ARYABHATTA’S DATE AN ANALYTICAL STUDY
Dr. M.L. Raja, M.B., B.S., D.O.,
AVINASH English ARYABHATTA’S DATE AN ANALYTICAL STUDY By- Dr. M.L. Raja
Published by AVINASH Printed at Sankav Offset Printerss, Erode Cover Design & Type setting A.P. Nallashivam
Published in January 2016 Yugabdom 5117 IPrice `160. ISBN: 978-93-84582-54-8BN: 978i
AVINASH Academy on Vibrant National Arts & Scientific Heritage Erode, Tamilnadu Ph : 94433 70129 E-mail : [email protected] PREFACE In the history our Nation, we can find thousands and thousands of great scholars and their works, in almost all fields of science. We can cite examples, at least a few hundred in each century, scattering over a very long period of time, exceeding a minimum of ten thousand years. Their works in the various fields of science are remarkably outstanding, highly astonishing and fully scientific with thorough and clear knowledge, exceeding the modern scientific achievements, at least in a few aspects. But, the most unfortunate thing is, we are very much ignorant of our ancestor’s glorious antiquity, Himalayan achievements, high technological skill and the vast knowledge and wisdom and their highly admirable scientific works are not at all included in our Nation’s educational curriculum. So, it is right time or even if late, it is better late than never, to bring forth these ancient scientific works of our glorious Nation, in the day-light, amongst the present and the future generations of our Nation. With that motive in mind, this book on Âryabha a is a very small, but a firm step in that direction, where the actual date and name of Âryabha a and his texts are detailed. On reading these types of works, revealing the true vision of our ancestor’s knowledge, we as a Nation, will definitely feel much proud of our heritage and our self confidence will be highly boosted. With that, our Nation’s scientific achievements will again reach its Himalayan peak, as in the ancient days. Further, whenever our Nation takes the lead in the scientific field, we can find that the science is totally Dharma based and is for the betterment of not only the Human society, but also for the whole animate and inanimate, in contrast to the selfish and self destructive western concept of science. Thus, the Dharma based and all encompassing Bhāratian concept of science is the need of the hour, which can lead and guide the whole world, in peaceful co- existence with prosperity and humanity, to prevent the total annihilation of the human race, which is almost on the verge, a fate came out of the western concept of science and living. Thus, Dr. Arnold Joseph Toynbee, the British Historian (1889- 1975), mentioned firmly, “It is already becoming clear that a chapter which had a Western beginning will have to have an Indian ending, if it is, not to end in the self-destruction of the human race. At this supremely dangerous moment in human history, the only way of salvation for mankind is the Indian way.” I humbly submit my pranāms to Srī Prof. Vasudevan Potti, Retd. Professor, of Vedānta who guided me in writing this book with correct Sanskrit Grammatical analysis and to Prof. B.Satagopan, Retd. Prof. & Head, Dept. of History and Politics & Addl. Professor in Economics, for his encouragement and whole hearted appreciation. It is a great honour to me to have their highly valuable opinions on this book and the same is given as Foreword for the book. I sincerely express my heartfelt thanks to the publishers, Kurukshetra Prakashan Kochi, the printers and all those helped in bringing out the book in an excellent and elegant manner.
Erode Dr. M.L. Raja Kaliyugaptam 5116, Pushya 1st Souramana (15-01-2015) A WORD IN APPRECIATION I have gone through the thought provoking article titled “The actual date of Aryabhatta” written by Dr.M.L.Raja, M.B.,B.S.,D.O., Director of AVINASH, Tamilnadu. Doctor has done research about the date of Aryabhatta. He quotes a sloka from Aryabhattiyam. There are two readings one is ¹É¹]ªɤnÉxÉÉÆ ¹ÉbÂʦÉ: (Shadbhih) and the other is ¹É¹]ªɤnÉxÉÉÆ ¹Éʹ]: (Shashtih). He extensively explains, quoting grammar rules on the word formation of Vyatītā: (were elapsed excessively). In his opinion, the actual date of Aryabhatta is B.C.2764. The author of the article Dr.Raja concludes - “It is proved absolutely that “Shadbhih” (¹ÉbÂʦÉ:) is the correct word and not “Shashtih” (¹Éʹ]:) grammatically and syntactically. Thus 2764 B.C.E. is the date of Aryabhatta.” Dr. Raja also cites other sources of evidence of his opinion such as Laghu Bhaskareeyam of Bhaskara (522/629 C.E.) and Pancha Siddhantika of Varahamihira etc. Thus, the article can be taken as a good and authentic research paper on the actual date of Aryabhatta. Dr. Raja deserves congratulations in taking pain in bringing truth about Aryabhatta. I expect more such research works in field of scientific heritage of Bharat. Prof. R.Vasudevan Potti, Retd. Professor of Vedanta, TC 28/1330, SIVADHAM, Sreekanteswaram, Thiruvanathapuram, KERALA – 695 023 EDITOR’S NOTE
Our Nation always have the credibility in Anciant Science and Phylosophy. We always have the abundant resource of well known scientists and thinkers who always have an Universal Vision. We called them Rishi, who sacrificed their precious life in search of knowledge and disceminate that to the world, with utmost goodfaith and unconditional selfless service. Here we are so happy to publish a valuable study on Aryabhatta by Dr. M.L.Raja.
Editor AVINASH About Author
Dr. M.L. Raja is an Eye Specialist with a qualification of M.B., B.S., D.O. As a Director of the research academy by name AVINASH (Academy on Vibrant National Arts and Scientific Heritage), he presented Scientific papers at various National and International conferences, on subjects pertaining to Vedic Sciences, discrete mathematics and history of Bharat. He is writing scientific articles related to Physics, Astronomy, Medicine and Mathematics, Tamil Literature and the history of our beloved Nation, in various magazines. He also authored books on Dr. Jagadish Chandra Bose, Swami Vivekananda and Astronomy. He can be contacted through,
Dr. M.L. Raja, M.B., B.S., D.O., Sree Krishna Hospital, 15, Sangagiri Road, Pallipalayam, Erode - 6, Tamilnadu, Bharat, PIN – 638006 Mobile: +91 9443370129, email: [email protected] About the Book This book elaborets the various concrete and conclusive evidences, which favour the date of Âryabha a at 2764 B.C.E. Besides this book also gives concrete and corroborative evidences, that Âryabha a not only wrote Âryabha îyam and (Laghu) Âryabha a Siddhānta: (Laghu Âryabha îyam) but also Mahāryabha a Siddhānta:, the ancient astronomical and mathematical text of our Nation, thus clearly proving that the author of Âryabha îyam and Mahāryabha a Siddhānta: were not two different persons, but one and the same Âryabha a. Further, based on the evidences given by G.Thibaut, Henry Thomus Colebrook and W.Brennand, it is found that the correct spelling and pronunciation is Âryabha a and not Âryabha a. DIACRITICAL MARKS FOR ROMAN TRANSLITERATION OF DEVANAGARI SCRIPT
1. Short Vowels + - A, a < - I, i = - U, u @ - , ±ÉÞ - ï 2. Long Vowels +É - Â, ā, â <Ç - Î, ī, î > - U,Û,ū, û B - E, e +Éä - O, o Bä - Ai, ai +Éè - Au, au 3. Anusvāra: and Visarga: -
+Æ - Ä : - , 4. Non-aspirant - % 5. Consonants E - K, k JÉ - Kh, kh MÉ - G, g PÉ - Gh, gh R - Ń, ń SÉ – C,c U - Ch, ch VÉ - J, j ZÉ - Jh, jh \É - Ñ, ñ ] - , `ö - h, h b - , f - h, h hÉ - N, iÉ - T, t lÉ - Th, th n - D, d vÉ - Dh, dh xÉ - N, n {É - P, p ¡Âò - Ph, ph ¤É - B, b ¦É - Bh, bh ¨É - M, m ªÉ - Y, y ®Â - R, r ±É - L, l ´É - V, v
¶É - Ś, ś ¹É - , ºÉ - S, s ½Â - H, h 6. Compound letters -
IÉÂ - K , k
YÉÂ - Jñ, jñ jÉÂ - Tr, tr Due to conversion from ms word to pagemaker and then to pdf some fonts are used with multiple symbols and some are left with routine symbols
Words with * mark are explained in the Glossary AN APPRECIATION By PROF B. SATAGOPAN
Controversies continue to centre round some of the major historical themes and issues such as the Aryan and Alexander’s invasion of India, despite the fact that the conventional history of India claims to have settled all of them once and for all and declares them as a closed chapter. It is refreshing to reflect in recent times, the approach and the anecdotes advanced by the conventional historians have come under critical scrutiny, review and revision by their modern counterparts. One such is the date and time of Acharya Aryabhatta, one of the reputed and leading scientists of Ancient India, believed to have pioneered the growth and development of Modern Science and Mathematics inclusive of Astronomy and Astrology. The traditional account of Aryabhatta associates him worth the Golden Age of the Imperial Gupthas of Hindu India as a front- ranking intellectual of the Gupthan royal court and an integral part of the ‘Navaratnas’ or ‘Nine Gems’. The date of Aryabhatta, in its considered view is 476 C.E. The above-quoted view relating to the date of Aryabhatta has been stoutly challenged as fallacious and erroneous by Dr.M.L.Raja, a medical professional by career and a passionate researcher by choice and preference, in his thought-provoking research article entitled ‘The Date of Aryabhatta – An Analytical Study’. He questions this traditional view regarding Aryabhatta’s date and summarily rejects it by battery of arguments, buttressed by internal and external evidences, drawn exclusively from different authoritative Sanskrit works on Ancient Indian Science and Technology, supplemented and corroborated by selected indologists and intellectuals of the west, to vindicate his stand. Dr. Raja’s in- depth analysis of all the evidences mobilised by him have led him to logically revise and refix the date of Aryabhatta at 2764 B.C.E. Thus according to the researcher Dr. Raja, Aryabhatta’s date is not 476 C.E. but irrevocably stands at 2764 B.C.E. In this context, it will be worthwhile to quote the author himself- “It is clearly found from the evidences examined, that the date of Aryabhatta at 476 C.E. stipulated by the traditional writers creates such controversy and paradoxical problems and it is not in harmony and congruent with the contemporary or just posterior historical dates and events. Further, it creates much confusion and distortion in the chronology also. On the other hand, the date 2764 B.C.E. not only does not create any paradoxes but also is coherent and reasonable with other dates and events”. Further the author emphatically argues that Aryabhatta not only wrote Aryabhattiyam and Aryabhatta Siddantha, but also Maharyabhatta Siddantha with concrete and conclusive evidences. It may not be out of relevance for us to familiarise ourselves with some popular Sanskrit works and the western writers whose erudition on the subject was made use of by the author to substantiate the view. I am giving hereunder some of them which forming the sheet-anchor of the researcher thesis: (a) Varahamihira’s Panchasiddantika, Brihat-Samhita, and Brihat Jatakam. (b) Kalidasa’s Jyotirvidabharanam, (c) Bhaskaracharya’s Siddantha Siromani (d) Bhaskara’s Laghu and Mahabaskariyam The following westerners also influenced Dr. Raja’s research analysis: 1) Henry Thomas Colebrook 2) Alexander Cunningham 3) John W. McCrindle 4) A.P. Sinnett 5) Sir William Jones 6) G. Thibaut 7) W. Brennand The author’s vision is clear, diction and communication is excellent and effective, analysis of the subject is scientific, logical reasoning immaculate and conclusions irrefutable. His knowledge of Sanskrit and grasp of the subject are quite laudable. The long list of references and rich glossary of terms at the end of the book bear ample testimony to his exhaustive study of the subject and its mastery by him. But how far this work will be appealing and understandable to the common mind with its limited or no knowledge of Sanskrit language and its grammar, appears to be a million dollar question. The learned elite, on the contrary, is sure to enjoy this brainstorming educative enlightening and inspiring work. I’m absolutely sure and certain that this research article will boost the emergence of more such research papers on similar issues and aspects of our history and culture crowning them with a greater glory and splendour. I whole-heartedly congratulate the author of this research article, Dr.M.L.Raja, for his brilliant and scholarly venture and appeal him to take up more such debated issues and themes and thereby enrich our history and culture.
Prof.B.Satagopan, M.A.(Econ), M.A.(Hist), M.A.(Pol), M.A.(Pub.Admin), Retd. Professor & Head of Department, Department of History and Politics & Additional Professor in Economics, D.G.Vaishnav College, Chennai, PIN 600106 Index
Introduction ...... 17 1. Varahamihira ...... 21 2. Date of Varahamihira ...... 26 3. Saka Era ...... 34 4. Kalidasa’s Jyotirvidabharanam ...... 37 5. Bhaskaracarya ...... 50 6. Date of BrahmaGupta ...... 56 7. Date of Bhaskara ...... 62 8. Laghu Bhaskariyam of Bhaskara...... 64 9. The Epoch used in Aryabhattiyam ...... 66 10. Internal Evidence from Aryabhattiyam ...... 69 11. Surya Siddhantha ...... 71 12. Vedanga Jyotisam ...... 75 13. Sanskrit Grammar...... 85 14. Date of Maharyabhatta Siddhantha ...... 97 15. Hollow Argument ...... 102 16. Bhaskara’s writings ...... 110 17. Conclusion ...... 116 18. The Name of Aryabhatta...... 118 19. Panca Siddhantika ...... 120 20. Kalasaka Vijnanam ...... 122 21. Aryabhatta Kalaprasamsa ...... 123 22. Amazing Contribution of Aryabhatta in Astronomy and Mathematics...... 124 23. Glossary ...... 131 24. References ...... 138
INTRODUCTION Âryabha a* mentioned his date in the tenth śloka of Kālakriyāpāda (3rd Adhyāya ) of his Âryabha īyam.1 However, scholars differ whether it is a bhi or a i in the first sentence of this śloka. Accordingly, the date of Âryabha a differs by 3240 years. Sree. Kotta Venkatachelam,* of Vijayawada, in his book “Kalaśaka Vijñānamu - Prathama Bhāgamu - Jyoti Siddhāntula Kāla Nirnayam” 2 (Telugu, published in 1949) at pages 56 to 60, gave the following with a bhi , as the actual 3-10th śloka. Here, he gave the statement (given in 1917 C.E.) of Tandulam Sree. Narayana Sastri of Chennai, that Narayana Sastri had seen many manuscripts of Âryabha īyam with a bhi in this 3-10th śloka (scanned copies of front cover and page 56 are attached at the end of this book). ¹Éʹ]ªɤnùÉxÉÉÆ ¹ÉbÂʦɪÉÇnÉ ´ªÉiÉÒiÉɺjɪɶSÉ ªÉÖMÉ{ÉÉnÉ:* jªÉÊvÉEòÉ Ê´ÉƶÉÊiÉ®¤nùɺiÉnä´É ¨É¨É VÉx¨ÉxÉÉä%iÉÒiÉÉ:** a yabdānām a bhiryadā vyatītāstrayaśca yugapādā * Tryadhikā vimśatirabdāstadeva mama janmano%tītā ** Meaning: 1. a i - Sixty, 2. Abdānām - Of the years (sixth [genitive] case), 3. a yabdānām - Of sixty years, 4. a bhi - By Sixes (third [instrumental] case of six – always plural in Sanskrit), 5. Yadā - When, 6. Vyatītā - Were elapsed excessively, 7. Traya - Threes (3 – first 18
[nominative] case, Masculine – always plural in Sanskrit), 8.Yugapādā - one part of the Mahāyuga, 9. Tri - Three, 10. Adhika - Excess, 11. Vimśati - Twenty, 12. Abdā - Years, 13. Tadā - At that time, 14. Eva – Indeed, 15. Mama - My, 16. Janmana - Since birth (fifth case of Janman – Birth), 17. Atītā - Were passed by. “When, all the three parts of Yuga were elapsed excessively, by sixes of sixty years, then 23 years were passed by since my birth, indeed” is the meaning of this śloka. In the present 28th Mahāyuga*, when all the three parts of Yuga namely K ta (Satya), Tretā, Dvāpara (3 x 1 = 3 parts in total) had been excessively elapsed, by three hundred and sixty years (360 - sixes of sixty years) of the present Kaliyuga, Âryabha a wrote this Âryabha īyam and at that time, he was 23 years old is the conclusion of this śloka. Thus, Âryabha a wrote Âryabha īyam at 360 Kali i.e. 2741 B.C.E. (3101 – 360 = 2741, as Kaliyuga started at 3102 B.C.E. completed) and thus he was born in 2764 B.C.E. (2741 + 23 = 2764). However, many scholars mentioned it is not a bhi but a i (first [nominative] case of sixty) and the śloka is as shown below. ¹É¹]ªɤnùÉxÉÉÆ ¹Éʹ]ªÉÇnÉ ´ªÉiÉÒiÉɺjɪɶSÉ ªÉÖMÉ{ÉÉnÉ: * jªÉÊvÉEòÉ Ê´ÉƶÉÊiÉ®¤nùɺiÉnä½ ¨É¨É VÉx¨ÉxÉÉä%iÉÒiÉÉ: ** a yabdānām a iryadā vyatītāstrayaśca yugapādā * Tryadhikā vimśatirabdāstadeha mama janmano%tītā ** Here, a i means Sixty (first [nominative] case of 19 sixty, singular, feminine). Hence, “When, all the three parts of Yuga and sixties of sixty years were elapsed excessively, then 23 years were passed by since my birth” is the reading. Accordingly, in the present 28th Mahāyuga, when all the three parts of Yuga namely K ta (Satya), Tretā, Dvāpara (3 x 1 = 3 parts in total) and 3600 years (sixties of sixty years) of the present Kaliyuga had been excessively elapsed, Âryabha a wrote this Âryabha īyam and at that time, he was 23 years old. Based on this reading, it was calculated that Âryabha a wrote Âryabha īyam at 3600 Kali i.e. 499 C.E. (3600 – 3101 = 499, as Common Era started at 3101 Kali completed). Thus, he was born in 476 C.E. (499 – 23 = 476). Thus, these two different readings denote two dates, 476 C.E. and 2764 B.C.E. Hence, it has become an absolute necessity to arrive at the correct and definite conclusion. Therefore, each date has to be analysed historically and chronologically i.e. whether it is consistent, coherent and reasonable or ludicrous, contradictory and paradoxical with other contemporary historical dates and events. In this regard, the date and writings of , 1.Varāhamihira*, author of B hat Samhitā, and B hat Jātakam and compiler of Pañca Siddhāntikā, 2.Kālidāsa*, author of Jyotirvidābhara am, 3.Bhāskarācārya*, author of Siddhānta Śiromanī and 4.Bhāskara*, the astronomer of Âryabha a tradition, who wrote Laghu and Mahā Bhâskarîyam and Commentary on Âryabha īyam and 20
5.The fact revealed in the 2nd śloka in Laghu Bhāskarîyam, 6.The epoch and the number of revolutions of Graha mentioned by Âryabha a himself in Âryabha īyam and 7. The actual meaning of Śaka Era (Śaka Kāla, Śakan pa Era), have to be studied and analysed well, to find out whether the date 476 C.E. is congruent with these dates or not. 8. In the same way, it has to be assessed that the date 2764 B.C.E. is congruent or paradoxical to the dates of the texts, which are anterior to Âryabha īyam. In this regard, the dates of Sūrya Siddhānta:* and Vedāńga Jyoti am* are important. 9. Further, the date and writings of Brahmagupta*, the author of Brahma Sphu a Siddhānta: and Kha akhādyakam and 10. The date of Âryabha a’s Mahāryabha a Siddhānta: have also to be analysed. 11. In the same way, the grammatical and syntactical study of the above-mentioned śloka is also to be carried out, before arriving at the correct date of Âryabha a.
