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Bibliography Primary sources [AB1930] Āryabhaṭīya of Āryabhaṭācārya with the commentary of Nīla- kaṇṭha Somasutvan. Ed. by K. Sāmbaśiva Śāstrī. Part 1, Gaṇi- tapāda. Trivandrum Sanskrit Series 101. Trivandrum, 1930. [AB1931] Āryabhaṭīya of Āryabhaṭācārya with the commentary of Nīla- kaṇṭha Somasutvan. Ed. by K. Sāmbaśiva Śāstrī. Part 2, Kāla- kriyāpāda. Trivandrum Sanskrit Series 110. Trivandrum, 1931. [AB1957] Āryabhaṭīya of Āryabhaṭācārya with the commentary of Nīla- kaṇṭha Somasutvan. Ed. by Sūranāḍ Kuñjan Pillai. Part 3, Golapāda. Trivandrum Sanskrit Series 185. Trivandrum, 1957. [AB1976] Āryabhaṭīya of Āryabhaṭa with the commentary of Bhāskara I and Someśvara. Cr. Ed. with introduction, English transla- tion, notes, comments and indexes by K. S. Shukla in collabo- ration with K. V. Sarma. New Delhi: Indian National Science Academy, 1976. [AmKo2012] Amarakośa. Enlarged by Raghunath Shastri Talekar; Revised, enlarged and improved from Chintamani Shastri Thatte’s edi- tion of 1882 by Vāmanācārya Jhalakikar. Delhi: Eastern Book Linkers, 2012. [AṅNi1899] Aṅguttara Nikāya. Ed. by E. Hardy. Part IV. Published for the Pali Text Society by Henry Frowde, Oxford University Press Warehouse. London, 1899. [ArŚā2010] Arthaśāstra of Kauṭilya. Ed. and Tr. by R. P. Kangle. Reprint. Delhi: Motilal Banarasidass, 2010. [BīGa1927] Bījagaṇita of Bhāskarācārya with expository notes, examples of Sudhakara Dvivedi. Ed. by Muralidhara Jha. Benares Sanskrit Series 159. Benares, 1927. [BīGa1930] Bījagaṇita of Bhāskarācārya with the commentary Navāṅkura by Kṛṣṇa Daivajña. Ed. by Dattātreya Viśṇu Āpaṭe. Ānandā- śrama Sanskrit Series 99. Pune: Vināyaka Gaṇeśa Āpaṭe, 1930. [BīGa1970] Bījagaṇitāvataṃsa of Nārāyaṇa Paṇḍita. Ed. by K. S. Shukla. Lucknow: Akhila Bhāratiya Sanskrita Parishad, 1970. [BīGa1980] Bījagaṇita of Bhāskarācārya. Tr. by S. K. Abhyankar. Pune: Bhāskarācārya Pratiṣṭhān, 1980. [BīGa1983] Bījagaṇita with Vimarśa, Vāsana with the Hindi commentary Sudhā by Devacandra Jha. Varanasi: Chaukhamba Kriṣnadāsa Akādami, 1983. © Hindustan Book Agency 2019 and Springer Nature Singapore Pte Ltd. 2019 423 K. Ramasubramanian et al. (eds.), Bhāskara-prabhā, Sources and Studies in the History of Mathematics and Physical Sciences, https://doi.org/10.1007/978-981-13-6034-3 424 Bibliography [BīGa2006] Bījagaṇita of Bhāskarācārya. Ed. by V. B. Panicker. Mumbai: Bharatiya Vidya Bhavan, 2006. [BīGa2008] Bījagaṇita with Vimarśa, Vāsana with the Hindi commentary Sudhā by Devacandra Jha. Varanasi: Chaukhamba Kriṣnadāsa Akādami, 2008. [BīGa2009] Bījagaṇita of Bhāskarācārya. Ed. by T. Hayashi, with notes. Vol. 10. Kyoto: SCIAMVS (Sources and Commentaries in Ex- act Sciences), 2009, pp. 3–301. [BīPa1958] Bījapallava of Kṛṣṇa Daivajña. Ed. by T. V. Radhakrishna Sas- tri. Sarasvati Mahal Sanskrit Series 78. Tanjore, 1958. [BīPa2012] Bījapallava of Kṛṣṇa Daivajña. Cr. Ed. by Sita Sundar Ram. Chennai: Kuppuswami Sastri Research Institute, 2012. [BkMs1995] Bakhshālī Manuscript: An ancient Indian mathematical trea- tise. Cr. Ed. by Takao Hayashi with English translation and notes. Groningen Oriental Studies Book (11). Groningen: Eg- bert Forsten, 1995. [BrSū1997] Brahmasūtraśāṅkarabhāṣyam(ekādaśaṭīkāsaṃyutam) with the commentary Bhāmatī of Vācaspati Miśra. Ed. by