r 23o 19′ 07′′

7r 07o 36′ 32′′ 7r 21o48′ 59′′ 8r 05o 53′ 09′′ 8r 19o 46′ 21′′

9r 03o 26′ 18′′

9r 16o 51′ 29′′

10r 00o 01′ 06′′

10r 12o 55′ 13′′ 10r 25o 34′ 42′′ 11r 08o 01 12′′

11r 20o 17′ 00′′

2o 24′ 58′′

14o 28′ 18′′ 26o 30′ 30′′

1r 08o 35′ 03′′

1r 20o 45′ 21′′

2r 03o 04′ 33′′

2r 15o 35′ 18′′

2r 28o 19′ 42′′

3r 11o 19′ 07′′ 3r 24o 34′ 08′′ 4r 08o 04′ 32′′

4r 21o 49′ 5r 05o 46′ 5r 19o 53′ 6r 04o 08′ 6r 18o 26′ 7r 02o 45′ 7r 17o 00′ 8r 01o 10′ 8r 15o 09′ 8r 28o 57′ 9r12o 30′ 9r 25o 49′ 10r 08o52′ 10r 21o 39′ 11r 04o 13′ 11r 16o 34′ 11r 28o 56′ 10o 52′ 22o 55′ 1r 04o 58′ 1r 17o 04′ 1r 29o 18′ 2r 11o 42′ 2r 24o 18′ 3r 07o 09′ 3r 20o 15′ 4r 03o 37′ 4r 17o 14′ 5r 01o 05′ 5r 15o 07′ 5r 29o 17′ 6r 13o 34′ 6r 27o 53′ 7r 12o 11′ 7r 26o 24′ 8r 10o 29′ 8r 24o 23′ 9r 08o 05′ 9r 21o 32′

4r 21o 49′ 17′′ 5r 05o 46′ 33′′ 5r 19o 53′ 55′′ 6r 04o 08′ 27′′ 6r 18o 26′ 49′′ 7r 02o 45′ 34′′ 7r 17o 01′ 11′′ 8r 01o 10′ 19′′ 8r 15o 09′ 55′′ 8r 28o 57′ 26′′ 9r 12o 30′ 57′′ 9r 25o 49′ 15′′ 10r 08o 51′ 55′′ 10r 21o 39′ 22′′ 11r 04o 12′ 50′′ 11r 16o 34′ 14′′ 11r 28o 46′ 09′′ 10o 51′ 38′′ 22o 54′ 02′′ 1r 04o 56′ 51′′ 1r 17o 03′ 34′′ 1r 29o 17′ 28′′ 2r 11o 41′ 31′′ 2r 24o 18′ 07′′ 3r 07o 0′ 05′′ 3r 20o 15′ 26′′ 4r 03o 37′ 23′′ 4r 17o 14′ 21′′ 5r 01o 04′ 56′′ 5r 15o 07′ 02′′ 5r 29o 17′ 58′′ 6r 13o 34′ 38′′ 6r 27o 53′ 37′′ 7r 12o 11′ 23′′ 7r 26o24′ 31′′ 8r 10o 29′ 45′′ 8r 24o 24′ 16′′ 9r 08o 05′ 45′′ 9r 21o 32′ 35′′

10r 04o 4′ 10r 17o 40′ 11r 00o 21′ 11r 12o 49′ 11r 25o 06′ 7o 14′ 19o 18′ 1r 01o 2′ 1r 13o 25′ 1r 25o 34′ 2r 07o 52′ 2r 20o 21′ 3r 03o 04′ 3r 16o 02′ 3r 29o 15′ 4r 12o 43′ 4r 26o 27′ 5r 10o 22′ 5r 24o 29′ 6r 08o 4′ 6r 23o 00′ 7r 07o 19′ 7r 21o 36′ 8r 05o 46′ 8r 19o 46′ 9r 03o 35′ 9r 17o 11′ 10r 00o 31′ 10r 13o 35′ 10r 26o 25′ 11r 09o 00′ 11r 21o 22′ 3o 35′ 15o 41′ 27o 44′

10r 04o 43′ 56

10r 17o 39′ 32

11r 00o 20′ 44

11r 12o 48′ 32

11r 25o 05′ 22

7o 14′ 02′′ 19o 17′ 43′′ 1r 01o 19′ 52′′ 1r 13o 23′ 59′′ 1r 25o 33′ 31′′ 2r 07o 51′ 36′′ 2r 20o 20′ 59′′ 3r 03o 03′ 48′′ 3r 16o 01′ 32′′ 3r 29o 14′ 51′′ 4r 12o 43′ 37′′ 4r 26o 26′ 51′′ 5r 10o 22′ 52′′ 5r 24o 29′ 16′′ 06r 08o 43′ 10′′ 6r 23o 01′ 17′′ 7r 07o 20′ 10′′ 7r 21o 36′ 18′′ 8r 05o 46′ 17′′ 8r 19o 47′ 04′′ 9r 03o 36′ 01′′ 9r 17o 11′ 08′′ 10r 00o 31′ 07′′ 10r 00o 31′ 07′′ 10r 26o 24′ 33′′

11r 08o 59′ 27′′ 11r 21o 22′ 04′′ 3o 34′ 54′′ 15o 40′ 55′′ 27o 43′ 29′′

[1] Āryabhaṭīyaṃ of Āryabhaṭa with the commentary Bhaṭadīpikā of Parameśvara, ed. by B. Kern, Leiden 1874 (repr. 1906, 1973)

[2] Āryabhaṭīya ofĀryabhaṭa,ed.withtr.andnotes by K. S. Shukla and K. V. Sarma, INSA, New Delhi 1976.