The Date 476 C.E. Now we have to analyse whether the date 476 C.E. is coherent or paradoxical to the other dates and events that are said to be contemporary or just posterior to this 476 C.E. 21
1. VARÂHAMIHIRA In his Pañca Siddhāntikā, in the 20th śloka of the 15th adhyāya (Jyauti opani ad), Varāhamihira wrote about Âryabha a as, 3 ±ÉR EòÉvÉÇ®ÉSÉ ºÉ¨ÉªÉä ÊnxÉ |É´ÉÞÊiiÉÆ VÉMÉÉn SÉɪÉǦÉ^:* ¦ÉÚªÉ: ºÉ B´É ºÉÚªÉÉænªÉÉi|ɦÉÞiªÉɽ ±ÉRÂóEòɪÉÉÆ** Lańkārdharāca samaye dina prav ttim jagāda ca Âryabha a * Bhūya Sa eva Sūryodayāt prabh tyāha Lańkāyām** Meaning : Âryabha a maintained that the beginning of the day is to be reckoned from midnight at Lańka* and the same teacher again said that the day begins from the Sunrise at Lańka. Since Varāhamihira has mentioned clearly Âryabha a and his astronomical statistics, Âryabha a must lived prior to Varāhamihira’s period. The date of compiling of Pañca Siddhāntikā by Varāhamihira is said to be 505 C.E. (at the latest), from the reading of the 8th śloka of the 1st adhyāya of Pañca Siddhāntikā. The detail will be discussed later. If we take the date of Âryabha a as 476 C.E., then it means that 1. Âryabha a wrote Âryabha īyam in 499 C.E. and 2. Varāhamihira compiled Pañca Siddhāntikā in 505 C.E., mentioning Âryabha a as an authority and his two methods of day reckoning in this text, in this 20th śloka of 15th adhyāya . Then, is it possible for the fame and the methods of Âryabha a to spread to various parts of the Nation, so as to reach Varāhamihira, within a short span of six (6) years, 22 that too 1500 years before, when transport and communications were slow? Besides, in this śloka, Varāhamihira mentioned Âryabha a’s two methods of day reckoning, one from midnight at Lańka and the second from the Sunrise at Lańka. Of these two, the day reckoning from Sunrise at Lańka was followed in Âryabha īyam, which was written at the very early age of 23 years of Âryabha a. 23 years itself is too young to write a text, so that the date of the next must be later to this. That means the second text following the day reckoning from midnight at Lańka, i.e. Laghu Âryabha a Siddhānta: (Laghu Siddhānta:), was written a few years later than Âryabha īyam, which means atleast a few years later than 499 C.E. Thus, the second text of Âryabha a will be contemporary to this Pañca Siddhāntikā of Varāhamihira. This makes Âryabha a’s date at 476 C.E. highly unacceptable and unexplainable. Even, if we take Âryabha īyam was the later (second) text, then also six years is too short in time to be mentioned by Varāhamihira. Thus, this śloka of Varāhamihira mentioning Âryabha a as a scholarly authority totally contradicts the date 476 C.E. Further, Varāhamihira mentioned in his Pañca Siddhāntikā (3rd śloka 1st adhyāya )4 that Lā adeva* wrote commentaries on Romaka (Lomaka) Siddhānta:* and Pauliśa Siddhānta:* Lā adeva was a direct pupil of Âryabha a, as found in Bhāskara’s commentary (3-10th śloka) of Âryabha îyam.5 Thus, Lā adeva could have written his commentaries on 23
Romaka (Lomaka) Siddhānta: and Pauliśa Siddhānta:, only after learning astronomy from Âryabha a. Then, as per this date 476 C.E., the date of his commentaries would have been much later to the his Guru’s text Âryabha îyam i.e. much later to 499 C.E. and at least a few years later than 505 C.E. Then, if the date of compilation of Pañca Siddhāntikā is 505 C.E., how could Varāhamihira mention Lā adeva and his commentaries? It may be argued that Varāhamihira was born in 505 C.E. and compiled Pañca Siddhāntikā at a later date i.e. after 505 C.E. However, the calculation of Aharga a (the time that was elapsed from an epoch) was done from the year of composition of the text only, at which year, the author knew the positions of Navagraha*. Thus, with this aharga a, one can compute the positions of all Navagraha, with the use of calculations of mean and true motion of the Graha as detailed in the text. In this 8th śloka of 1st adhyāya of Pañca Siddhāntikā, Varāhamihira mentioned the year 427 of Śaka Era for aharga a purpose only. Besides, Varāhamihira, in his Pañca Siddhāntikā (3rd śloka 1st adhyāya ),4 mentioned that Lā adeva wrote commentaries on Romaka (Lomaka) Siddhānta: and Pauliśa Siddhānta:. Lā adeva was direct pupil of Âryabha a. 5 Then, even if take that Varāhamihira was born in 505 C.E. and compiled Pañca Siddhāntikā later, he could have not mentioned Lā adeva and his commentaries in his Pañca Siddhāntikā. This is because, the year of Lā adeva’s commentaries on Romaka (Lomaka) Siddhānta: and Pauliśa 24
Siddhānta: would have also been a few years after this date of Âryabha īyam (as per this date 499 C.E.) i.e. almost around the same time of Pañca Siddhāntikā. Then, how could Varāhamihira mention Lā adeva’s commentaries on Romaka (Lomaka) Siddhānta: and Pauliśa Siddhānta:, that too mentioning Lā adeva as a scholarly authority? It may be argued that 505 C.E. as the date of Romaka Siddhānta: (as in the 10th śloka of 1st adhyāya of Pañca Siddhāntikā, Varāhamihira mentioned that this was the method according to Romaka Siddhānta:6 ) and so, the date of Varāhamihira is latter than 505 C.E. At first, in this 1 - 10th śloka, he clearly mentioned that this was the method of calculation (i.e. the mathematical calculations) according to Romaka Siddhānta: and also mentioned that this was also according to Pauliśa Siddhānta:. Thus, only the mathematical calculations were adopted by him from Romaka and Pauliśa Siddhānta:. Thus, it does not mean the date of Romaka and Pauliśa Siddhānta:. Secondly, Bhāskara mentioned in his commentary on Âryabha îyam (1st śloka of 2nd adhyāya ) that Âryabha a learned knowledge at Kusumapura*, where Romaka Siddhānta: was already taught and famous.7 Hence, the date of Romaka Siddhānta: can not be after the date of Âryabha a and is not at all around 505 C.E. Thus, the year of compilation of Pañca Siddhāntikā by Varāhamihira was at the latest 505 C.E. and we cannot put it later than 505 C.E. Thus, if Âryabha īyam was written at 499 C.E. and the date of Âryabha a is 476 C.E., it creates 25 much paradox and we cannot explain the mentioning of Âryabha a as an authority, his methods of day reckoning and his pupil Lā adeva’s commentary in Pañca Siddhāntikā by Varāhamihira. It was not possible for the fame and the methods of Âryabha a and Lā adeva to reach Varāhamihira, within a short span of six (6) years, 1500 years before, when transport and communications were slow. Besides, if we take as Âryabha īyam as the first written text and the text with midnight day reckoning as the second written text, written a few years after Âryabha īyam, i.e. a few years later to 499 C.E., as per the date 476 C.E., then it becomes a contemporary text to Pañca Siddhāntikā. Then the date 476 C.E. becomes unreal and false one. 26
2. DATE OF VARÂHAMIHIRA Varāhamihira clearly mentioned his period in the same Pañca Siddhāntikā, in the 8th śloka of the 1st adhyāya as, 8 ºÉ{iÉÉʶ´É ´Éän ºÉÆJªÉÆ ¶ÉE E ÉÉÉ ±É¨É{ÉɺªÉ SÉèjÉ ¶ÉÖC±ÉÉnÉè * +rÇɺiÉʨÉiÉä ¦ÉÉxÉÉè ªÉ´ÉxÉ{ÉÖ®ä ºÉÉ訪ÉÊn´ÉºÉÉtä ** Saptāśvi Veda sankhyam Śakakālamapāsya Caitra Śuklādau* Arddhāstamite Bhānau Yavanapure Saumyadivasādye** Meaning : 1. Sapta - Seven, 2. Aśvi - Two, 3. Veda – Four, i.e. 427 years, 4. Sankhyam - Reckoning or Counting from, 5. Śakakālam - Śaka Era, 6. Apāsya - Having left - completed, 7. Caitra - Caitra month, 8. Śukla - The bright or light half of a lunar month, 9. Âdi - Beginning, 10. Ardha - Half, 11. Astama - Setting, 12. Bhānau - Sun, 13. Yavanapure - The city Yavanapuri, 14. Saumya - Budhan – the planet Mercury, 15. Divasa - Day. The meaning is, deduct the year 427 of Śaka Era elapsed (i.e. deduct 427 from the number of years in Śaka Era for which the aharga a is wanted) at the beginning of the bright half of Caitra lunar month, when the Sun has half set at Yavanapuri at the beginning of Wednesday. This means Varāhamihira had compiled Paca Siddhāntikā in the year 427 of Śaka Era. This Śakakālam (Śaka Era) is the era of the Śaka king Cyrus II, (explained in detail in the forthcoming 33rd to 36th pages). In the 2nd śloka of the 12th adhyāya (Paitāmaha Siddhānta) of Pañca Siddhāntikā, this 27 era was mentioned as Śakendra Kālam (the era of Śakendra, the king of Śaka people i.e. King Cyrus II).9 ‘Pañca Siddhāntikā of Varāhamihira’, the Text edited with Sanskrit commentary and English translation by G.Thibaut* and M.M.Sudhakara Dvivedi,* (Chowkhamba Sanskrit Series Office, Varanasi, 1968 & first edition in 1889), in the page 2 of text at the 8th śloka of the 1st adhyāya , mentioned it as Saumya in the left hand columns of text i.e., as found in manuscript.8 Saumya divasādye means the beginning of Wednesday (Saumya means the Mercury, Budha, the son of Moon). Nevertheless, it was altered as ‘Soma divasādye’ which means the beginning of Monday (Soma means Moon). This is because, if we calculate the first day of the bright half of Caitra lunar month of 427 Śālivāhana Śaka elapsed, it will not fall on Wednesday. However, Śakakālam was assumed to mean Śālivāhana Śaka only and to make it congruous with that opinion, Saumya was altered into Soma.8 (Scanned copy of this page is at the end of this book). This was well explained in the book, ‘Chronology of Kashmir History Reconstructed’ of Śrî Kota Venkatachelam, in pages 241 to 255, where Śrî V.Thiruvenkatacharya, M.A.,L.T., Madras Educational Services (Retd.) concluded with the golden words, “Never reject data, [which are] contrary to your theory.” 10 Varâhamihira’s B hat Samhitâ Now one has to found out, the starting year of this Śaka Era, to know the correct date of Varāhamihira. This was 28 clearly mentioned by Varāhamihira, in his B hat Samhitā in the 3rd śloka of 13th adhyāya as, 11 +ɺÉx¨ÉPÉɺÉÖ ¨ÉÖxɪÉ: ¶ÉɺÉÊiÉ {ÉÞl´ÉÓ ªÉÖÊvÉʹ`ö® ä xÉÞ{ÉiÉÉè * ¹É] ÊuE {É\SÉ ÊuªÉÖiÉ: ¶ÉEòEòɱɺiɺªÉ ®ÉYɶSÉ ** Âsan Maghâsu Munaya Śâsati P thvîm Yudhi hire N patau* a dvika pañca dviyuta Śakakâlastasya Rajñaśca** Meaning: 1. Âsan - Inhabit – present in, 2. Maghā - The constellation of Magha group of stars, 3. Munaya - Sapta i Man alam – Seven Sages – group of Stars – Great Bear Constellation, 4. Śāsati - Ruled (or) governed, 5. Yudhi hira - Yudhi hira Dharma Raja of Pañca Pān ava, 6. N pa - King, 7. at - Six, 8. Dvika - Two, 9. Pañca - Five, 10. Dvi - Two, i.e. 2526 years, 11. Śakakâla - Śaka Era, 12. Tasya Rājña - Of that monarch (Yudhi hira), 13.Ca – and (denoting the stationing of Sapta i Man alam in Magha constellation). “The Seven Sages (The Great Bear) were stationed in the asterism Magha, when the King Yudhi hira* was ruling. The commencement of the Śaka Era took place 2526 years after the period of that Monarch and the stationing of Seven Sages at Magha” is the meaning. Yudhi hira of Pañca Pān ava won the Mahābhārata war* in 3138 B.C.E. and ruled for 36 years up to 3102 B.C.E. In 3102 B.C.E., (completed) the Kaliyuga started and Yudhi hira went for vanavāśa* for 25 years up to 3076 B.C.E. and left the world in 3076 B.C.E., until then the Sapta i Man alam was in Magha constellation, as per the astronomical data. Therefore, 29
2526 years after this, the Śaka Era started is the statement of Varāhamihira. Bha otpala in his commentary to B hat Samhitā, on explaining this śloka, interpreted the word ‘Śakakâla’ as Śaka N pakâla i.e. the era of the Śaka King.12 Further, on explaining this śloka in his commentary to B hat Samhitā, Bhattotpala quoted the writing of V ddha Garga 12 (Garga i Senior) as, iÉlÉÉ c vÏgg& R:- kil Öapr sNxa E tu iSwtaSte ipt&dEvtm!, munyae xmRinrta> àjana< palne rta>. KaliDvâpara sandhau tu sthitâste Pit daivatam , Munayo Dharmaniratâ Prajânâm pâlane ratâ . Here, Sage Garga clearly told that the Sapta i Man alam (Muni) was stationed in Magha constellation (Pit daivatam), at Kali Dvâpara Yuga junction (Sandhi). Thus, the period of reign of Yudhi hira and Kali Dvâpara Yuga junction (Sandhi) were contemporary, as at the time of both, the Sapta i Man alam (Muni) was stationed in Magha constellation. Here, the word twa c has the meaning “and likewise, and so it has been said, accordingly” (‘A Sanskrit – English Dictionary,’ Monier Williams, Oxford Clarendon Press, London 1872, page 359 & ‘A Sanskrit-English Dictionary’, Sir. Monier Monier - Williams, Motilal Banarsidass Publishers, Delhi 2002 page 433). Thus, it definitely proves that these statements of V ddha Garga and Varāhamihira are denoting the very same event and period. Bhattotpala quoted the writing of V ddha Garga here, exactly to point out that the reign of Yudhi hira and the end of Dvâpara Yuga & the beginning of Kali yuga were one and the same, in terms of time. Besides, in the 2nd śloka of 30
13th adhyāya of B hat Samhitā,12 Varāhamihira mentioned that he wrote the movements of Sapta i Man alam, according to the doctrine (Matam) of V ddha Garga. Thus, it proves that the reign of Yudhi hira and Kali Dvâpara Yuga junction were contemporary. This śloka of B hat Samhitā, mentioning the beginning year of Śaka Era, was mentioned in the same form, except the word Rājñaśca is mentioned as Rājyasya, in Kalha a’s Râjatarańginî (1st Taranga 56th śloka).13 It is a historical text detailing the chronology of Kashmir Kings from 3450 B.C.E. to 520/1148 C.E. Kalaha a wrote it in 520/1148 C.E. He was the son of the King of Shanbagapuri in Kashmir, who was also the Chief Minister of Kashmir. Âryabha a himself mentioned in the 5th śloka of 1st adhyāya (Gītikapāda ) of Âryabha īyam that Mahābhārata war took place before the beginning of the Kaliyuga. 14 kaha e mnva e F mnyu gau > Zo gtaSt e c mn u ygau > Una c , kLpadye gpadaRu g c géidvsaCcu -artat ! pvU mR ! . Kāho Manavo ha Manuyugā Śkha Gatāste Ca Manu Yugā Chnā ca * Kalpāderyugapādā Ga ca Gurudivasācca Bhāratāt Pūrvam ** Here, he calculated the number of years, elapsed from the beginning of the present ŚrīŚvetavarāha Kalpa* (6 [Ca] Manvantra, 27 [Chnā] Yuga and 3 [Ga] Yugapāda {Satya, Tretā and Dvāpara, i.e. before the beginning of Kaliyuga, as Kaliyuga was excluded fully} of the present 28th Yuga of the 31 present Vaivasvata [7th] Manvantara*) up to the period of Mahābhārata war. If Mahābhārata war happened after the beginning of Kaliyuga, then the number of years elapsed in Kaliyuga before Mahābhārata war, would have also been included in this śloka. Thus, this śloka of Âryabha īyam reveals that Mahābhārata war took place before the beginning of this Kaliyuga. King Yudhi hira won this Mahābhārata war. Thus, King Yudhi hira’s period was around the beginning of Kaliyuga (3102 B.C.E. completed). Abul-Fazl ibn Mubarak,* a vizier in the court of King Akbar, wrote “Ayeen Akberi” (Ain i Akbari) during the reign of Akbar. This book was rendered English from Persian by Francis Gladwin and was published in London in the year 1800 C.E. (printed by G.Auld Greville Street). In the first volume of this book, in third part, at page 263, on detailing “The Æra of the Hindoos,” Abul-Fazl wrote,15 “In the beginning of the fourth or present jowg [yuga], Rajah Joodishter [Yudhi hira] was universal monorch, and the commencement of his reign became an epoch of an æra of which to this time (being the fortieth year of the reign [of Akbar]) there have elapsed 4696 years.” Akbar came to power in 1556 C.E. and his 40th year of reign was 1595 C.E., which was 4696th year of Yudhi hira (Dharma Rājā of Pañca Pān ava). 4696 years before 1595 C.E. is 3101 B.C.E. (4696 -1595), which was the beginning of Jayabhyudaya Yudhi hira Śaka. Thus, Abul-Fazl clearly mentioned that Yudhi hira lived around the beginning of Kaliyuga (3102 B.C.E. completed). 32