Yogeśvara- datta Śarma. Delhi: Nāga Prakāśakaḥ, 1997. [BSS1902] Brāhmasphuṭasiddhānta of Brahmagupta. Ed. with a commen- tary by Sudhakara Dvivedi. Benaras, 1902. [BSS1966] Brāhmasphuṭasiddhānta of Brahmagupta with Vāsana Vi- jñāna. Ed. with Hindi commentaries by Ramswarup Sharma et al. 4 vols. New Delhi: Indian Institute of Astronomy and Sanskrit Research, 1966. [BSS2003] Brāhmasphuṭasiddhānta of Brahmagupta (Ch. 21) with com- mentary of Pṛthūdaka. Cr. Ed. with English translation and notes by Setsuro Ikeyama. 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Gaṇakataraṅgiṇī or Lives of Hindu Astronomers by Mahama- hopadhyaya Sudhakara Dvivedi, edited by his son Padmakara Dvivedi, Benaras: Jyotish Prakash Press, 1933. Further Reprint Ed. by Bharat Bhushan Mishra. Varanasi: Siva Samskrita Sam- sthan, 2002). Benaras: The Medical Hall Press, 1892. [GaTa1933] Gaṇakataraṅgiṇī or lives of Hindu astronomers by Sudhakar Dvivedi. Ed. by Padmakara Dvivedi. (Benaras: The Medical Hall Press, 1892; [Gaṇakataraṅgiṇī appeared serially in the pe- riodical The Pandit, NS 1892]. Benaras: Jyotish Prakash Press, 1933. [GaTi1937] Gaṇitatilaka of Śrīpati with a commentary by Sīṁhatilaka Sūri. Cr. Ed. by H. R. Kapadia. Baroda: Gaekwad’s Oriental Series, LXXVIII, 1937. [GaYu2008] Gaṇita-yukti-bhāṣā : Rationales in mathematical astronomy of Jyeṣthadevā. Cr. Ed. with English Tr. by K. V. Sarma with explanatory notes by K. Ramasubramanian, M. D. Srinivas, and M. S. Sriram. 2 vols. Culture and History of Mathemat- ics Series 4. New Delhi: Hindustan Book Agency jointly with Springer, 2008. [GrLā2006] Grahalāghavam of Gaṇeśa Daivajña. Ed. by S. Balachan- dra Rao and S. K. Uma. New Delhi: Indian National Science Academy, 2006. [GSK2009] Gaṇitasārakaumudī of Ṭhakkura Pherū: The moonlight of the essence of mathematics. Ed. by S. R. Sarma, Takenori Kusuba, Takao Hayashi and Michio Yano (SaKHYa) with introduction, translation, and mathematical notes. New Delhi: Manohar pub- lishers, 2009. [GSS1912] Gaṇitasārasaṅgraha of Mahāvīra. Ed. with English translation and notes by M. Raṅgācārya. Madras: Government Press, 1912. [GSS2000] Gaṇitasārasaṅgraha of Mahāvīra. Tr. by K. Padmavathamma. Hombuja, Karnataka: Śri Siddhānta Kīrthi Granthamālā, 2000. [KaKu1991] Karaṇakutūhala of Bhāskarācārya with the commentaries Gaṇaka kumuda kaumudī by Sumatiharṣagaṇī and Vāsanāvib- hūṣaṇa by Sudhakara Dvivedi. Ed. with Hindi translation by Satyendranāth Miśra. Krishnadas Sanskrit Series 129. Varanasi: Krishnadas Academy, 1991. [KaKu2008] Karaṇakutūhala of Bhāskaracārya, with English translation, notes, appendices. Ed. by S. Balachandra Rao and S. K. Uma. [Indian Journal of History of Science, 42.1-2(2007) and 43.1 426 Bibliography and 3(2008)]. New Delhi: Indian National Science Academy, 2008. [KhKh1925] Khaṇḍakhādyaka of Brahmagupta with the commentary Vāsanābhāṣya by Āmarāja. Ed. by Babua Misra. Calcutta: Uni- versity of Calcutta, 1925. [KhKh1970] Khaṇḍakhādyaka of Brahmagupta. Ed. by Bina Chatterjee. New Delhi: Bina Chatterjee, 1970. [KtRa1911] Kathāratnākara of Hemavijayagaṇī. Jamnagar: Hiralal Hansaraj, 1911. [LaMa1944] Laghumānasa of Muñjalācārya with text, English translation and notes by N. K. Majumdar. Calcutta: Indian Research In- stitute, 1944. [LaMa1952] Laghumānasa of Muñjalācārya with the commentary of Param- eśvara. Ed. by Dattātreya Viśṇu Āpaṭe. Ānandāśrama Sanskrit Series 123. Pune: Ānandāśrama Press, 1952. [LaMa1990] Laghumānasa of Muñjalācārya. Cr. Ed. translation with notes by K. S. Shukla. New Delhi: Indian National Science Academy, 1990. [Līlā1937] Līlāvatī of Bhāskarācārya with the commentaries Buddhi- vilāsinī by Gaṇeśa Daivajña and Vivaraṇa by Mahīdhara. Ed. by Dattātreya Viśṇu Āpaṭe. 