[3] Āryabhaṭīya of Āryabhaṭācārya with the Mahābhāṣya ofNīlakaṇṭhaSomasutvan,PartI, Gaṇitapāda, ed. by Sāmbaśiva Śāstrī, Trivandrum Sanskrit Series 101, Trivandrum 1930.

[4] Āryabhaṭīya of Āryabhaṭācārya with the Mahābhāṣya ofNīlakaṇṭhaSomasutvan,PartII, Kālakriyāpāda, ed. by Sāmbaśiva Śāstrī, Trivandrum Sanskrit Series 110, Trivandrum 1931.

[5] Āryabhaṭīya of Āryabhaṭācārya with the Mahābhāṣya of Nīlakaṇṭha Somasutvan, Part III, Golapāda, ed. by Śūranāḍ Kuñjan Pillai, Trivandrum Sanskrit Series 185, Trivandrum 1957.

[6] Āryabhaṭīya ofĀryabhaṭawiththecommentary of Bhāskara I and Someśvara, ed. by K. S. Shukla, INSA, New Delhi 1976.

[7] Candracchāyāgaṇita of Nīlakaṇṭha Somayājī, with auto commentary, ed. and tr. by K. V. Sarma, VVRI, Hoshiarpur 1976.

[8] Candravākyas of Vararuci, C. Kunhan Raja, Adyar Library, Madras 1948.

[9] Karaṇapaddhati ofPutumanaSomayājī,tr.with mathematical notes by Venketeswara Pai, K. Ramasubramanian, M.S. Sriramm and M. D. Srinivas, HBA, Delhi and Springer, London 2018

[10] Tantrasaṅgraha of NīlakaṇṭhaSomayājī, with Laghuvivṛti, ed. by S. K. Pillai, Trivandrum 1958.428

[11] Tantrasaṅgraha of Nīlakaṇṭha Somayājī, with Yuktidīpikā (forchaptersI IV)and Laghuvivṛti (forchaptersV VIII)ofŚaṅkaraVārīyared.by K. V. Sarma, VVRI, Hoshiarpur 1977.

[12] Tantrasaṅgraha ofNīlakaṇṭhaSomayājī,tr.by V. S. Nara simhan, Indian Journal History of Science, INSA, New Delhi 1998 99

[13] Tantrasaṅgraha of Nīlakaṇṭha Somayājī, tr. with mathematical notes by K. Ramasubramanian and M. S. Sriram, HBA, Delhi and Springer, London 2011.

[14] Vākyakaraṇa with the commentary by Sundararāja, ed. by T. S. Kuppanna Sastri and K. V. Sarma, KSRI, Madras, 1962

[15] Veṇvāroha by Mādhava, ed. with Malayalam commentaryofAcyutaPiṣāraṭibyK.V.Sarma, TheSanskritCollegeCommittee,Tripunithura, Kerala 1956.

सन्दर्भ शोधपत्र

[1] Hari K. Chandra, Vākyakaraṇa: A study, Indian Journal of History of Science, pp. 127 149, 36, 2001.

[2] Hari K. Chandra, Computation of the true moon by Mādhava of Saṅgamagrāma, Indian Journal of History of Science,pp.231 253,38, 2003.

[3] Madhavan S., Veṇvāroha from a modern perspective, Indian Journal of History of Science, pp. 699 717, 49,2012

[4] Mahesh K., Pai R. Venketeswara and Ramasubramanian K., ’Turning an algebraic identity into an infinite series’, in History of Mathematical Science II,eds.B.S.Yadavand S. L. Singh, Cambridge Scientific Publishers, UK 2010, pp. 61 81.

[5] Mahesh K., Pai R. Venketeswara and Ramasubramanian K., Mādhava series for π and its fast convergent approximations, Astronomy and Mathematics in Ancient India, ed. J. M. Delire, Peeters Publishers, Leuven 2012, pp. 175-198

[6] PaiR.Venketeswara,JoshiDineshMohanand Ramasubramanian K., The Vākya method of findingthemoon’slongitude, Gaṇita Bhāratī, pp. 39 64, 31, No. 1 2, 2009

International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456 6470

[7] Pai R. Venketeswara, Mahesh K. and Ramasubramanian K., Kriyākalāpa: A Commentary of Tantrasaṅgraha in Keralabhāṣā, Indian Journal of History of Science, pp. T1 T47, 45, No. 2, 2010.

[8] Pai R. Venketeswara, Ramasubramanian K., and Sriram M. S., Rationale for Vākyas pertaining to the Sun in Karaṇapaddhati, Indian Journal of History of Science, pp. 245 258, 50, No. 2, 2015.

[9] Pai R. Venketeswara, Ramasubramanian K., Srinivas M. D. and Sriram M. S., The Candravākyas of Mādhava, Gaṇita Bhāratī, Vo. 38, No. 2 (2016) pages 111 139.

[10] Sarma U. K. V., Pai Venketeswara, Joshi Dinesh Mohan and Ramasubramanian K., ‘Madhyamnayanaprakāraḥ: A Hitherto Unknown Manuscript Ascribed to Mādhava’, Indian Journal of History of Science, pp. T1 T29, 46, No. 1, 2011.