These writings of Abul-Fazl were quoted and explained by Sir. Alexander Cunningham,* in the page 7 of his book,16 “Book of Indian Eras with Tables for calculating Indian Dates”, (first edition 1883 C.E.) where he wrote conclusively, “Now the fortieth year of Akbar was A.D.1595, which deducted from 4696 gives B.C.3101 as the period of Yudhishthra as well as of the Kaliyuga”. Henry Thomas Colebrooke, in the page xliii of his book ‘Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bháscara’ published in London in the year 1817, wrote in his notes and illustrations under the heading ‘Age of ÁRYABHA A’ as (given verbatim),17 “It is to be observed, that he [Âryabha a] does not use the Śaca or Sambat of Vicramáditya nor the Śaca era of Śáliváhana: but exclusively employs the epoch of the war of the Bhárata, which is the era of Yudhist’hira and the same with the commencement of Cali Yuga. Hence it is to be argued, that he flourished before this era was superseded by the introduction of the modern ephochas.” Hence, in 1817 itself it was accepted by Henry Thomas Colebrooke himself, that the epoch of the war of the Bhárata, the era of Yudhi hira and the commencement of Kali Yuga, were contemporary. Thus, the reign of Yudhi hira and Kali Dvâpara Yuga junction were definitely contemporary, as per the above strong evidences. As shown above, Varāhamihira mentioned in the 3rd śloka of 13th adhyāya of his B hat Samhitā, that Śaka Era was started 2526 years after the reign of Yudhi hira and 33 the stationing of Seven Sages in Magha constellation. For 100 years from 3176 B.C.E. i.e. up to 3076 B.C.E., at which year Yudhi hira left the world to Heaven, Seven Sages were in Magha constellation. Therefore, 550 B.C.E. (3076 – 2526) was the year at which, Śakakâla mentioned by Varāhamihira, was started. Therefore, this Śakakâla is the era of Śaka King i.e. of the Śaka king Cyrus II (Cyrus the Great, who ended Persian vassalage to the Medes by capturing Ecbatana and ousting the Median dynasty at 550 B.C.E. and founded the Achaemenid Empire of 550–330 B.C.E.). His era was followed in those days in Kashmir and other nearby places of Bhārat.18 Thus, Varāhamihira’s Śakakâla is this era only and hence, the year 427 of Śaka Era, year of compilation Pañca Siddhāntikā by Varāhamihira, is 123 B.C.E. (550 – 427). So, Varāhamihira lived in the first century B.C.E. Then, it was not at all possible for Varāhamihira to mention Âryabha a and his methods, if the date of Âryabha a is 476 C.E. Now, we have to analyse the exact and correct meaning of Śakakâla (Śaka Era), which was mentioned by Varāhamihira in his B hat Samhitā, in this 3rd śloka of 13th adhyāya . 34
3. ŚAKA ERA (ŚAKAN PA ERA) Śaka Era (Śaka Kāla) began at 550 B.C.E. King Cyrus II of Pārasîkam started this Śakan pa Era (Śaka Era - Śaka Kāla - Śaka Bhûpa (King) Kāla - Śakendra (Ruler) Kāla - Cyrus Era) in 550 B.C.E. He was the King (N pa) of Śaka people. So Śaka N pa Era is definitely his era only. He defeated his enemies and became the King of Pāraśîkam in 550 B.C.E. He belongs to Paraśaka, a division of Śaka people.18 Their place was known after their name Paraśaka, as Paraśakam, later known as Pāraśîkam. Though, King Vikramāditya (57 B.C.E.)* and his great grand son King Śālivāhana (78 C.E.)* of Ujjayanî,* won these Śaka and become Cakravarties of Bhārat, they were not born in Śaka family. Therefore, they cannot be Śaka and Śaka N pa (Śaka King, N pa - King). They can only be Śakāri i.e. enemy or conquerors or ruler (so, rarely as Śakendra) of Śaka and are not at all Śakan upa (Śaka King). We are not mentioning King Aśoka* as Kalinga King but only as Maurya and Magadha King, though he won Kalinga. Hence, Śakan pa Era, Śaka Era, Śaka Kāla or a mere Śaka does not mean either Vikramāditya Era of 57 B.C.E. or the Śālivāhana Era of 78 C.E., but it means only Cyrus Era of 550 B.C.E. Śālivāhana Era was mentioned as Śaka var a (number of years in that era) only. However, in the case of later astronomical texts, Śaka also means Śālivāhana Era, as it is the latest of all the eras and due to the diminishing usage of previous eras. This 35 is because, the Sanskrit word ‘Śaka’ has two distinct meanings. The first one is ‘power and strength.’ The root is ‘Śak.’ From this only the Śaka people who are powerful and strong, got their name.19 In the legends, it was mentioned that they were produced by the holy cow of Vasi ha, Kâmadhenu from her sweat to destroy the army of Viśvāmitra (Kauśika Rājā).20 So Śaka Era means the era of these Śaka people only. The second meaning is ‘era or epoch - Kāla’ where the root is Vedic with the meaning ‘to know’ – to know from which event, the years are counted.18 In that meaning only, it is named as Vikrama Śaka and Śālivāhana Śaka, where Śaka means Era (Kāla –Time). Thus, the word, Śaka has two different meanings. The two meanings for the word ‘Śaka’ can be understood easily through the following two types of titles given to the King Vikramāditya of Ujjainī (57 B.C.E.) First type denotes the people of Śaka as in Śakāri (enemy of Śaka) and in Śakāntaka (destroyer of Śaka) and the second type denotes era as in Śakakāraka, Śakak ta and Śakakart (founder of an era). Besides, if we assume that Śaka Kāla (Śaka Era) is denoting Vikrama Śaka and Śālivāhana Śaka, then the meaning will be Era Era or Kāla Kāla or Śaka Śaka, which doesn’t make any meaning. This is because, in “Vikrama Śaka and Śālivāhana Śaka” the word Śaka already has the meaning of era (Kāla). Hence, what is the necessity of repeating again the word “Kāla,” in “Śaka Kāla?”19 Thus, in the word ‘Śaka Kāla,’ Śaka means strength, thereby denotes 36
Śaka King Cyrus only and not ‘Era’ as it was denoted already by the word ‘Kāla’ in Śaka Kāla. (Śaka - Śaka King, Kāla – Era). Hence, Śaka Kāla mentioned in the foreseen 3rd śloka of 13th adhyāya of B hat Samhitā meant only Cyrus era of 550 B.C.E. and thus, Varāhamihira’s period was 123 B.C.E. This contradicts 476 C.E. as the date of Âryabha a. 37
4. KÂLIDÂSA’S JYOTIRVIDÂBHARANAM Kālidāsa wrote Jyotirvidābhara am, an astrological text. In this text, in the 21st śloka of the 22nd adhyāya , Kālidāsa mentioned as, 21 ´É¹Éê: ʺÉxvÉÖ® n¶ÉÇxÉɨ¤É® MÉÖhÉèªÉÉÇiÉä Eò±ÉÉè ºÉʨ¨ÉiÉä ¨ÉɺÉä ¨ÉÉvÉ´É ºÉÆÊYÉEä SÉ Ê´ÉʽiÉÉä OÉxlÉ ÊGòªÉÉä{É Gò¨É:* Var ai Sindhura Darśanāmbara Gu airyāte Kalau Sammite Māse Mādhava Samjñike Ca Vihito Grantha Kriyopa Krama * Meaning : 1. Varshai - Year, 2. Sindhura - Elephant – so the number Eight, 3. Darśana - at darśana – so the number Six, 4. Ambara - Sky – so the number Zero, 5. Gu a - Tri Gu a – so the number Three i.e. 3068 years, 6. Yāte - was elapsed, 7. Kalau - Kaliyuga, 8. Sammite - Measured out, 9. Māse - Month, 10. Mādhava - Vaiśākha Month. This means that the poet Kālidāsa started writing this text, Jyotirvidābhara am, in the month of Vaiśākha (and ended in the Month Kārtika ) in the year 3068 (completed) of Kaliyugābdam. Kali 3068 is 33 B.C.E. (3101 – 3068). Therefore, the great poet Kālidāsa lived in first century B.C.E. is the definite conclusion arrived from this śloka. In the same text Jyotirvidābhara am, in the 10th śloka of 22nd adhyāya , Kālidāsa mentioned as, 22 vÉx´ÉxiÉÊ®: IÉ{ÉhÉE ɨɮʺÉƽ ¶ÉR EÖ ´ÉæiÉɱɦÉ^ PÉ]JÉ{ÉÇ® E ÉʱÉnɺÉÉ:* JªÉÉiÉÉä ´É®É½Ê¨Éʽ®Éä xÉÞ{ÉiÉä: ºÉ¦ÉɪÉÉÆ ®ixÉÉÊxÉ ´Éè ´É®¯ ÊSÉxÉÇ´É Ê´ÉGò¨ÉºªÉ** 38
Dhanvantari K apa akâmarasimha Śankur Vetālabha a Gha akharpara Kālidâsâ * Khyāto Varāhamihiro N pate sabhāyām ratnâni vai Vararucirnava Vikramasya ** This means that the nine gems in the court of the King (N pa) Vikramāditya were Dhanvantari, K apa aka, Amarasimha, Śañku, Vetālabha a, Gha akharpara, Kālidāsa, the celebrated (Khyāta is past passive participle, denotes a little earlier period than others) Varāhamihira and Vararuci. According to the 21st śloka mentioned before, Kālidāsa lived in first century B.C.E. Therefore, we can conclude that Varāhamihira who along with Kālidāsa was also there, in the court of Vikramāditya and all the three lived in the first century B.C.E. Further, according to the Almanac’s of Bhārat, Traditions and Indian Government’s calculations, the Vikrama Era of this King Vikramāditya started in 57 B.C.E. and the present year 2014 C.E. is 2070 - 2071 year (2014 + 57) of the Vikrama Era. From this also, we can conclude that the King Vikramāditya of Ujjainî, Kālidāsa and the celebrated Varāhamihira, all lived in first century B.C.E. only. This also creates problems in accepting the date 476 C.E. However, some scholars raise objection to accept the text, Jyotirvidābhara am as an authantic one. The objection raised by them was that Kālidāsa, who had written the great Kāvya like Sākuntalam, Kumārasambhavam, Raghuvamśam, Meghadûtam etc., could have not been an author of Jyotirvidābhara am, which is an astrological text, 39 that too entirely different in style and subject. Hence, they say that the reliabilty of Jyotirvidābhara am itself is under question and thus we cannot accept the narrations of Jyotirvidābhara am on Vikramāditya, Kālidāsa and Varāhamihira. Before jumping into any conclusion, we have to consider the following explanations. 1. i. Srīdharācārya, wrote Pā īga ita, Bījaga ita (Refer Bhaskarācārya’s Bījaga ita), both mathematical texts, Jātaka-paddhati an astrological text and Nyāya- kandalī, a philosophical work (Refer Sudhākara Dvivedī’s Ga aka-tarańginī, page 22 and 24). 23 Thus he wrote on different subjects like astronomy, astrology and also on philosophy. ii. Parameśvara wrote Goladīpikā, astronomical text and also the astrological text Âcārasańgraha. 24 iii. Varāhamihira himself wrote B hat Samhitā, a text of encyclopedia containing various details on different subjects and B hat Jātakam, an astrological text and compiled Pañca Siddhāntikā, a pure astronomical text and these three texts were written in different styles and on different subjects. vi. Some Kings in our Nation were multitalented. For example, King Mahendravarman I of Pallava Dynasty was talented in Arts and also wrote a play ‘Mattavilasa Prahasana’. King Harsha Vardhana also wrote three Sanskrit plays, namely Nagananda, Ratnavali and Priyadarsika. 40
v. Dr. Jagadish Chandra Bose was talented both in Physics (Radio-coherer etc) and Botany (Crescograph etc). Besides, in 1896, Bose wrote Niruddesher Kahini, the first major work in Bangla science fiction. vi. Even to-day, some authors wrote both historical and social novels and also science fictions, where we can find the style and subjects differ much. Thus, one person may be talented in various subjects, that too, we can not rule out this possibility in the case of highly knowledgable and multitalented Kālidāsa. He could have chosen different styles for different subjects. 2. Kālidāsa who wrote the great Kāvya and the text Jyotirvidābhara am might be of two different persons of different period. Another objection raised was that though Jyotirvidābhara am was written in Kali 3068 (33 B.C.E.), how could it mention King Śālivāhana and his era of Kali 3179 (78 C.E.),25 an event of 111 years later. This text even mentioned the starting year of the era of future Kings, namely Vijayābhinandana (21,179 Kali i.e. 18,078 C.E.), Nāgārjuna (31,179 Kali i.e. 28,078 C.E.) and Balī (4,31,179 Kali i.e. 4,28,078 C.E.), who are yet to born. 25 Jyotirvidābhara am is a text of astrology and history, rather than astronomy and the prediction of future events, alongwith narrating the present events is natural to the text. Thus, based on these flimsy objections, one cannot question the authenticty of a text and cannot reject the entire text. 41
Besides, some scholars feel that King Vikramāditya and Śālivāhana of Ujjainî are not historical persons but of mythical origin. Here also, the following explanations have to be read before coming to any conclusion. i. KALHANA’S RÂJATARAŃGINĪ This text describes the rulers of Kashmir in chronological order from Mahābhārata war up to the time of its author Kalha a (520/1148 C.E.). 125th śloka of 3rd Tarańga 26 mentioned as, “tÇanehSyuJjiyNya< ïImaNh;Raprai-x> , @kCDTÇZc³vtIR iv³maidTy #Ty-Ut!.” The meaning is Vikramāditya, who had the title (para abhidha:) as Śrī Har a, ruled under one Umbrella at Ujjaini, as a Great Cakravarti. Destruction of Śaka people by Vikramāditya is mentioned by Rāja Tarańginī in 128th śloka of 3rd Tarańga as, “By destroying the Śaka, Vikramāditya made the task light for Śiva who is to descend to the Earth for extermination of Mleccha.” 26 King Vikramāditya sent Māt gupta from Ujjaini to rule Kashmir, as there was no ruler after the sudden demise of Hira ya and Toramā a. As Vikramāditya was the Chakravarti of whole Bhārat, he was duty-bound to take care of Kashmir and thus sent Mat gupta. This history of Mat gupta was given in detail in 129 to 290 sloka of 3rd Tarańga . 27 Further, in 5th and 6thśloka of 2nd Tarańga , the text mentioned as, “Then they brought Pratāpāditya, a relative of King Vikramāditya and inaugurated him as King of Kashmir,” and these sloka cautioned that this Vikramāditya should not 42 be confused with another Vikramāditya who was Śakāri, the destroyer of Śaka. 28 ii. ALBERUNI These two Vikramādityas and their period were clearly distinguished by Alberuni (Abu Raihan), the Persian traveller, in the page 7 of 2nd Volume of Tahqiq ma lil-Hind written in 1030 C.E., (Alberuni’s India – translated into English by Edward C.Sachau – Munshiram Manoharlal), as, 29 “Now the year 400 of Yazdajird, the gauge year corresponds to the following years of Indian Eras. 1. To the year 1488 of the era of Sri Harsha, 2. To the year 1088 of the era of Vikramaditya.” This 400th year of Yazdazird (Yazdegerd III or Yazdgerd III or Yazdeger III) is 1031-32 C.E. Thus, 1488 years before 1031 C.E. is 457 B.C.E. at which Srī Har a era started and 1088 years before 1031 C.E. is 57 B.C.E. at which the era of Vikramāditya started. This Srī Har a, ruled Ujjaini 400 years before Vikramāditya. He is the son of Chandra Sarma, who latter took up Sanyāsam with the name Śrī Govinda Bhagavat Pāda, the Guru of Srimad Âdiśańkara of 509 - 477 B.C.E. Thus, Śrī Har a who ruled Ujjaini in 457 B.C.E. had the title as Vikramāditya and King Vikramāditya of 57 B.C.E. had the birth name Vikramāditya and the title name Śrī Har a. In page 6 of 2nd volume of this text,29 Alberuni detailed the victory of Vikramāditya over Śaka King as, “The here mentioned Saka tyrannized over their country between the 43 river Sindh and the ocean, after he had made Aryavarta in the midst of this realm his dwelling place. The Hindus had much to suffer from him, till at last they received help from the east, when Vikramaditya marched against him, put him to fight and killed him in the region of Karur, between Multan and the castle of Luni. Now this date become famous, as people rejoiced in the news of the death of the tyrant, and was used as the epoch of an era, especially by the astronomers. They honour the conqueror by adding Sri to his name, so as to say Sri Vikramaditya.” iii. ALEXANDER CUNNINGHAM Vikramāditya’s victory over Śaka people was also mentioned by A.Cunningham in his “Book on Indian Eras” in the page 52, quoting Abu-Rihan (Alberuni), as,30 “Saka was the name of the King who reigned over the country situated between the Indus and the sea; Vikramaditya marched against him and killed him in a battle fought near Korur, between Multan and the fort of Luni.” Further, Cunningham wrote in the 49th page of this book, 30 “The era of Vikrama also said to have been established by Vikramarka Raja 470 years after Mahavira or in 527 -470 =57 B.C.” He also wrote “Satrunjaya Mahatmya professes to have been written 477 years after Vikrama or in A.D. 420,” i.e. 57 B.C. (477 -420) as the date of Vikaramaditya. iv. JOHN W. McCRINDLE John W.McCrindle, the western scholar, who authored many books and translations of Greek classical Literatures, 44 especially on Alexander, mentioned in 31 “Ancient India as described by Ptolemy” edited in 1885 at Edinburgh (Munsiram Manoharlal, 2000) in pages 154 and 155 as, “Ozene - This is the translation of Ujjayani, the Sanskrit name of the old and famous city Avanti, still called Ujjain. It was the capital of celebrated Vikramaditya, who having expelled the Skythians and there after established his power over the greater part of India, restored the Hindu monarchy to its ancient splendour. ….the date of the expulsion of Skythians by Vikramaditya which forms the era in Indian Chronology called Samvat (57 B.C.)