2 vols. Ānandāśrama Sanskrit Se- ries 107. Pune: Vināyaka Gaṇeśa Āpaṭe, Ānandāśrama Press, 1937. [Līlā1954] Līlāvatī of Bhāskarācārya with the Malayalam commentary of P. K. Koru. Kozhikode: Mathrubhumi Printing and Publishing, 1954. [Līlā1961] Līlāvatī of Bhāskarācārya with the Tattvaprakāśikā commen- tary of Pundit Sri Lashanlal Jha. Varanasi: Chowkhambha Vidyabhavan, 1961. [Līlā1975] Līlāvatī of Bhāskaracārya with the commentary Kriyākra- makarī of Śaṅkara and Nārāyaṇa. Ed. by K. V. Sarma. Vishveshvaranand Indological Series 66. Hoshiarpur: Vishvesh- varanand Vedic Research Institute, 1975. [Līlā1989] Līlāvatī of Bhāskarācārya: A treatise of mathematics of Vedic tradition. Ed. and Tr. by K. S. Patwardhan, S. A. Naimpally and S. L. Singh. Delhi: Motilal Banarasidass, 1989. [Līlā2001] Līlāvatī of Bhāskarācārya: A treatise of mathematics of Vedic tradition. Ed. and Tr. by K. S. Patwardhan, S. A. Naimpally and S. L. Singh. First edition. Delhi: Motilal Banarasidass, 2001. [Līlā2006] Līlāvatī of Bhāskarācārya: A treatise of mathematics of Vedic tradition. Ed. and Tr. by K. S. Patwardhan, S. A. Naim- Bibliography 427 pally and S. L. Singh. (Published in 1989. First edition 2001). Reprint. Delhi: Motilal Banarasidass, 2006. [Līlā2008] Jha, Pandit Shrilashanlal. Shrimad Bhaskaravirachita Lilavati. [In Hindi]. Chaukhamba Prakashan, 2008. [MaBk1960] Mahābhāskarīya of Bhāskara I. Ed. by K. S. Shukla. Lucknow: Lucknow University, 1960. [MaBt1929] Mahābhārata : Ādiparva with the commentary of Nīlakaṇṭha. Printed and published by Shankar Narhar Joshi. Pune: Chi- trashala Press, 1929. [MaSi1910] Mahāsiddhānta of Āryabhaṭa. Ed. with his own commentary by Sudhakara Dvivedi. Varanasi: Braj Bhushan Das and Co., 1910. [Muṇ1999] Muṇḍakopaniṣad. Complete Works of
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  • Determination of Ascensional Difference in the Lagnaprakaraṇa

    Determination of Ascensional Difference in the Lagnaprakaraṇa

    Indian Journal of History of Science, 53.3 (2018) 302-316 DOI:10.16943/ijhs/2018/v53i3/49462 Determination of Ascensional Difference in the Lagnaprakaraṇa Aditya Kolachana∗ , K Mahesh∗ , Clemency Montelle∗∗ and K Ramasubramanian∗ (Received 31 January 2018) Abstract The ascensional difference or the cara is a fundamental astronomical concept that is crucial in de- termining the durations of day and night, which are a function of the observer’s latitude and the time of the year. Due to its importance, almost all astronomical texts prescribe a certain procedure for the determination of this element. The text Lagnaprakaraṇa—a hitherto unpublished manuscript attributed to Mādhava, the founder of the Kerala school of astronomy and mathematics—however discusses not one, but a number of techniques for the determination of the cara that are both inter- esting and innovative. The present paper aims to discuss these techniques. Key words: Arkāgraguṇa, Ascensional