…. about a century and a half after Vikramaditya era, Ujjain was still a flourishing city.” v. A.P.SINNETT A.P.Sinnett, the western scholar who was President, the Simla Electric Thoesophical Society wrote in his book,32 “Esoteric Buddhism” (Indological Book House, Varanasi) in the page 151 as, “The party of primitive Buddhism was entirely worsted, and the Brahman ascendancy completely re-established in the time of Vikramaditya about 80 B.C.” vi. SIR WILLIAM JONES He was an English judicial officer in East India Company. He was the founder and first president of Asiatic Society, Calcutta. In his presidential address as the 10th anniversary discourse at Asiatic Society on 28th February 1793, he mentioned “two certain epochs between Rama who conquered Silan a few centuries after the flood, and Vicramaditya, who died in Ujjayini fifty seven years before beginning of our 45 era.” [1. The Asiatic Researches, 4th volume page xiv, published 1798 C.E. London and 2. The Works of Sir William Jones, volume 3, page 220, published in 1807 C.E. London].33 Thus, William Jones not only accepted Rāma and Vikramāditya as historical persons but also the period of Vikramaditya as 1st century B.C.E. In his work, “On the chronology of the Hindus” 34 which he wrote as a President of Asiatic Society in January 1788, which was published in ‘The Works of Sir William Jones’ in volume 4, year 1807, London, he mentioned in page 40, “After the death of Chandrabija, which happened, according to Hindus, 396 years before Vicramaditya, or 452 B.C., we hear no more of Magadha as an independent kingdom.” Thus, he mentioned the period of Vikramāditya as 56 B.C.E. (452 – 396). In the page 43 he added,34 “We may arrange the corrected Hindu chronology, according to the following table, supplying the word about or nearly, (since perfect accuracy can not be attained and ought not to be required), before every date. Vicramaditya - 56 Y.B.C.” (Y.B.C. - Years Before Christ). Thus, in his chronological table, given next page of 46, he mentioned Vicramāditya lived 1844 years before William Jones’ time (1788 C.E.), i.e. 56 B.C.E. (1844 –1788). vii. BHAVI YA MAHÂPURÂNAM Here the word ‘Bhavi ya’ means Bhavi ya Kāla and thus, Bhavi ya Mahāpurā am describes the incidents of future period also i.e. after the period of writing this text. Thus, 46 the date of Bhavi ya Mahāpurā am is ancient to these incidents. The 14 and 15 śloka of Pratisarga Parva, Prathama Khā a, 7th Adhyāya of this text (3-1-7-14 &15) mentioned the year of birth of Vikramāditya as, 35 {ÉÚhÉÉæ iÇzC< Ut e v; Re kla E àaPt e -ykr< ,e zkana < c ivnazw R +ayxmR R ivvÏy& e . The meaning of these śloka and up to 24th śloka is, “In 3000 Kaliyuga (101 B.C.E.), due to attack of Śaka people, there was terror. To destroy these Śaka and to protect and enhance Dharma, by the orders of Śiva, from Kailāśa, he was born as the son of Gandarvasena, the King of Ujjaini. Kalhana’s Rāja Tarangi ī mentioned in the same way in the 128th śloka of 3rd Taranga as, “By destroying the Śaka, Vikramāditya made the task light for Śiva who is to descend to the Earth for extermination of Mleccha.”26 He was named as Vikramāditya by his father. At the age of 5, he went to forest to do Tapas. He returned Ambavati (Ujjaini) at the age of 12. When he was about to ascend the Simhāsana with 32 Idols, a Vetāla came and guided him with Dhārmic rules to be adopted by him on governing.” Then, Vikramāditya came to power in 3020 Kali (81 B.C.E.) and ruled for 100 years up to 3120 Kali (19 C.E.). It is mentioned in śloka 3-4-1-22 as, 35 izva}aya c npitiv& ³mStnyStt>,R ztv; ¡ kt& < raJym ! dv-KtStta=-vte !,, dzv;¡ The boundaries of Vikramāditya Kingdom, as per 3-3-2- 47
10 śloka was, 36 pZicm e isNxn*Ntu e ste bNxu e ih diIÉhÉä , %Ttr e bdrISwan e pvU eR c kiplaiNtk e . Thus, the boundaries were on the west Sindhu River, on south Rameśwaram, on north Badari (Himalayas) and on east Kapila (Assam). After Vikramāditya, the Kingdom was divided into 18 parts namely, Indraprastham, Pāncālam, Kuruk etram, Kāpilam, Antharvedī, Vraja, Ajameram, Marudnva (Rajasthan), Gaurjjaram, Mahāra ram, Drāvi am, Kalingakam, Âvantyam, Udupam (Udupi), Vangam, Gaudam, Maghadam and Kausalyam (3-3-2-11 to 13 śloka).36 Thus, we can understand the vastness of his Empire. Bhavi ya Mahāpurā am also described his dynasty. He belongs to Pramara (Panwār) dynasty of Agnikula Vamśa. There are 4 Agni vamśa. 1.Pramara of Sama Veda in Ambavati (Ujjaini), 2. Capahāni (Vayahani) of Yajur Veda in Ajameram, 3.Sukla (Calukya) of Rig Veda in Dvāraka and 4. Parihāraka of Atherva Veda in Kalinjarapuram (3-1-6-47 & 48 and 3-1- 7-1 to 14 and 3-1-4-12 to 15). 37 King Pramara started his dynasty in 2710 Kali (391 B.C.E.) as stated in 3-1-7-7 & 8 śloka as, 38 {ÉÚhÉæ Ö e c shöaNt e staU vcnmävIt ! , sPtivzitzt< e v; eR dzaBde caixk e kla E . àmra e nam -pal>U kt& < raJy < c ;qsma>! , Bhavi ya Mahāpurā am also mentions that for 100 years after Vikramāditya, Nation was in peace. Then again, Śaka marched from Himalaya and Sindhu mārga and attacked. Then Śalivahana, great grand son of Vikramāditya, defeated 48
Śaka, maintained Dharma and peace and ruled well for 60 years (3-3-2-9 to 33).39 Thus, Bhavi ya Mahāpurā am strongly confirms that King Vikramāditya of Pramara Dynasty is definitely a historical person of first century B.C.E. However, some scholars are not accepting the authenticity of Bhavi ya Mahāpurā am, as it mentions Mahāmada, Musala and Īśaputra and other related events. But, many feel that these narrations may be interpolated during British rule, with the intension of reducing the reliability of this Purā a. Because, it is a fact, that our Purā a never talk about foreign incidents. Then, even if it is there, it will not reduce the text’s reliability. For example, we are not thinking low of history books or brand them as unreliable, just because they describe recent things. Besides, the narrations of recent things will not reduce the authenticity of ancient incidents described in the text. Further, the present available text of Bhavi ya Mahāpurā am may be a re-edited one where the recent incidents would have been included, that makes the text and the ancient incidents described more authentic. viii. The Almanac’s of Bhārat, Traditions and Indian Government’s calculations The Almanacs of Bhārat are still following the Vikrama Samvat of 57 B.C.E. of this King Vikramāditya and the year 2013 C.E. is 2069 - 2070 year (2013 + 57) of the Vikrama Era. The Government of Bhārat and the common people are 49 still following it and it is the tradition of Bhārat. The historians and astronomical scholars who wrote the commentaries and English translations of our Nation’s Astronomical texts are using these Vikrama Samvat and Śālivāhana Śaka to derive the dates of various astronomers and astronomical texts. But on the contrary, they are doubting the historicty of the very same Kings in a paradoxical and unjustifiable way. Henry Thomas Colebrooke, in the page xliii of his book ‘Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bháscara’ published in London in the year 1817, wrote in his notes and illustrations under the heading ‘Age of ÁRYABHA A’ as (given verbatim),17 “It is to be observed, that he [Âryabha a] does not use the Śaca or Sambat of Vicramáditya nor the Śaca era of Śáliváhana:’’ Hence, in 1817, Henry Thomas Colebrooke mentioned Vikrama Samvat and also used clearly the word ‘Śālivāhana’ itself to denote Śaka var a of 78 C.E. 50
5. BHÂSKARÂCÂRYA Bhāskarācārya, in the 28th śloka of Kālamānādhyāya of Madhyamādhikāra of Grahaga itādhyāya of Siddhānta Śiromanī, mentioned clearly that this Śakan pa Era (Cyrus Era of 550 B.C.E.) came to end in 3179 Kali. The śloka is, 40 xÉxnÉpÒxnÖ MÉÖhÉɺiÉlÉÉ ¶ÉE xÉÞ{ɺªÉÉxiÉä Eò±Éä´ÉÇiºÉ®É: * MÉÉäpÒxuÊpEÞÞÞ iÉÉR E n»ÉxÉMÉMÉÉäSÉxÉpÉ: ¶ÉEòɤnùÉÊx´ÉiÉÉ: Nanda Adri Indu Gu āstatha Śakan pasyânte Kalervatsarâ * Godrīndvadrik tāńkadasranagagocandrā Śakābdānvitā Meaning : 1. Nanda - Nava (nine) Nanda – so Nine, 2. Adri - Seven Hills – so Seven, 3. Indu - Moon – so One, 4. Gu a – Trigu a - so Three i.e. 3179 years, 5. Śakan pasya – (Era) of Śaka King (N pa – King) 6. Anta – End, (Ante is 7th case [Locative case] of Anta meaning at the end, limit, boundary), 7. Kaler – in Kaliyugābdam, 8. Vatsarā - Years, 9. Godrīndvadrik tāńkadasranagagocandrā - 197,29,47,179 (Go is 9, Adri is 7, Indu is 1, Adri is 7, K ta is 4, Ańka is 9, Dasra is 2, Naga is 7, Go is 9, Candra is 1), 10. Śakābda – Śaka years, 11. Anvitā - Gone alongwith, joined, connected with (past passive participle, in past tense). Here ante, in the locative case, indicates the ending of the Śakan pasya Era. If it were to mean ‘up to that or till,’ then it would have been used in the 5th ablative case of Śakan pa era as Śakan pasya kālāt or Śakan pāt. Even the 5th case of anta ( +Ntat! antāt ) mean ‘up to the end of’ only and 51 not as ‘up to the beginning of Śakan pa era’. Fifth ablative case is used to mean “the time from, since, after etc.” Example: ‘Saptâhât pa ita g ham gata ’, which means, ‘The scholar went home after a week.’ Here Saptâhât is in 5th ablative case. The seventh locative case is used to denote ‘at, whence, when’. Example: ‘Saptâhe pûr e pa ita g ham gata ’, which means, ‘When the week was completed, the scholar went home.’ Here, Saptâhe is in 7th locative case. Hence, ante in 7th locative case in this śloka means ‘at the end of Śakan pa Era’. If it is to mean ‘up to Śakan pa Era’, then it should have used in 5th ablative case as Śakan pasya kalāt only. (Saptâha means seven days, a week, Monier Williams,”A Sanskrit – English Dictionary,” Oxford Clarendon Press, London May 1872, page 1065).41 Sûrya Siddhānta: mentioned in Madhyamādhikāra (1st adhyāya) as “sUyRaBd ºÉRÂóJªÉªÉÉ }eya> k&tSyaNte gta +mI, Sūryābda sańkhyayā th 42 Jñeyā Ktasyānte gatā amī ,” (47 śloka), “ +iSmn! kty& gSyaNtu e sv eR mXygta ¢ha>, Asmin K tayugasyānte sarve th 42 madhyagatā Grahā ,” (57 śloka), where K tasyānte and K tayugasya ante, (K tayugasya – of this K tayuga, ante – ‘end’ in 7th locative case) means ‘at the end of K tayuga’ only and not at all ‘up to or till K tayuga’. If it is to mean ‘up to the Śaka era’ then it would have been used in the 5th ablative case as used by Âryabha a himself. He used it in the 5th ablative case with the meaning of ‘up to’ in the 5th st śloka of 1 adhyāya as Bhāratāt pūrvam, where ‘-artat!’ in the 5th ablative case means up to Bhārata war and pūrvam 52
14 means before that. Besides , in the second line of this śloka, the word ‘Śakābdā anvitā ’ means that the Śaka years (abdā - years) were gone alongwith the years of 6 Manvantara, 27 mahāyuga and 3 yuga (197,27,44,000 years) and 3,179 years of Kaliyuga i.e. 78 C.E. (anvitā - were gone alongwith, past passive participle, in past tense). Thus 197,29,47,179 years (197,27,44,000 + 3,179) were elapsed and this includes the years of the Śakan pa i.e. of the Śaka King also (Śakābdānvitā ). Thus, it further emphasises that the Śakan pa era came to an end in 3179 Kaliyuga (78 C.E.). Besides, the word ‘anta’ means definitely the end of the era and not at all the begining of or up to the era. Thus, the Śakan pa era had gone, ended at 3179 Kali (78 C.E.). Since Bhāskarācārya mentioned very clearly using the word ‘Śakan pasya’ which definitely mean Cyrus II, the King of Śaka people, we cannot take it to mean even the King Vikramāditya of Ujjainī of 57 B.C.E. [Ref. Śaka Era (Śakan pa Era) discussed earlier]. Vikramāditya was Śakāri (enemy of Śaka), Śakakāraka and Śakart (founder of an era) and rarely Śakendra (the ruler of Śaka) and he could not be Śaka and hence cannot be called as Śakan pa (Śaka King). It is important to note that the word Śaka in the title of Vikramāditya is used here with two different meanings. 1. Denotes the people of Śaka, as in Śakāri (+ir – ari, enemy) Śakāntaka (+Ntk> Antaka , destroyer) of Śaka people and it cannot be enemy or destroyer of era or epoch, 2. Denotes era, as in Śakak ta, Śakakāraka or Śakakart (kt& , karak and krt! & means founder) i.e. founder of an era and cannot be founder or creator of Śaka people. Hence, one has to be 53 careful in understanding the meaning exactly and correctly, whenever and wherever Śaka and its related words were used. Thus, Bhāskarācārya himself clearly mentioned in this śloka that the Era of Śakan pa ended (Śakan pasya Ante) in Kaliyugābdam 3179 year, i.e. 78 C.E. (3179 – 3101). Since Śālivāhana Śaka began only in Kaliyugabdam 3179 year, i.e. 78 C.E. (3179 – 3101), at which the Sakan pa Era came to an end, the Śakan pa Era mentioned by Bhāskarācārya is definitely not Śālivāhana Śaka but the Era of Cyrus II, the King of Śaka people. Thus, the Śaka Kāla mentioned by Varāhamihira is the Cyrus Era of 550 B.C.E. and Varāhamihira’s period is 123 B.C.E. Thus, it makes very difficult to accept the date 476 C.E. Further, Bhāskarācārya mentioned his date in Siddhānta Śiromanī, in the Golādhyāya Praśnādhyāya 58th śloka as, 43 rs ghÉu pUhÉR mhI sm zkn&p smye=-vNmmaeTpiÄ> , rs guhÉ v;eRhÉ mya isÏaNtizraemhÉI rict> . Rasa Gu a Pūr a Mahī sama Śakan pa samaye=bhavan Mamotpatti , Rasa Gu a var e a Mayā Siddhānta Śiroma ī racita . Meaning : 1. Rasa – Taste, flavour, since they are six in number, hence it denotes the number six, 2. Gu a – There are three Gu a in all constituents of Nature, it denotes the number three, 3. Pūr a – Zero, 4. Mahī - The Earth, hence the number one (thus it denotes 1036), 5. Sama – equal, same, 6. Śakan pa - The King of Śaka 7. Samaya – Time, 8. Abhavan – Happened (past tense), 9. Mama – Mine (6th 54 genitive case of I, +hm ! ) 10. Utpatti - Birth, 11. Var e a – By the year, 12. Mayā - By me, 13. Siddhānta Śiroma ī - The text Siddhānta Śiroma ī, 14. Racita - was written. Thus, Bhāskarācārya was born in 1036 of Śakan pa samaya and at the age of 36, he wrote Siddhānta Śiroma ī. He mentioned clearly that this Śakan pa samaya came to an end in 3179 Kaliyugābdam i.e. 78 C.E. (3179 – 3101).40 Thus, it clearly proves that his date is not at all 1144 C.E. (1036 +78). This calculation of his date at 1114 C.E. is based on the wrong assumption that the Śakan pa samaya mentioned in this 58th śloka, as Śālivāhana Śaka, which was started in 78 C.E. (3179 Kali), at which year this Śakan pa samaya came to an end as per the 28th śloka of Kālamānādhyāya of Madhyamādhikāra of Grahaga itādhyāya of Siddhānta Śiromanī,40 as shown before. Thus, Bhāskarācārya was born in 1036 Śakan pa samaya, which was started by Cyrus II at 550 B.C.E. Hence he was born in 486 C.E. (1036 – 550 = 486) and wrote Siddhānta Śiroma ī at 522 C.E. (486 + 36 =522). In Kara akutūhalam, another text of Bhāskarācārya, he mentioned in the 2nd śloka of 1st adhikāra (Madhyamādhikāra ), 1105 Śaka as the epoch for calculating Aharga a. On writing the commentary to this text, the scholar Sumatihar a (1621 C.E.)*, interpreted the word ‘Śaka ’ as Śakan pa [gatābta pi a ].44 (Śakan pa = Śaka King, Gata = was elapsed, passed by, Abtā = years, Pi a = quantity, sum, total). Thus, Bhāskarācārya used the era of Śakan pa only, which was started at 550 B.C.E. and hence his date is 486 C.E. 55
In the 2nd śloka of 1st adhikāra (Madhyamādhikāra ) of Grahaga itādhyāya of Siddhānta Śiroma ī, Bhāskarācārya praised Varāhamihira and Brahmagupta as, 45 ktI& jyit ij:hÉjau e ghÉkc³cUfamihÉjyiNtR liltake ty! > àiwt tNÇ s*uk!ty>, vrahimihrady> smvlaKye y;ae < ktI& > k&tI -vit maozae=Py tnu tNÇ bNx=LpxIe >. K tī Jayati Ji ujo Ga akacakracū āma ir Jayanti Lalitoktaya Prathita Tantra Sadyuktaya , Varāhmihirādaya Samavalokya Ye ām K tī K tī Bhavati Mād śo=pya Tanu Tantra Bandhe=lpadhī . In this śloka Bhāskarācārya praised the charming, extensively spread, celebrated and virtuous works of victorious Brahmagupta (Ji ujo = Ji u ja = Ji u’s son = Brahmagupta) and of the authors starting from victorious Ga akacakracū āma i Varāhmihira. Hence, Brahmagupta and Varāhmihira lived much earlier to Bhāskarācārya. As shown above, the year of writing of Siddhnta Śiroma ī by Bhāskarācārya is 522 C.E. Then, if we accept 505 C.E. as the year of compilation of Pañca Siddhāntikā by Varāhamihira, is it possible for the fame and works of Varāhamihira to spread to various parts of the Nation, so as to reach Bhāskarācārya, within a short span of seventeen years, that too 1500 years before, when transport and communications were slow. Hence, the date of Varāhamihira was much before 522 C.E. i.e. at least a few hundred years before. Then the date of Âryabha a at 476 C.E. is paradoxical and contradictory. 56
6. DATE OF BRAHMAGUPTA Brahmagupta mentioned his date in his texts Brahma Sphu a Siddhānta: and Kha akhādyakam. In the 7th and 8th śloka of Samjñādhyāya (23rd adhyāya ) of Brahma Sphu a Siddhānta: he mentioned it as, 46 ïIcapvzitlk< e ïIVyaºmuOa e n&p e zkn&pahÉam! , pÁcazTs
Kaliyugābdam, (78 C.E.) at which year, this Śakan pa era came to an end, as per these two śloka of Brahmagupta. However, there are a few clarifications are to be explained. As per this derivation, the date of Brahma Sphu asiddhānta was at zero C.E. Then, how could Brahmagupta mentioned the end of Śakan pa era in 78 C.E. i.e. 78 years after this? This has to be explained before arriving the date of Brahmagupta. The possible explanations are, 1. The Śakan pa era of Brahmagupta and hence that of Bhāskarācārya may be the era of Śrī Har a of Ujjainī who started his era at 457 B.C.E. (Refer Alberuni’s India*, Edward C.Sachau, London, Turbner & Co., Ludgate Hall, 1888 & Munshiram Manoharlal Publishers, 2001, page 7th of 2nd Volume).49 Then the date of Brahma Sphu asiddhānta will be 93 C.E. (550 – 457 = 93) i.e. after 78 C.E. 2. This may be the era of the King Vikramāditya of 57 B.C.E. Then the date of Brahma Sphu asiddhānta will be 493 C.E. (550 – 57 = 493) i.e. after 78 C.E. However, the word Śakan pa means King Cyrus only. It has to be given its adequate importance before arriving any conclusion. 3. Kālidāsa in his Jyotirvidābhara am in the 110 and 111 śloka of 10th adhyāya (Rājasattādhyāya ), mentioned clearly the periods of various eras in Kaliyuga. He mentioned the founder of eras from King Yudhi hira of Pañca Pān ava (0 Kali i.e. 3101 B.C.E.) 25 He even mentioned the starting year of the era of future Kings, namely Vijayābhinandana (21,179 Kali i.e. 18,078 C.E.), Nāgārjuna (31,179 Kali i.e. 28,078 C.E.) and Balī 60
(4,31,179 Kali i.e. 4,28,078 C.E.), who are yet to born. Basically, Jyotirvidābhara am is a text of astrology and history, rather than astronomy. As it is an astrological text, the prediction of future events is natural to the text. He mentioned that 135 years after the era of Vikramāditya of 57 B.C.E. (3044 Kali), the era of Śālivāhana (3179 Kali i.e. 78 C.E.) will begin.25 The date of Jyotirvidābhara am is 3068 of Kaliyugābdam. (Based on the 21st śloka of the 22nd adhyāya , which is already described). Kali 3068 is 33 B.C.E. (3101 6 3068), i.e. prior to zero C.E. Thus, based on this text, Brahmagupta might have written that the era of Śakan pa ends in 78 C.E. However, the date of Brahmagupta can be correctly arrived by fixing the date of the King ŚrīVyāghramukha of ŚrīCāpavamśa. Unfortunately, till date, no conclusive evidences are found out. Hence, efforts should be made to find out the period of this ŚrīCāpavamśa and that of ŚrīVyāghramukha. With that, we can come to a definite conclusion on the date of Brahmagupta. Bhāskarācārya mentioned Brahmagupta in the 2nd śloka of 1st adhikāra (Madhyamādhikāra ) of Grahaga itādhyāya 45 and also mentioned in his svavāsanābhā yam for the 28th śloka of Kālamānādhyāya of Madhyamādhikāra of Grahaga itādhyāya of Siddhānta Śiromanī that this śloka is of Brahmamānam (as per the calculations of Brahmagupta).40 Hence, if the date of Brahmagupta is fixed correctly, the date of Bhāskarācārya can also be fixed, though Bhāskarācārya did not mentioned of any king or reign as done 61 by Brahmagupta. However, for Varāhamihira, there are adequate proofs showing that he lived during the reign of King Vikramāditya of Ujjainī i.e. first century B.C.E., which were dealt before. Thus, as per these śloka of Brahma Sphu a Siddhānta:, it is very clear that the era mentioned by Brahmagupta is not at all the era of King Śālivāhana (78 C.E.) of Ujjayanî, as he mentioned that the era used by him (Śakan pa era) came to an end at 78 C.E., at which year only the Śālivāhana era was started. If at all one can say that the era may be of SrīHar a of 457 B.C.E. or at the latest, the era of Vikramāditya. Even if we accept it as the era of Vikramāditya, it itself creates paradoxes. Because, 550th year (the year of Brahma Sphu a Siddhānta:) in Vikramāditya era of 57 B.C.E. is 493 C.E. (550 – 57). Then, how could one place the date of Âryabha īyam at 499 C.E., i.e. after 493 C.E.? 62
7. DATE OF BHÂSKARA Bhāskara himself told that he was not a direct disciple of Âryabha a. He frequently mentioned, “that is what we heard about Âryabha a.” (Bhâskara’s commentary on Âryabha īyam [Dasagîtik-Sûtra-Vyākya and Âryabha a- Tantra-Bhā ya] under the heading Jyoti aśāstraprādurbhāve Vyākhyākāramatam, on explaining the 1st and 2nd śloka of Gîtikapāda [1st adhyāya ]).50 Bhaskara’s period was estimated at 629 C.E., at which year he was said to have written his commentary on Âryabha īyam.51 Thus, at the latest his date is 629 C.E. So the difference of period between Âryabha a and Bhāskara is just 130 years. This is because as per the date 476 C.E., Âryabha a wrote Âryabha īyam in 499 C.E., at the age of 23 years. If it were so, then he would have lived up to 550 C.E. The year of Bhāskara’s commentary on Âryabha īyam is 629 C.E. Even if he was just 29 years at that period, he would have born, at the latest, in 600 C.E. So just a fifty years of difference between Âryabha a and Bhāskara cannot be stated as Kāle Mahati (so much time), by Bhāskara. If we took the date of Bhāskara as 522 C.E., as per some scholar’s opinion,51 then Bhāskara would become junior contemporary of Âryabha a. Further, on his commentary to Âryabha īyam at 3-10th śloka, Bhāskara mentioned that Pā urañgasvāmi, Lā adeva and Niśańgu were the direct pupils of Âryabha a and he did not mentioned his name in the list.5 This clearly 63 shows that Bhāskara was not a direct pupil of Âryabha a. If the date of Âryabha a is 476 C.E., then, the dates of Pā urañgasvāmi, Lā adeva and Niśańgu would have been between 500 to 550 C.E. Then, Bhāskara would have been a junior contemporary to them. However, Bhāskara mentioned here in that manner that he was neither contemporary and nor a direct pupil to Pā urañgasvāmi, Lā adeva and Niśańgu (direct pupils of Âryabha a). If he had learned Astronomy of Âryabha a tradition from these direct pupils of Âryabha a, then he would have mentioned it proudly in his commentary to Âryabha īyam. However, there is no such thing found in Bhāskara’s writings. Thus, Bhāskara was separated from Âryabha a by a much longer period. At the latest Bhāskara’s date is 629 C.E. or as per some scholar’s opinion, 522 C.E. Thus, it makes difficult to accept the date 476 C.E. 64
8. LAGHU BHÂSKARÎYAM OF BHÂSKARA
Bhāskara’s period is estimated as 522 C.E. or at the most 629 C.E., which is the year in which he wrote his commentary on Âryabha īyam. He mentioned in the second śloka of Laghu Bhāskarîyam as, 52 E ɱÉä ¨É½ÊiÉ nä¶Éä ´ÉÉ º¡Ö q a wR— ySy dzRnm! , VɪÉiªÉɪÉǦÉ^: ºÉÉä%ʤvÉ |ÉÉxiÉ |ÉÉä±±ÉR ÊPÉ ºÉt¶ÉÉ: ** Kāle mahati dese vā sphu ârtham yasya darśanam * Jayatyâryabha a so%bdhi prānta prollanghi sadyaśā ** Meaning : Victorious is Âryabha a, whose excellent fame had crossed the bounds of the oceans and whose science (Astronomical treatise) leads to accurate results, in a lot of countries, even after the lapse of so much time (Kāla – Time, Mahati – excessive, huge, vast). We have to give much importance to the word, “after the lapse of so much time, (Kāle Mahati)”. Even after the lapse of so much long time, Âryabha a’s statistical data on astronomy were found to be correct in many countries is the meaning of this śloka. Further, Bhāskara mentioned that the fame of victorious Âryabha a had crossed the boundaries of the oceans. Hence, the time difference between Âryabha a and Bhāskara should be so much (Kāle Mahati), which was required for the fame of Âryabha a to cross the Oceans to reach a lot of countries, at that ancient period. Further, Bhāskara told that Âryabha a’s astronomical data, though 65 calculated so much time before, leads to accurate results, even after the lapse of so much time, i.e. at the period of Bhâskara itself. This statement should be given its due importance. Therefore, the difference of period between Âryabha a and Bhāskara is not definitely just 23 years (522 – 499) or 130 years at the maximum (629 – 499), as per the date 476 C.E. ‘Sûrya Siddhānta:’ with the commentary of M.M.Sudhākara Dvivedī,62 mentioned that the word ‘alpha’ (a very little) meant 130 years (details explained latter 62) and it is highly paradoxical to interpret the very same 130 years from the words ‘Kāle Mahati’ whose meaning is excessive, huge, abundant, vast in time. Kāle Mahati denotes a very ancient period and not at all a recent past of just 130 years of ‘alpha’ (a very little) period. It must be more than thousands of years, as Bhâskara used the superlative degree in this śloka i.e. so much long time – Kāle Mahati. Thus, this 2nd śloka of Laghu Bhāskarîyam completely contradicts the date 476 C.E. 66
9. THE EPOCH USED IN ÂRYABHA ĪYAM Âryabha a calculated the number of years elapsed up to the beginning of the present 28th Kaliyuga of the present Vaivasvata (7th) Manvantara.* In the 5th śloka of 1st Adhyāya (Gītikapāda ) of Âryabha īyam, he mentioned as, 14 kaha e mnva e F mnyu gau > Zo gtaSt e c mn u ygau > Una c , kLpadye gpadaRu g c géidvsaCcu -artat ! pvU mR ! . Kāho Manavo ha Manuyugā Śkha Gatāste Ca Manu Yugā Chnā ca * Kalpāderyugapādā Ga ca Gurudivasācca Bhāratāt Pūrvam ** Here, he calculated the number of years elapsed from the beginning of the present ŚrīŚvetavarāha Kalpa (6 [Ca] Manvantra, 27 [Chnā] Yuga and 3 [Ga] Yugapāda {Satya, Tretā and Dvāpara} of the present 28th Yuga of the present Vaivasvata {7th} Manvantara) up to the Period of Mahābhārata war only, leaving Kaliyuga. Further, when mentioning the year of composition of Âryabha īyam and his birth in 3- 10th śloka, he used the beginning of the present Kaliyuga, as the epoch.1 If he had lived a few thousands of years after the beginning of Kaliyuga, he would have used some other epoch like Śaka era (King Cyrus era – 550 B.C.E.), Śrî Har a era (457 B.C.E.), Vikramāditya era (57 B.C.E.) or Śālivāhana era (78 C.E.) as done by latter astronomers of Bhārat. The same was expressed by Henry Thomas Colebrooke, in the page xliii of his book ‘Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and 67
Bháscara’ published in London in the year 1817. He wrote in his notes and illustrations under the heading ‘Age of ÁRYABHA A’ as (given verbatim),17 “It is to be observed, that he [Âryabha a] does not use the Śaca or Sambat of Vicramáditya nor the Śaca era of Śáliváhana: but exclusively employs the epoch of the war of the Bhárata, which is the era of Yudhist’hira and the same with the commencement of Cali Yuga. Hence it is to be argued, that he flourished before this era was superseded by the introduction of the modern ephochas.” Thus, the epoch used by Âryabha a creates much paradox with the date 476 C.E. Bhāskara in his MahāBhāskarîyam used the starting year of Śālivāhana Śaka, i.e. 3179 Kaliyugāptam (78 C.E.) as his epoch, as found in the 4th śloka of the 1st adhyāya .53 However, when he started describing the planetary procedure of the Âryabha īyam (Âśmakîya, Âśmaka - Tantra and Âśmakîya -Sāstra), in the 21st to 29thśloka of the 1st adhyāya , Bhāskara used Kali era only as the epoch, as used by Âryabha a, in Âryabha īyam. 54
Henry Thomas Colebrooke, in his book ‘Algebra with Arithmetic and Mensuration from the Sanskrit of Brahmegupta and Bháscara,’17 (published in London, 1817 C.E.) mentioned the name as ÁRYABHA A only (with double ) in all the places (pages xli to xliv) and not at all as ARYABHATA with single T. In the same way, W.Brennand in his book “Hindu Astronomy” published by Chas. Straker & Sons Ltd., London in 1896, wrote it 68
as Âryabha a with double ‘ ’ only, in all the places (pages xi, 137 to 139).55 In his name “Âryabha a,” the word ‘Ârya’ means honourable and esteemed person and ‘Bha a’ denotes a learned man and a philosopher. Pañca Siddhāntikā of Varhamihira, the Text edited with Sanskrit commentary and English translation by G.Thibaut and M.M.Sudhakara Dvivedi, (Chowkhamba Sanskrit Series Office Varanasi, 1968 {1889}) in the page 45 at the 20th sloka of 15th Adhyāya (Jyauti opani ad), mentioned his name as Âryabha a in the left hand column text.56 But, the text given in the in the right hand column mentioned it as Âryabha a.56 On this discrepancy, G.Thibaut mentioned clearly in his preface to this book, written on 15th December 1888, “The right hand columns of the text, give the ‘emended’ text; the left hand columns, the text of the better one of our two Manuscripts, which we thought advisable to exhibit in extenso.” 56 Scanned copies of these pages are given at the end of this book. Thus, the manuscript mentioned the name as Âryabha a only, but it was altered as Âryabha a. Thus, it was misspelt as Âryabha a, where ‘Bha a’ means a mercenary, a hired soldier, warrior, servant, slave, uncivilized person or demon. Obviously one can say, it is totally irrelevant and wrong, to what was read about Âryabha a, as a great astronomer and mathematician and not as a mercenary or the rest. 69
10. INTERNAL EVIDENCE FROM ÂRYABHA ĪYAM In the 3rd śloka of 1st adhyāya (Gîtika Pāda ) of Âryabha īyam, Âryabha a mentioned that in one Mahāyuga of 43,20,000 years, the Earth rotates itself on its own axis 158,22,37,500 times and the moon revolves round 5,77,53,336 times.57 So, Âryabha a mentioned that 158,22,37,500 rotations of the Earth are equal to 5,77,53,336 lunar orbits, in terms of time. So the number of rotations of the Earth per Lunar orbit is 27.39646936 (158,22,37,500 ÷ 5,77,53,336), at Âryabha a’s period. According to the Astronomical formulas and constants (www.jqjacobs.net/astro/ aryabhata.html)58,59 that the value of this ratio at 2000 C.E. is 27.39646289, for 500 C.E., it is 27.39646514 and for 1604 B.C.E., it is 27.39646936. 2000 C.E. - 27.39646289 1604 B.C.E. - 27.39646936 500 C.E. - 27.39646514 Âryabha a’s Value -27.39646936 We can find that this value reduces, on the advancement of time and Âryabha a’s value differs much from that of 500 C.E. This disproves 476 C.E. as the date of Âryabha a. Besides, the number of days per lunar orbit, according to Âryabha īyam is 27.32166848. [(158,22,37,500 – 43,20,000 = ) 157,79,17,500 ÷ 57,753,336].57 This value for 2000 C.E. is 27.32166080, for 500 C.E., it is 27. 32166380 and for 1604 B.C.E., it is 27.32166801. 58,59 70
2000 C.E. - 27.32166080 1604 B.C.E. - 27.32166801 500 C.E. - 27.32166380 Âryabha a’s Value -27.32166848 Here also the value decreases, as the time advances and Âryabha a’s value denotes a period, prior to 1604 B.C.E., rather than that of 500 C.E. This completely contradicts 476 C.E. The Date 2764 B.C.E. Now we have to analyse the date 2764 B.C.E. It should be congruous, complementary and harmony with the other historical and chronological dates and events. It also should not create any paradox and controversies. 71
11. SÛRYA SIDDHÂNTA: In the 20th śloka of 15th adhyāya (Jyauti opani ad) of Pañca Siddhāntikā, Varāhamihira mentioned 3 that Âryabha a maintained that the beginning of the day is to be reckoned from midnight at Lańka and he again said that the day begins from the Sunrise at Lańka. The Âryabha a’s method of reckoning of days from midnight at Lańka is mentioned by Bhāskara, in his Mahābhāskarîyam (Mahāryabha a Karma Nibandha:),60 in the śloka 21st to 35th of the 7th adhyāya which deals with astronomical constants. These astronomical constants of this midnight day-reckoning are exactly similar to that of Sûrya Siddhânta:, as given in Varāhamihira’s Pañca Siddhāntikā in the 16th adhyāya 61 (Sûrya Siddhānte Madhyagati ), dealing with the mean motions of Graha. Here, Sûrya Siddhānta: adopted the midnight day-reckoning, as mentioned in the 1st śloka of this 16th adhyāya .61 Thus, because of these common features between these two texts, the view that the text of Âryabha a with midnight day- reckoning was based on Sûrya Siddhānta: was enhanced further. Thus, if the date of Âryabha a is 2764 B.C.E., then the date of Sûrya Siddhānta: must be prior to this period. The date of Sûrya Siddhānta: was clearly mentioned in the 2nd, 23rd, 46th, 47th and 57th śloka of the Madhyamādhikāra (1st adhyāya ).62 The 2nd śloka is, +Lpaviz:q e t u kt& e mya e nam mhasru >, rhSy < prm < puhy< ij}asu}aRnmuTtmm! .2. 72