difference, Cara, Carajyā, Carāsu, Dyuguṇa, Dyujyā, Earth-sine, Kujyā, Lagnaprakaraṇa, Mādhava, Mahīguṇa 1. INTRODUCTION of the rising times of the different zodiacal signs (rāśis) at a given latitude. The ascensional difference (cara henceforth) is an The Lagnaprakaraṇa1 (Treatise for the Compu- important astronomical element that is involved in tation of the Ascendant) is a work comprised of a variety of computations related to diurnal prob- eight chapters, dedicated to the determination of lems. It is essentially the difference between the the ascendant (udayalagna or orient ecliptic point), right ascension and the oblique ascension of a and discusses numerous techniques for the same. body measured in time units. At the time of rising, However, as a necessary precursor to determin- the cara gives the time interval taken by a body to ing the ascendant, the text first discusses various traverse between the horizon and the six o’ clock methods to obtain the prāṇakalāntara,2 as well as circle or vice-versa depending upon whether the the cara.
  • Editors Seek the Blessings of Mahasaraswathi

    Editors Seek the Blessings of Mahasaraswathi

    OM GAM GANAPATHAYE NAMAH I MAHASARASWATHYAI NAMAH Editors seek the blessings of MahaSaraswathi Kamala Shankar (Editor-in-Chief) Laxmikant Joshi Chitra Padmanabhan Madhu Ramesh Padma Chari Arjun I Shankar Srikali Varanasi Haranath Gnana Varsha Narasimhan II Thanks to the Authors Adarsh Ravikumar Omsri Bharat Akshay Ravikumar Prerana Gundu Ashwin Mohan Priyanka Saha Anand Kanakam Pranav Raja Arvind Chari Pratap Prasad Aravind Rajagopalan Pavan Kumar Jonnalagadda Ashneel K Reddy Rohit Ramachandran Chandrashekhar Suresh Rohan Jonnalagadda Divya Lambah Samika S Kikkeri Divya Santhanam Shreesha Suresha Dr. Dharwar Achar Srinivasan Venkatachari Girish Kowligi Srinivas Pyda Gokul Kowligi Sahana Kribakaran Gopi Krishna Sruti Bharat Guruganesh Kotta Sumedh Goutam Vedanthi Harsha Koneru Srinath Nandakumar Hamsa Ramesha Sanjana Srinivas HCCC Y&E Balajyothi class S Srinivasan Kapil Gururangan Saurabh Karmarkar Karthik Gururangan Sneha Koneru Komal Sharma Sadhika Malladi Katyayini Satya Srivishnu Goutam Vedanthi Kaushik Amancherla Saransh Gupta Medha Raman Varsha Narasimhan Mahadeva Iyer Vaishnavi Jonnalagadda M L Swamy Vyleen Maheshwari Reddy Mahith Amancherla Varun Mahadevan Nikky Cherukuthota Vaishnavi Kashyap Narasimham Garudadri III Contents Forword VI Preface VIII Chairman’s Message X President’s Message XI Significance of Maha Kumbhabhishekam XII Acharya Bharadwaja 1 Acharya Kapil 3 Adi Shankara 6 Aryabhatta 9 Bhadrachala Ramadas 11 Bhaskaracharya 13 Bheeshma 15 Brahmagupta Bhillamalacarya 17 Chanakya 19 Charaka 21 Dhruva 25 Draupadi 27 Gargi
  • Review of Research Impact Factor : 5.7631(Uif) Ugc Approved Journal No

    Review of Research Impact Factor : 5.7631(Uif) Ugc Approved Journal No