Alpāvaśi e tu K te Mayo nāma Mahāsura , Rahasyam Paramam Pu yam Jijñāsur Jñānam Uttamam. 2. Meaning is “When, but (tu) a little (alpa) of the K ta yuga (K te) was remaining (avaśi e), the great Asura named Maya was desirous of knowing (Jijñāsu ) the pure, sacred, holy and exalted secret science (Astronomy)”. Thus, it is very clear that the period of this śloka and hence that of Sûrya Siddhânta: is at the end of K ta yuga i.e. before Dvāpara and Tretā yuga and 5115 years of Kaliyuga, till date. Hence, this does not contradict the date of Âryabha a at 2764 B.C.E. (337 Kaliyuga). As per Ka apayavargabhavairihetyādinā method, as found in the book ‘Sûrya Siddhānta:’ with the commentary of M.M.Sudhākara Dvivedī, edited by Dr. Śrī K a Candra Dvivedī, in page 2, alpa means 130 years (+ - 0, l -3, p – 1, hence, 130), i.e. just 130 years before the end of K ta Yuga. 62 The date of Sûrya Siddhânta:, at the end of K ta yuga, is further confirmed by the following 23rd śloka of Madhyamādhikāra (1st adhyāya ).63 +:qaiv
Yugānām trighanam yātam tathā K tayugam tvidam , Projjhya S estata Kālam pūrvoktam Divya sańkhyayā. The meaning is that the 27 (Mahā)yuga were elapsed and likewise K ta yuga was also elapsed and this śloka did not mention anything about the next forthcoming Tretā yuga itself. Thus, the date of Sûrya Siddhânta: was at the end of K ta yuga only. In the 47th śloka of 1st adhyāya , it was mentioned as, 42 syU RaBd sRÂóOyya }yae > tSyaNt& e gta +mI, ¬ > octku:k ymaÔ iGn zr rNØ inzakra .47. Sūryābda sańkhyayā Jñeyā K tasyānte gatā amī , Khacatu ka Yamādryagni Śara Randhra Niśākarā . 47. 74
The meaning is, “At the end of the K ta yuga (K tasyānte), the number of Solar years (Sūryābda sańkhyayā) that were elapsed (gatā) are 195,37,20,000.” (Khacatu ka -0000, Kha - 0, catu ka -4, Yama -2, Adri -7, Agni -3, Śara – 5, Randhra – 9, Niśākara - 1). Thus, this śloka also stopped counting the years from the beginning of the present Kalpa up to the end of K ta yuga only. This shows assertively that the period of Sûrya Siddhânta: was at the end of K ta yuga only. In the 57th śloka of 1st adhyāya , it was stated clearly as, 42 +iSmn ! kty& gSyaNtu e sv eR mXygta ¢ha>, ivna tu patmNdaeCcan! me;adaE tuLytaimta> . 57. Asmin K tayugasyānte sarve madhyagatā Grahā , Vinā tu Pātamandoccān Me ādau tulyatāmitā . 57 . This śloka clearly and assertively shows the time of Sûrya Siddhānta: was at the end of K ta yuga. The meaning is, “At th the end of this (Asmin – 7 case of ‘ #dm ! – this’) K ta yuga (Asmin K tayugasya ante, K tayugasya – of this K tayuga, ante – ‘end’ in 7th locative case) all Graha, by their mean motion, except their nodes (Pāta) and apsides (Mandocca), are equally at the beginning of Me a Rāśi (Me ādau)”. Here the word this (as well as in the 23rd śloka), shows that the date of Sûrya Siddhānta: is at the end of K ta yuga, i.e. well before Tretā and Dvāpara and Kaliyuga beginning. Thus, it is neither paradoxical nor contradictory to the date of Âryabha a at 2764 B.C.E. On the other hand, it is in full congruence to this date. 75
12. VEDÂŃGA JYOTI AM 1. First of all, Âryabha a did not mention in his texts anything about Vedāńga Jyoti am and its methods. Because of the method of description of the time calculations, calendar, Lunisolar year and a few astronomical calculations by Vedāńga Jyoti am, we think that it must be older than Âryabha īyam and other texts of Âryabha a. However, there is no direct link between Vedāńga Jyoti am and Âryabha īyam. Neither text mentions the other. 2. Date of Vedāńga Jyoti am is calculated based on the verses 5th and 6th of g Vedapā ha and 6th and 7th verses of Yajur Vedapā ha .65 Accordingly, it is interpreted that at the time of this text, the winter solstice was at the beginning of the asterism* Śravi hā (Dhani hā) and that of summer solstice was at the midpoint of the asterism Âśle ā. Thus, the date of this text of Sage Lagadha is said to be 1370 B.C.E. as per the rate of precession of equinox* of 1° angle in 72 years approximately.65 However, the rate of precession have been mentioned differently in various ancient astronomical texts of Bhārat. In fact, some texts mention it as oscillation and not as precession, which will be dealt later. Hence, this date is based on the rate of modern estimation and we cannot say this was the same at ancient period. Further, there are different opinions on the interpretation of these verses also. For example, in the book “Vedic Astronomy” detailing Vedāńga Jyoti am, Prof. Prabhakar Vyankatesh Holay of Nagpur, wrote in the pages 78 to 82 in the chapter 17, 76 mentioned the date as 2884 (2976) B.C.E. for g Vedapā ha and that of Yajur Vedapā ha . as 2260 (2352) B.C.E.66 Thus, the date of Vedāńga Jyoti am has to be analysed properly, so as to derive the correct date. 3. Further, Prof P.V.Holay mentioned in the page 81 of this book, “Some authors of the g text must have changed the versions in RV5 and RV6 to suite the astronomical positions suitable to their time.” 67 This is further emphasized by two facts. 1. The author of the g text mentioned in the verses 2 & 3, “After worshiping Time and Saraswati, I explain the Great Soul Lagadha’s knowledge of time (àhÉMy izrsa kalmi-va* srSvtIm!, kal}an< àvIyaim lgxSy mhaTmn>. verse 2).68 2. I explain the astronomy and the movements of graha as it are known to earlier times and to the priests for performing 68 sacrifices” (verse 3). Lagadhasya Mahātmana (lgxSy mhaTmn>) means ‘of the great Soul Lagadha’ (Mahātmana is sixth genitive case of Mahātman, which means the Great Soul, exceedingly wise, noble, eminent, illustrious). Sage Lagadha could not have praised himself like this, as a great soul etc. Thus, Sage Lagadha was mentioned here as a great soul by some other author with great reverence and respect. Here the prose reading is, mhaTmn> lgxSy kal}an < àvIyaim, which means that I explain ( àvIyaim, the letter im denotes the first person singular), the great soul Lagadha’s knowledge of time. Hence, the author of this text was some one else other than Sage Lagadha. Thus, the time shown in the verses 5 and 6 of g Vedapā ha is the time of this unknown author and not the 77 time of Sage Lagadha. However, the knowledge described in this text was present much earlier to the period of this author i.e. during the period of Sage Lagadha and even prior to him. Since the author received this knowledge either from the writings or from the traditional teachings of Sage Lagadha, he acknowledged Sage Lagadha with much gratitude. This unknown author would have altered the astronomical events as per his observation of celestial movements during his time, taking only the knowledge from Lagadha’s teachings. 4. Sûrya Siddhānta: in the 9th and 10th śloka of the 3rd adhyāya (Tripraśnādhikāra ) mentioned that the equinox oscillates* between 3° Mīna to 27° Me a i.e. on either side of 0° (Mīna and Me a junction), 27° forwards in Me a and 27° backwards in Mīna. The śloka are, 69 iÇzt< ! kTya& e ygu e -ana < c³ < àak ! pirlMbt e , td! ghÉu aÑidnU -E KtadR ! *gu hÉa*dvaPyt e . 9 . tÎaiSǸnae dzaPtaza< iv}yae +ynai-xa> , tTs śabda of Strīlińga , here it is ‘K tya ’, #Tya;R àyaegae }eyae va UNdae-¼-yat! ‘k&ty>’ #TySy Swane ‘k&Ty>’ #it k&tm! refer page 78 of the book “Sûrya Siddhānta:” with the commentary by Sudhakara Dvivedi, from Sampurnananda Sanskrit University, Varanasi),70 3. Yuge – in one Yuga of 43,20,000 years, 4. Bhānām - of twenty seven (Bha - number 27, Masculine, th 6 case), 5. Cakram – Circle, -ana< c³< - of -c³< which means -a – Earth days) in a yuga, 11. Bhaktād – in division, 5th case, 12. Dyuga ād – the number of days so for passed in the yuga, 13. Yad – which, 14. Avāpyate – obtainable, 14. Taddos (Tad + dos - part of an arc defining its sine) – That part of an arc defining its sine i.e. Rsine, 15. Trighnā - multiplied (ghnā) by three (tri), 16. Daśāptāmśā - Daśa -Ten, Amśa – part (divided), {360° x [3÷10] =108°, per each oscillation – explained latter} Âpta – obtained, 17. Vijñeyā - To be perceived or known, 18. Ayana - Oscillation of Equinox, 19. Abhidhā - Name or appellation. Thus, the meaning is, in an Yuga of 43,20,000 years, the ayana oscillates 600 times up to 27 degrees in eastward as well as westward movement (from 0 degree ayanama i.e. the junction of Me a and Mīna Rāśi). This 600 is multiplied by the number of days passed so for in this yuga and divided by the total number of days of the yuga, gives the total number of oscillations happened so far from the beginning of the yuga. The whole number will show the completed oscillations and the fraction shows the present progressing oscillation from 0 degree. Multiply the Rsine (of incomplete oscillations expressed in degrees, minute and seconds) with three and divide it by ten, to obtain the degrees of Ayana. From the longitude of the Graha (¢hat!) as corrected by this (tTs S)qu < ok ! tLytau < gCUedyne iv;uvd! Öye , àak! c³< cilt< hIne UayakatR ! krhÉagte . 11 . +Ntraz< rwavE Ty& pZcaCUe;EStwa=ixke , 12, Sphu am d k tulyatām gacchedayane Vi uvad Dvaye, Prāk Cakram calitam hīne chāyārkāt kara āgate. 11. Antarāmśairathāv tya Paścācche aistathā=dhike , 12, The meaning is that the ayana calanam (at the two equinoxes iv;uvd! Öye Vi uvat – equinox, Dvaye – two,Vernal and Autumnal equinoxes), as calculated, is in motion from the beginning of Me a of 0° and Tulā Rāśi of 180° respectively. The ayana calanam is eastward (àak! c³< Prāk Cakram) when the longitude of the Sun (+kR Arka – the Sun) calculated is less ( hIne hīne) than that derived from the shadow ( Uaya chāyā - the shadow). When it is more (+ixke adhike), then it is on westward motion (pZcat! Paścāt). The last line of the 11th śloka and the first line of the 12th śloka further emphasises that the eastward motion of the Ayana mentioned in the first line of the 9th śloka includes the westward motion also, by Upalak a am, which is explained clearly before. Thus these 9,10,11 and 12th śloka of 3rd adhyāya (Tripraśnādhikāra ) of Sûrya Siddhānta: mentioned that the vernal and autumnal equinoxes* are moving in oscillatory pattern by 27 degrees from the fixed points of the beginning of Me a of 0° and Tulā Rāśi of 180° respectively. The word +av&Ty āv tya (+av&iTt> āv tti ) in the first line of the 81 12th śloka of 3rd adhyāya has the meaning of ‘turning towards, return, coming back, reversion, recurrence to the same point or place, repetition’. Thus, this clearly shows that there is only oscillation of equinoxes and not precession, as per Sûrya Siddhānta:. Thus the vernal equinox moves in oscillatory pattern from the beginning of Me a of 0°, first eastward up to 27° in Me a Rāśi* i.e. +27° and then it turns back westward by 27° again to reach 0° Me a i.e.–27°. Then it again proceeds westward by 27° to reach 3° Mīna Rāśi i.e. again –27°. After this it again turns back eastward and moves by 27° to reach 0° Me a i.e. +27°. Thus, a total of 108° (27° X 4) {360° x [3÷10] =108°, 9 &10 śloka} makes one full oscillation. In a yuga of 43,20,000 years this ayana calana completes 600 oscillations i.e. 600 X 108° (600 X 108 X 60 X 60"). Thus in one year, the ayana calana is 600 X 108 X 60 X 60" ÷ 43,20,000 that is 54". The modern estimation is 50.29". Thus, for one full oscillation it takes 7200 years (43,20,000 ÷ 600). Accordingly, in 2013 C.E. (Kaliyuga 5114 elapsed), the vernal equinox is at –22° 42' 36" (westward) i.e. 07° 17' 24" of Mīna Rāśi. (Total years of this Mahāyuga are 43,20,000 and the number of years passed up to 2013 C.E. are 17,28,000 of Satya (K ta) Yuga, +12,96,000 of Tretā, +8,64,000 of Dvāpara, +5114 years of Kaliyuga = 38,93,114. In 43,20,000 years, there are 600 complete oscillations. Hence, in 38,93,114 years, the total 82 oscillations will be 540.71027778, i.e. 540 completed oscillations +0.71027778 progressing oscillation. 108° is the full oscillation. Hence, 0.71027778 X 108 =76.71° is the present oscillation and this will be after +27° and –27° i.e. 1st and 2nd quarter (after 54°). Hence, it is in the 3rd quarter (so, westward) in Mīna Rāśi at 76.71°– 54°=22.71°=22° 42' 36" i.e. 07°17'24" of Mīna Rāśi). The modern calculation is –24°02’45" (precession i.e. westward) hence 05°57’15" of Mīna Rāśi (on 1st April 2013, Lahiri’s Indian Ephemeris). Thus, there is not much difference except of 1° 20' 09" which will be covered within about 96 years (at the rate of 50.29" per year) and considering 43,20,000 years, this is very minute and can be due to the altered fixation of the time of 0° Ayana, in the modern days. Hence, this method fits well with modern derivation. The date of the Vedāńga Jyoti am is calculated based on the statement that winter solstice* was at the beginning of the asterism* Śravi hā (Dhani hā) i.e. 293° 20' nirāyana and that of summer solstice was at the midpoint of the asterism Âśle ā i.e. 113° 20' nirāyana. Thus, the vernal and autumnal equinoxes was at 23° 20' and 203° 20' respectively (90° less than respective solstice) i.e. +23° 20' eastward from 0° Me a (0° Aśvinī) and 180° Tulā Rāśi (6°40' of Citrā). In the year 2013 C.E., they are at 335° 57' 15" and 155° 57' 15" (–24°02’45" westward on 1st April 2013, Lahiri’s Indian Ephemeris). If this oscillation of 83 ayana in eastward and westward as stated by Sûrya Siddhānta: is applied here, then the total oscillation is 23°20' + 24°2’45" = 47° 22' 45". For 54" of oscillation, it requires one year. Thus, for 47° 22' 45" of oscillation the total years reqiured is 3158.61 (47° 22' 45" ÷ 54"= 3158.61). Then the date will be either 3159 years or 10,359 years (3159+7200 of one oscillation) before 2013 C.E. i.e. either at 1146 B.C.E. (3159 – 2013) or 8346 B.C.E. (1146 + 7200) [23°20' + 24°2'45" = 47° 22' 45" ÷ 54"= 3158.61 years ≈ 3159 years]. The new findings in under water archeology at Bet Dwarka and excavations at Lothal, Nausharo, Mehrgarh (Mehrgarh I is at 7500 to 5500 B.C.E.), Dholavira, Kunal and Kalibangan sites of Saraswati Sindhu civilisation show that their dates are more than 5000 years old. Based on the calculations, scientists and marine archeologists pegged the age of the wall, whose base is about three meters below the present sea level, at Valneshwar Konkan, from Shrivardhan in Raigad to Vengurla in Sindhudurg of Konkan coastal area of Bhārat, at around 6,000 BC. Thus, the date 8346 B.C.E. cannot be set aside as impractical and not sensible. Besides, this occurrence of winter and summer solstice at a particular ecliptic star is a repeatable event, repeating once in 7200 years in oscillation of equinox. Thus, the date of Vedāńga Jyoti am will not contraindicate the date of Âryabha a at 2764 B.C.E. 84 5. Âryabha īyam and Vedāńga Jyoti am are different types of texts with different approach, purpose and description. Thus, the date of one text cannot fix the other text’s date. 6. Science and development are always not parallel. Vice versa also can happen in history. There are many historical evidences. Europe during the period of Greek, was with certain level of development in Mathematics and Science. Nevertheless, during the period of 500 C.E. to 1500 C.E., it went into dark ages. If we assume that science and development always go parallel with time, then the period of Greek would be more modern than the dark age of Europe i.e. after 500 C.E. to 1500 C.E., but this is not the fact. Therefore, there is no contradiction and no paradox exists between the dates of Âryabha īyam and Vedāńga Jyoti am. 85 13. SANSKRIT GRAMMAR In grammatical and syntactical analysis, the word denoting action in the first sentence of 3-10th śloka of Âryabha īyam, is “Vyatītā (VytIta>)”. It has K idanta “Ni hā ” affix “ta” (Past Passive Participle suffix) and it holds the key. It is a ‘Past Passive Participle’ word denoting past tense and shows that the sentence is in passive voice. The word Vyatīta is Vi + Ati + E + Ta ( iv ++it + # { #hÉ } + t ). Vi + Ati ( iv + +it ) = Vyati ( Vyit - Ya Sandhi ), Vyati + E [ #(hÉÂ)] = Vyatī ( VytI - Dīrga Sandhi ), Vyatī + Ta ( t ) = Vyatīta (VytIt). The Plural, Masculine word of ‘Vyatīta’ in the first (nominative) case is “Vyatītā ” ( VytIta> - like Rāma Sabda ). “Vi ( iv )” is Indeclinable Preposition - Prādaya - Avyaya - Upasarga .73 “Ati” is another Upasarga , with the meaning ‘Over, Beyond, Overstep, exceedingly, excessively’74 In Sanskrit Language, more than one Upasarga can join a single verb. “E” [ #(hÉÂ)] is the transitive verb ( skmRk ) with the meaning of pass, go, approach, escape, reach, retire and appear. 75 The exact meaning will depend on the Upasarga joined with it and the nature of the sentence. “Ta ( t )” is the affix at the end and is the most important one. “Ta” is K idanta ( k&dNt>) suffix of “Ni hā ” ( in:Qa>) type. There are two suffixes in Ni hā type. They 76 are “Ta ( t )” and “Tavat ( tviÉ )”. Pā ini* denotes them as “kta” and “ktavatû” as both will not undergo Gu a and V ddhi changes. ( KtKtvt U in:Qa Pā ini 1-1-26). Both denote Past 77 Tense ( in:Qa { -tU e } Pā ini 3-2-102). But, Ta ( t ) denotes 86 object (Karman – kmnR ! ) on whom or on which the action was done or in the intransitive sentences, the action (Bhāva - -av ), as per Pā ini’s A ādhyāyī 3 – 4 - 69 and 70 Sûtra and hence is Karma Ni hā . Hence, the sentence will be in Passive Voice. Tavat ( tviÉÂ) denotes the agent (Kart - kt& R ) who or which did the action and hence is Kart Ni hā . Hence, the sentence will be in Active Voice. These are shown by Pā ini’s A ādhyāyī* 3 – 4 - 69 and 70 Sûtra as follows78. l> kmiR hÉ c -av e cakmkR _ye > 3-4-69 La karma i ca bhāve ca akarmakebhya tyare ve kTyKtolw& aR > 3-4-70 Tayoreva [Tayo Eva] k tya kta khalarthā Thus, the Ten Lakārā (Lat, Lit, Lut to L t) denotes the object (karma ī) or the agent (Kart – as denoted by “ca”) in Transitive Sentences and in Intransitive Sentences (Akarmaka), the action (Bhāva) or the Agent (as denoted by “ca”) [3-4-69]; But, in the sentences with k tya ( kTy& ) and kta ( Kt - t ) affixes and with words meaning khal ( ol ! ), denote only (Eva) the object or action (Tayo - Of those two) [3-4-70]. Thus, they will not denote agent. Hence, these sentences will be in Passive voice only and not in Active voice. Thus, “Ta (Kta)” is Past Passive Participle suffix. Since, this sentence is in passive voice, the “ta” suffixed word denoting action, should agree in number, gender and case with the object (Karma i) only and not with the agent (Kart ). Besides, the object will be in first (Nominative) case and the agent who did the action, will be in third (Instrumental) case. 87 There are four exceptions to this, where the sentence will be either in passive or in active voice. They were mentioned by Pā ini’s A ādhyāyī in 3-4-71 and 72 Sûtra.79 Accordingly, when it denotes, 1. The beginning of an action (+aidkmiR hÉ Kt> ktirR c Pā ini 3-4-71), 2. With the words meaning motion (Gatyartha - gTywR = git motion + +wR meaning). The Siddhānta Kaumudī, Jnanendra Saraswati and Jayak ish a at page142, as an explanation to Pâ ini 2-3-12 80 Sûtra, mentioned as ¢am < ¢amay va gCcit , c:qayae < ikm,! mnsa hir < ìjit , c:qayae < ikimit - xaTvwSyR i³yaêpTvaTàZn>, zrIr i³yaya @v ¢hhÉimTyÄrmu ! ,Śarīra kriyāyā eva, Thus, the word Gatyartha denotes the bodily motion only ( zrIr i³yaya @v Śarīra – bodily, kriya – activity - bodily action - motion, eva – alone – only, c:qae Ce ā – motion, movement). A ādhyāyī of Pā ini by Śrīśa Chandra Vasu, (Pâ ini 2-3-12 Sûtra Volume 1 page 281, Motilal Banarsidass),81 & The Siddhanta Kaumidi by Śrīśa Chandra Vasu, Volume 1, No. 585, page 355, (Motilal Banarsidass) 82 explained this word Gatyartha, with the following examples as ¢am< or ¢amay gCcit (he goes to village) is Gatyartha but mnsa hir < ìjit (he goes mentally to Hari) is not Gatyartha . Thus, Gatyartha denotes only physical motion. 3. In intransitive sentences (+kmRk) and 4. When joined with verbs Śli (to embrace), Śī (to lie down), Sthâ (to stand), Âs (to sit), Vas (to dwell), Jan (to produce), Ruh (to mount) and J i (to grow old) [2, 3 and 4 - the Pâ ini 3-4-72], the “Ta” suffix denotes either the agent or object (as denoted by ca (c) in both these 3-4-71 and 72 Sûtra). Thus, only in these four exceptions, the sentence with “Ta” suffixed word denotes either the agent 88 or the object. In all the other, it will denote object or action only and thus, the sentence will only be in passive voice. Besides, in all these four exceptions also, the sentence with “Ta” suffix can be in passive voice, denoting object or action. In this 3-10th śloka, the word “Vyatītā ” with “Ta” suffix, 1. Does not denote the beginning of an action, 2. The word “Vyatītā ” [with two Upasarga , Vi (iv) & Ati (+it) and the past passive participle suffix “ta ( t )”, joined with the verb “E - # - # ( hÉ )”], has the meaning “ has been elapsed, abandoned, departed, disregarded, left and passed by” 83 and not at all motion or moving physically. In this sentence, it shows number of years that were elapsed beyond the three yuga. Thus, the sentence itself is concerned with the time and not at all physical motion. The authentic detail given above for the word “Gatyartha ( gTyw R )” completely ruled out the Gatyartha exception in this sentence. Besides, 84 the word Gati ( git ) means motion in general and not elapsing of time. 3. The verb “E - # - # ( hÉ )” is transitive 75 (skmRk ) and hence the word VytIta> is also transitive. Besides, this sentence has the object Yugapādā (ªÉÖMÉ{ÉÉnÉ:) and hence it is a transitive sentence. The word ‘elapsed’ is transitive as it shows that something was elapsed by some other thing and 4. The fore mentioned verbs, “Śli ” etc., are not there in this sentence of 3-10th śloka. Hence, these four exceptions cannot be applied to this sentence. Hence, this sentence of 3-10th śloka is in passive voice only and not in active voice. 89 Pā ini’s A dhyāyī 3-2-187 and 3-2-188 Sûtra85 mentioned that “Ta ( iÉ )” suffix denotes present tense, 1. In sentences with verbal roots ñi ( i|, 3-2-187) and 2. With the verbal roots meaning Inclination, Understanding and Respect (3-2-188). But this sentence of 3-10th śloka, do not have these verbal roots and hence it denotes past tense only. Past Passive Voice Thus, the word “Vyatītā ” ( VytIta>) with the “Ta ( iÉ )” suffix, in this sentence of 3-10th śloka of Âryabha īyam, denotes that the sentence is in passive voice and is in past tense. Since it is in passive voice, the word denoting action should be in accordance, in Number, Gender and Case, only with the object, on which the action was done and not with the agent and the agent should be in third (Instrumental) Case. Besides, the numbers 1, 2, 3 and 4, should be in accordance with the noun to which they are applied, in Number, Case and Gender. (Numbers from 5 to 19, in number and case and numbers after 19, in case only, to the noun they are applied). th Thus, in this sentence of 3-10 Śloka, Traya ( Çy> = 3) which is of First [Nominative] case, Masculine and Plural, shows that the noun to which they are applied i.e. the object Yugapādā (ªÉÖMÉ{ÉÉnÉ:) is in Plural, Masculine and Nominative Case. Hence, the word denoting action (with K idanta kdNt& > - Ni hā in:Qa> suffix “Ta” ) “Vyatītā ” should also be in Plural, Masculine Gender and in First (Nominative) Case in accordance with the object Yugapādā . Exactly, “Vyatītā ” is 90 in Plural, Masculine Gender and in First (Nominative) Case (like Rāma Śabda ). Besides, the agent (Kart - kt& R ) should be in Third (Instrumental) Case, as it is a passive voice sentence. Thus, the word a bhi , which is in third (Instrumental) case, is correct and the word a i , in first (Nominative) case is not correct, grammatically and syntactically. Thus, in the first sentence of 3-10th Śloka, 1. The word Trayaśca Yugapādā (all the three quarters of Yuga) is the object and is in plural, masculine and first case, 2. The word Vyatītā is the word denoting action and is in plural, masculine and first case, in accordance with the object and 3. a yabdānām a bhi (by sixes of sixty years) is the agent doing action and is in third instrumental case, as it is passive voice. Here, the following important things to be noted. 1. The meaning of the verbal noun, Vyatītā is “were elapsed83 excessively”, abandoned, left behind (“The Student’s Sanskrit English Dictionary,” Vaman Shivram Apte, Motilal Banarsidass Publishers, reprint 2000, page 537 & “A Sanskrit – English Dictionary,” Monier Williams, Oxford Clarendon Press, London, May 1872, page 937). 2. In the object Traya ca Yugapādā (all the three quarters of Yuga), the word “Trayaśca” denotes all the three quarters of Yuga. (Traya – Çy> = Three — Çy> + c = ÇyZc – visarga sandhi ). Here the word ca ( c ) was added to Traya , so as to denote all the three quarters of yuga. Thus, ca ( c ) was added here with that purpose 91 only and hence was written after Traya a only and not after Yugapādā . 3. In the agent, a yabdānām a bhi (by sixes of sixty years), the word “ a yabdānām” denotes, indicates and qualifies which “sixes” did the action of elapsing excessively. Thus, it is a Viśe a am ( ivze;hÉm! ) and “ a bhi ” is the Viśe yam ( ivze:ym! ). Here the Viśe a am is in the sixth (Genitive) case and it need not agree with Viśe yam, in case ( iv-iKt>). This is 86 a hīvibhaktyantam Vyadhikara a Viśe a am ( ;:QIiv- KTyNt< VyixkrhÉ ivz;e hÉm ! Pandit L.Anantarama Sastri, ‘Samskrita Vyakarana Pravesika,’ pages 75-76). This is like “Rûpyakā ām a bhi ” (rPykaU hÉa < ¹ÉbÂʦÉ:). Hence, in this first sentence of 3-10th śloka that a bhi is the agent and is in third case, as it is in passive voice and a yabdānām is simply the qualifying Viśe a am to highlight the Viśe yam of a bhi . This can be clarified by citing an example. In the sentence “Sītāyā Rāme a rak ita Dharma ( sItaya> ramhÉe riIÉt> xm>R ),” rak ita is the past passive participle denoting action, with Ni hā “Ta” affix and with the meaning “was protected.” Which was protected then? It is Dharma , which is the object and is in first case, as it is in passive voice. Who protected Dharma ? It is Rāma , who is the agent and is in third case (Rāme a), as it is passive voice. Which Rāma protected Dharma ? It is Sītā’s (Sītāyā ) Rāma . Thus, Sītā is in sixth (genitive) case. Sītāyā is the qualifying 92 word - Viśe a am ( ivz;e hÉm! ) and Rāme a is the qualified word -Viśe yam ( ivze:ym! ). Exactly like a yabdānām a bhi Vyatītā Traya ca Yugapādā (in plural, the example cited above is in singular). Besides, in Sanskrit, the numerals can come alone and denote meaning, substantively. For example, Siddhānta Kaumudī, on giving explanation to the Pā ini Sûtra 1-4-51, 87 gives examples like, dvtTte < zt< m:u hÉÉit where zt< (100) is in second case and gives full meaning. In 1-55th śloka of Sūrya Siddhānta , the number 12 is used as, “Öadz¹ grau yae taR -ghÉÉ vtRmankE>, raizi-> sihta> zuÏa> ;ò(a SyuivRjyady>.” (The departed revolutions of Jupiter ( grau yae taR -ghÉÉ ) is multiplied 88 nd by 12, [ Öadz 12, ¹ multiplied by]). In 2 - 22 śloka 89 Âryabha īyam, the number one is used as skE sgCU pdana< ³mat! ( s + @k = skE , the number of terms plus one, the same increased by the number of terms). Thus, in the first sentence of this 3-10th Śloka, the word Vyatītā (in plural, masculine and first case) is the word denoting action and has the meaning of “were elapsed 83 excessively.” What were elapsed excessively then? All the three quarters of Yuga (Trayaśca Yugapādā ) – the object and is in plural, masculine and first case. By whom or by which, they were elapsed excessively? It was by sixes of sixty years ( a yabdānām a bhi - the agent which did the action) and is in third (instrumental) case, as it is passive voice. Thus, the meaning is very simple and straight, “When, all the three quarters of Yuga were elapsed excessively, by sixes of sixty 93 years (360 years), twenty three years (23) were passed by, indeed at that time, since my birth.” Thus, the following 10th śloka of the Kālakriyāpāda (Third Adhyāya ) of Âryabha īyam with the word “ a bhi ” is correct, grammatically and syntactically. ¹É¹]ªɤnùÉxÉÉÆ ¹ÉbÂʦɪÉÇnÉ ´ªÉiÉÒiÉɺjɪɶSÉ ªÉÖMÉ{ÉÉnÉ: * jªÉÊvÉE É Ê´ÉƶÉÊiÉ®¤nùɺiÉnä´É ¨É¨É VÉx¨ÉxÉÉä%iÉÒiÉÉ: ** Accordingly, Âryabha a was 23 years old at Three Hundred and Sixty years (360) of Kaliyuga (3101 – 360 = 2741 B.C.E.) and consequently it favours 2764 B.C.E. as the date. Thus, the grammatical analysis of the word Vyatītā shows that (1). a i , as agent (Kart ) in this 3-10th Śloka of passive voice is syntactically wrong, as a i is in first nominative case and not in third instrumental case, which is discussed eloboraely so far. (2). Here, because of the word Vyatītā and the Ni hā “Ta” suffix, the sentence is in passive voice only. In spite of this, even if we consider a i as agent (Kart ) in active voice then also it is not correct as a i is in singular and the word Vyatītā , denoting action is in plural. In active voice, the agent and the verbal noun should agree in number, gender and case. Nevertheless, the sentence itself is in passive voice and not at all in active voice. (3). We cannot consider a i as object and Yugapādā as agent, because Yugapādā as agent, should be in third instrumental case, in passive voice or a i as object, should be in second accusative case in active voice. But both are in first 94 nominative case, (which is possible only if both are agents in active voice or if both are objects in passive voice, which is going to be discussed in the following paragraph). Hence, this is also ruled out. Besides, it cannot give proper meaning to the sentence. (4). Further, we can not take a i and Yugapādā in- combine as agent (Kart ) in active voice, as the sentence is definitely in passive voice, as discussed elaborately so for. Thus, it absolutely ruled out this possibility. (5). a i and Yugapādā in-combine as agent (Kart ) in passive voice is wrong, as a i and Yugapādā should be in third instrumental case, on the contrary both are in first nominative case. (6). If we analyse, considering both a i and Yugapādā as two separate objects, then also it is wrong grammatically. Pā ini’s A ādhyāyī, in the 1-4-51 sûtra +kiwt < c (akathitam ca), mentioned about the use of two objects in a sentence.90 Patanjali i’s Vyākara a Mahābhā ya* and Siddhānta Kaumudī,* the Sanskrit grammar texts, explained this sûtra and the 7-1-69 sûtra of Pā ini [ iv-a;a ichhÉmulae> - vibhā ā ci amulo ]. (1. Siddhānta Kaumudī, Jnanendra Saraswati and Jayak ish a91 - pages 129, 130, 445 & 446 and 2. The Siddhānta Kaumudī, Srīsa Candra Vasu 92 - Numbers 539 & 2765 {pages 329 to 331 of Volume 1 & 672 and 673 of Volume 2 Part 1} and 3. Patanjali i’s Vyākara a Mahābhā ya – text and commentary, Kaiya a Upādyāya & Nāgeśa Bha a,93 volume 2, pages 263 to 273 and volume 6 page 61). Accordingly, the 12 verbal roots Duh (to milk), Yāc (to beg), Pac (to cook), Da (to punish), Rudha (to obstruct or confine), Praccha (to ask), Ci (to 95 collect), Brû (to tell), Śās (to instruct), Ji (to win, as a praise of wager), Manth (to churn), Mu (to steal) and other 4 verbal roots Nī, H , K is, Vah (to carry or to convey) alone (total 16) have two separate objects in the same sentence. The secondary object is known as Gau a Karma i ( gahÉE kmiR hÉ ). Of the 16, in the 12 verbal roots starting from Duh, the primary object ( àxan kmiR hÉ Pradhāna Karma i) will be in second (Accusative) case and the secondary object (Gau a Karma i) will be in first case, in the passive voice. In the next 4 verbal roots starting from Nī, the primary is in first case and the secondary is in the second case, in passive voice. 1. Vyatītā is not of these 16 verbal roots. 