    Review Of ReseaRch impact factOR : 5.7631(Uif) UGc appROved JOURnal nO. 48514 issn: 2249-894X vOlUme - 8 | issUe - 2 | nOvembeR - 2018 __________________________________________________________________________________________________________________________ ANCIENT INDIAN CONTRIBUTIONS TOWARDS MATHEMATICS Madhuri N. Gadsing Department of Mathematics, Jawahar Arts, Science and Commerce College, Anadur (M.S.), India. ABSTRACT Mathematics having been a progressive science has played a significant role in the development of Indian culture for millennium. In ancient India, the most famous Indian mathematicians, Panini (400 CE), Aryabhata I (500 CE), Brahmagupta (700 CE), Bhaskara I (900 CE), Mahaviracharya (900 CE), Aryabhata II (1000 CE), Bhaskara II (1200 CE), chanced to discover and develop various concepts like, square and square roots, cube and cube roots, zero with place value, combination of fractions, astronomical problems and computations, differential and integral calculus etc., while meditating upon various aspects of arithmetic, geometry, astronomy, modern algebra, etc. In this paper, we review the contribution of Indian mathematicians from ancient times. KEYWORDS: Mathematics , development of Indian , astronomical problems and computations. INTRODUCTION: Mathematics having been a progressive science has played a significant role in the development of Indian culture for millennium. Mathematical ideas that originated in the Indian subcontinent have had a profound impact on the world. The aim of this article is to give a brief review of a few of the outstanding innovations introduced by Indian mathematicians from ancient times. In ancient India, the most famous Indian mathematicians belong to what is known as the classical era [1-8]. This includes Panini (400 CE), Aryabhata I (500 CE) [9], Brahmagupta (700 CE), Bhaskara I (900 CE) [5, 6], Mahavira (900 CE), Aryabhata II (1000 CE), Bhaskaracharya or Bhaskara II (1200 CE) [10-13].
  • Equation Solving in Indian Mathematics

    Equation Solving in Indian Mathematics

    U.U.D.M. Project Report 2018:27 Equation Solving in Indian Mathematics Rania Al Homsi Examensarbete i matematik, 15 hp Handledare: Veronica Crispin Quinonez Examinator: Martin Herschend Juni 2018 Department of Mathematics Uppsala University Equation Solving in Indian Mathematics Rania Al Homsi “We owe a lot to the ancient Indians teaching us how to count. Without which most modern scientific discoveries would have been impossible” Albert Einstein Sammanfattning Matematik i antika och medeltida Indien har påverkat utvecklingen av modern matematik signifi- kant. Vissa människor vet de matematiska prestationer som har sitt urspring i Indien och har haft djupgående inverkan på matematiska världen, medan andra gör det inte. Ekvationer var ett av de områden som indiska lärda var mycket intresserade av. Vad är de viktigaste indiska bidrag i mate- matik? Hur kunde de indiska matematikerna lösa matematiska problem samt ekvationer? Indiska matematiker uppfann geniala metoder för att hitta lösningar för ekvationer av första graden med en eller flera okända. De studerade också ekvationer av andra graden och hittade heltalslösningar för dem. Denna uppsats presenterar en litteraturstudie om indisk matematik. Den ger en kort översyn om ma- tematikens historia i Indien under många hundra år och handlar om de olika indiska metoderna för att lösa olika typer av ekvationer. Uppsatsen kommer att delas in i fyra avsnitt: 1) Kvadratisk och kubisk extraktion av Aryabhata 2) Kuttaka av Aryabhata för att lösa den linjära ekvationen på formen 푐 = 푎푥 + 푏푦 3) Bhavana-metoden av Brahmagupta för att lösa kvadratisk ekvation på formen 퐷푥2 + 1 = 푦2 4) Chakravala-metoden som är en annan metod av Bhaskara och Jayadeva för att lösa kvadratisk ekvation 퐷푥2 + 1 = 푦2.