2. a i and Yugapādā are both in nominative (first) case and none in accusative (second) case. Hence, a i is wrong either as an agent (Kart ) or as the object in passive voice. Besides, “ca ( c )” was added after Traya only and not after Yugapādā and or a i . Hence, it denotes all the three parts of Yuga and not the action of joining words. If it were to denote combination, then it would have been written after Yugapād and or a i . Further, Yugapādā is the object and Traya (3) just denotes how many parts of Yuga i.e. giving details of Yugapādā . Hence Traya is not the object, but it qualifies the object and “ca ( c )” is added here to further qualify Traya , stressing that all the three parts of Yuga were elapsed and thus definitely not to combine Yugapādā and a i . Thus, the word ca ( c ) was added only to denote all the three quarters of yuga. Further, the words a i and 96 Yugapādā are not consecutive and adjacent, as the word denoting action Vyatītā and yadā are in-between. [Ca ( c ) can be used in the sense of combination of joining words or assertions and the joined words are normally consecutive and should be either nouns or verbs alone and not mixed]. Thus, the use of a i is wrong syntactically and grammatically in this sentence of the 10th śloka of Kālakriyāpāda (Third Adhyāya ) of Âryabha īyam. Hence, this grammatical analysis of this 3-10th śloka contradicts the date 476 C.E. and favours 2764 B.C.E. only. 97 14. DATE OF MAHÂRYABHA A SIDDHÂNTA: Âryabha a himself mentioned it clearly that he had written Mahāryabha a Siddhānta: when the Kaliyuga had just progressed only a very little from its beginning. The 2nd śloka of the 2nd adhyāya (Pārāśaryamatāntarādhikāra ) of this text, mentioned it as, 94 BiÉÊiºÉrÉxiÉuªÉÆ <ǹÉtÉiÉä Eò±ÉÉèªÉÖMÉä VÉÉiɨÉ * º´ÉºlÉÉxÉä oE iÉÖ±ªÉÉ +xÉäxÉ JÉä]É: º¡Öò]É: EòɪÉÉÇ: ** Etat Siddhāntadvayam ē adyāte Kalauyuge jātam * Svasthāne d ktulyā anena khe ā sphu ā kāryā ** Meaning :- Etat – This (singular), Siddhāntadvayam - The Siddhānta in dvayam – in pair form (Mahāryabha a Siddhānta: contains one Pûrvārdha Rûpa known as Grahaga itādhyāya and the second one Uttarārdha Rûpa known as Golādhyāya ), ē at - a very little, slight, yāte - was elapsed, Kalauyuge - in Kaliyugam, jātam – was brought into existence. Thus, Âryabha a mentioned it clearly that his Mahāryabha a Siddhānta: which is in pair form (Pûrvārdha Rûpa – Grahaga itādhyāya and the Uttarārdha Rûpa – Golādhyāya ) was brought into existence (written), at the very early years of Kaliyuga. Further, in the 1st and 2nd śloka of this 2nd adhyāya ,95 Âryabha a clearly distinguished his Siddhānta: (established text, treatise) from Parāśara’s Matam (view, concept, 98 doctrine). He mentioned the text of Parāśara as Matam (Pārāśaryam Matam) and his text as Siddhānta: distinctively. So, Siddhāntadvayam mentioned in this 2nd śloka denotes only Mahāryabha a Siddhānta: which is in pair form. If it denoted both these texts, then it would have been mentioned as mtisXdaNtuªÉÆ (Mata and Siddhantadvayam) instead of isXdaNtuªÉÆ in the first line of this śloka. Even if it denotes both texts, then also it mean that both texts were written at the early years of Kaliyuga only. Besides, in the Madhyamādhyāya (1st adhyāya ), Âryabha a explained the calculation of Aharga a (number of days elapsed from a chosen epoch) 96 in the śloka 25, 35, 36, 48, and 51. He mentioned the calculation of aharga a from the beginning of the present Kalpa up to the beginning of the present Kaliyuga only. For aharga a of dyuga a, he used the words, Kalijayuta (25th śloka) Kalijakshepa (35th and 51st śloka) Kalimukha (36th śloka) and Kalivaktra (48th śloka), meaning the beginning of Kaliyuga. Here Âryabha a chose the beginning of the present ŚrīŚvetavārāha Kalpa as his epoch and calculated the number of years elapsed up to the beginning of the present 28th Kaliyuga of the present Vaivasvata (7th) Manvantara. This confirms that Âryabha a lived at the very early years of the Kaliyuga. If he had lived a few thousands of years after the beginning of Kaliyuga, he would have mentioned the number of years elapsed in Kaliyuga also and would have not stopped counting the years up to the beginning of the Kaliyuga. Further, he would have used some other epoch like Śaka era (King Cyrus era – 550 99 B.C.E.), Śrî Har a era (457 B.C.E.), Vikramāditya era (57 B.C.E.) or Śālivāhana era (78 C.E.) as done by latter astronomers of Bhārat. However, Âryabha a stopped calculating the number of years elapsed abruptly up to the beginning of Kaliyuga itself, as found in 19th śloka of Madhyamādhyāya (1st adhyāya ) of Mahāryabha a Siddhānta: The śloka is, 97 SÉÉ ¨ÉxɴɶUÉ ªÉÉiÉÉ: ºÉxvÉªÉ <½ ®lÉʨÉiÉÉÊxÉ SÉ ªÉÖMÉÉÊxÉ * MÉÉ ªÉÖMÉSÉ®hÉÉ BäCªÉÆ EÖòÊvÊlÉ®vÉÉä¦ÉÒPÉÖxÉÉäxÉÉäxÉÉ: ** Cā ManavasChā yātā sandhaya iha Rathamitāni ca yugāni * Gā yugacara ā aikyam kudhithiradhobhîghunononā ** Here Âryabha a mentioned the number of years elapsed since the beginning of the Kalpa, up to the beginning of the Kaliyuga i.e. the total years of six (Cā) manvantara, seven (Chā) manvantra sandhi, twenty seven (Ratha) Mahāyuga and three (Gā) parts of yuga namely K ta (Satya), Tretā and Dvāpara, in Katapayādi sañkhyā as, ku – 1, dhi – 9, thi – 7, ra – 2, dho – 9, bhî – 4, ghu – 4, no – 0, no – 0, nā – 0. Thus, kudhithiradhobhîghunononā: is 197,29,44,000. So, the number of years for, 6 manvantara (1 manvantara = 71 mahāyuga; 1 mahāyuga = 43,20,000 years) } = 6 × 71 × 43,20,000 = 184,03,20,000 100 7 manvantara sandhi (1 manvantara sandhi = 1 K tayuga) = 7 x 17,28,000 } = 1,20,96,000 27 mahāyuga 27 x 43,20,000 = 11,66,40,000 1 K tayuga = 17,28,000 1 Tretāyuga = 12,96,000 1 Dvāparayuga = 8,64,000 Total years from the beginning of the ŚrīSvetavārāha Kalpa up to the beginning of the present Kaliyuga = 197,29,44,000 This proves that Âryabha a mentioned the number of years elapsed up to the beginning of the Kaliyuga only. Besides, he also mentioned the number of days elapsed from the beginning of the Kalpa up to the beginning of this Kaliyuga only, in seventeeth śloka of second adhyâya (Pārāśaryamatāntarādhikāra ) in katapayādi sañkhyā98 as ºÉ®xÉSÉMÉPÉvɨɦɮEä vÉÉ E ±ªÉÉnÉè tÖMÉhÉ B¹É:* i.e. up to the beginning of the Kaliyuga (Eò±ªÉÉnÉ)è the total number of days (tÖMÉhÉ) are Saranacagaghadhamabharakedhā (sa – 7, ra – 2, na – 0, ca – 6, ga – 3, gha – 4, dha -9, ma –5, bha – 4, ra – 2, ke – 1, dhā – 9) = 72,063,49,54,219. Thus, the number of days per year as per Mahāryabha a Siddhānta: are 365.25869 (72,063,49,54,219 ÷ 197,29,44,000). This is in confirmation with the value got from the astronomical constants given in the 7th and 13th śloka of Madhyamādhyāya (1st adhyâya ) of Mahāryabha a Siddhānta:99 In the 7th śloka, 101 the total number of (apparent) revolutions of the Sun (the Earth) in one Kalpa, are mentioned as 432,00,00,000. This is the number of years in one Kalpa, because the Earth revolves round the Sun at the rate of one revolution per one year. In the 13th śloka, the total numbers of days in one Kalpa are given as 1,57,791,75,42,000. Then, the number of days in one year will be 365.25869 (1,57,791,75,42,000 ÷ 432,00,00,000). Thus, all these evidences strongly conclude that Âryabha a wrote Mahāryabha a Siddhānta: at the very early years of Kaliyuga. 102 The Hollow Argument In spite of the foreseen strong evidences favouring the date of Mahāryabha a Siddhānta: at the very early years of Kaliyuga, its date was unilaterally fixed at c950 C.E., on flimsy grounds. This was based on the mathematical formulas found in Mahāryabha a Siddhānta: and the other ancient mathematical texts of our Nation. The formula for calculating the area of a quadrilateral and the π values given in these Bhāratian ancient texts were given much importance in fixing their chronology. 1. ŚrīMahāvîrācārya,* the ancient mathematician of Bhārat, wrote a mathematical text, known as Ga itasārasañgraha:. His period was estimated as c 850 C.E., since he had wished prosperity to the Rā trakûta King Amoghavar a N patuńga,*100 whose period of reign was C.E. 814 – 878. In the 50th śloka of 7th adhyāya of this text,100 he mentioned the formula for calculating the area of a quadrilateral as [](s-a) (s-b) (s-c) (s-d) , where a,b,c,d are the sides of the quadrilateral and s = (a + b + c + d) ÷ 2. However, Srîdharācārya* in his Pā îga itam101 mentioned two formulas. In the117th śloka, he mentioned the above formula for quadrilaterals having either equal or unequal sides, but always with unequal altitudes. In 115th śloka he mentioned another formula for quadrilaterals of equal altitudes as ½ (base + face) X altitude. The 78th śloka in 103 the Pā yadhyāya (15th adhyāya ) of Mahāryabha a Siddhānta:102 mentioned this second formula but it stressed the importance of the diagonal in this 78th and the 70th śloka of same adhyāya . Based on this, it was concluded that Mahāvîrācārya who gave a rudimentary formula, must be earlier than the two. Then came Srîdharācārya, who gave a better formula and the Mahāryabha a Siddhānta: as the latest of all the three, because it stressed the importance of the diagonals of quadrilaterals. However, Mahāvîrācārya gave the second formula also, in the same 50 śloka of 7th adhyāya [not for inequi-lateral quadrilaterals].100 But, it was overlooked, totally paving the way to hasty decisions and thus Bharat’s antiquity was reduced miserably. Since the period of Mahāvîrācārya was fixed at c 850 C.E., it was told that the period of Srîdharācārya might be between C.E. 850 to 950. On what basis it was allotted 100 years for this, nobody explained. Is it only 100 years required to develop a formula? Why not more or even less? No answers. Then, it was told that the period of Mahāryabha a Siddhānta: must be latter to Srîdharācārya, since it stressed the importance of the diagonals103 and thus, it may be fixed at about c 950 C.E. So, all are assumptions and guess work only, since no author had quoted the other’s name or even the name of the text. Further, developing and using mathematical formulas depends on individual perception and knowledge. Therefore, a person of earlier period may 104 develop a correct formula, which may not be available to the persons of latter period, due to various reasons prevalent at that time or even available, the junior can have a different view. Further, we cannot say that the progress of science and technology always goes parallel with time and the vice versa can also happen in the history of science and technology. The same thing holds good for these above examples also. 2. Srîdharācārya103 mentioned the value of π (pi) as 10 (3.1622776). Mahāryabha a Siddhānta:104 in the 92nd śloka of the Pā yadhyāya (15th adhyāya ), gives the value of π as 22 ÷ 7 (3.142857143), which is nearer to modern value of π (3.141592653…) than that of Srîdharācārya. Therefore, it was maintained that Srîdharācārya’s Pā îga itam must be ancient to Mahāryabha a Siddhānta:. If we fix the chronology of the ancient texts in this way, then Âryabha îyam of Âryabha a would become the latest of all the texts, since it gives the more accurate value of π (3.1416) than other texts and further, it alone mentioned that it is an approximate value, using the word, āsanna – nearer to absolute. The value of π as given in various texts are, Sûrya Siddhānta: = 10(3.1622776) Srîdharācārya = 10(3.1622776) Mahāryabha a Siddhānta: = 22 ÷ 7 (3.142857143), 105 21,600 ÷ 6,876 or 600 ÷ 191 (3.141361256) Bhāskarācārya (Lîlāvatî) = 22÷7 (3.142857143), 3,927 ÷ 1,250 (3.1416) Âryabha îyam = 62,832 ÷ 20,000 (3.1416 - āsanna – near absolute) Modern estimation = 3.141592653….. Based on this, if we try to fix the chronology, then Sûrya Siddhānta: and Srîdharācārya’s Pā îga itam would become contemporary and Srîdharācārya’s Pā îga itam would be ancient than even Âryabha îyam. Then comes Mahāryabha a Siddhānta: and the next would be Bhāskarācārya’s Lîlāvatî and more recent would be Âryabha îyam. Obviously, this order is wrong and very confusing. Thus, the chronology arrived with the correctness of formulas and values, does not hold good, independently. We need some more concrete evidences like mentioning of the year, any one epoch, a period, any event or a reign of a king or the name of the other author or the name of other’s text, to arrive chronology. Here we find that no author had quoted the other’s name or even other’s text. In spite of this, the chronology of Bharat’s ancient texts was fixed according to one’s own will and wish unilaterally, with more and more ifs and buts, assumptions and personal views, despite the fact that Mahāryabha a Siddhānta: mentioned very 106 clearly94 in the 2nd śloka of 2nd adhyāya (Pārāśaryamatāntarādhikāra ), that it was written at the very early years of Kaliyuga. Senior Âryabha a Though Âryabha a clearly mentioned that he wrote Mahāryabha a Siddhānta: at the very early years of Kaliyuga, the date of Mahāryabha a Siddhānta: was assumed to be at c950 C.E., as seen above. This is because, in the late 18th and in the 19th century of C.E., the common accepted assumption and belief was that the human antiquity and history was just four thousands of years old only. It could not be extented before that, as one has to allot two to three thousand years for the ice age and great deluge, from the assumed date of creation of the world (22nd October 4004 B.C.E.). The Venerable Bede, writing in about 723 C.E., dated the age of the world since creation as 3952 B.C.E. and scholars like Scaliger (3949 B.C.E.), Johannes Kepler (3992 B.C.E.), Isaac Newton (c. 4000 B.C.E.) and John Lightfoot (3929 B.C.E.) had all come to similar calculations. James Ussher, the Irish Archbishop of Armagh and Primate of All Ireland between 1625 and 1656, published a treatise on the calendar in 1648. This was a warm-up for his most famous work, the Annales veteris testamenti, a prima mundi origine deducti (Annals of the Old Testament, deduced from the first origins of the world), which appeared in 1650, and its continuation, Annalium pars postierior, published in 1654. 107 In this work, he calculated the date of creation of the world to have been at the nightfall on 22 October 4004 B.C.E. This is known as the time of the Ussher chronology. However, Âryabha a mentioned in the 14th śloka of 13th adhyāya (Pātādhikāra ) of Mahāryabha a Siddhānta: about a senior Âryabha a, even much ancient to the period of Mahāryabha a Siddhānta:.105 It mentioned the word ‘Mahākālāt’ that means a very ancient period. If the date of Mahāryabha a Siddhānta: is accepted as such at the very early years of Kaliyuga, then the date of this Senior Âryabha a would be atleast a thousand years before Kaliyuga, i.e. six thousand years before present (as Kaliyuga started at 5116 years before present). Then the period of Veda, Kalpa sūtras etc., would become much ancient to this. Thus, it will totally shatter the above mentioned assumption. Hence, to be congruent and fit in with the above mentioned assumption and belief, i.e. the history and antiquity of human beings is of limited one within four thousands of years from present time, the date of this Senior Âryabha a mentioned in Mahāryabha a Siddhānta: has to be curtailed within this limit. Accordingly, the period of this senior Âryabha a and the date of Mahāryabha a Siddhānta: were fixed. Thus, the senior Âryabha a was assumed to be the author of Âryabha îyam (named as Âryabha a I) and his date was fixed at 476 C.E. Then the period of the author of Mahāryabha a Siddhānta: (named as Âryabha a II), must be latter to 476 C.E. and hence fixed at c950 C.E., on flimsy grounds, as discussed before. 108 However, due to modern development of science and technology, now it has been found that the human antiquity and history goes beyond 10,000 years, atleast. The recent excavations in various parts of the world and Bharat, proved this. For example, DR.S.R. Rao, Senior Archeologist, Graham Hancock, from Edinberg United Kingdom and Glenn Milne, Geologist at the University of Durham UK, and National Institute of Oceanography did underwater study at Poompuhar, the ancient capital of Chola Kingdom in Tamilnadu,and its date was estimated from 7000 to 11,000 years ago. Glenn Milne using inundation maps and bathymetric data estimated the date of Gulf of Cambay at 7000 years ago. Later by inputting the approximate long/lat. co-ordinates of the cities, followed by the NIOT’s (National Institute of Ocean Technology, Chennai) empirical measurement of the depth of those cities (40 metres), he estimated the date as 12,000 years. NIOT’s carbon-dating of cut wood, recovered from a shallow layer on top of the city in Gulf of Cambay, is of 9,500 years old. The long wall of the Konkan coast near Valnesvar of Maharastra sea shore is of 24 kilometers in lengh with 2.5 meter breath and 2.7 meter hight 3 meters below the present sea level and was estimated as of 8,000 years old. “The structure is not continuous throughout the 225 kilometres from Shrivardhan to Raigad, but it is uniform and hence manmade” said Dr Ashok Marathe, Retd. Professor, Department of Archaeology, Postgraduate and Research Institute, Deccan College, Pune. Further, the Saraswathy Sindhu civilisation 109 excavation sites proved the antiquity of human living in the world. For example Mehrgarh was of 8500 years, Nausharo 6600 to 6800 years, Lothal 5700 years and Kalibangan 5500 years before present. Hence, based on the recent findings, one should re-analyse the datas and should come to a correct conclusion, scientifically. The 14th śloka of 13th adhyāya (Pātādhikāra ) of Mahāryabha a Siddhānta: is, 105 vÏay& -”R àaKtate ! isÏaNtatNmhakalat ! , paQgE tmR Cu Ued < ivzi;te < tNmya SvaKTyae . V ddha Âryabha a proktāt Siddhāntādyan Mahākālāt , Pā haigatamucchedam viśe itam tan Maya svoktyā . Meaning:- 1. V ddha – Senior, 2. Proktāt – said, mention, teach, explain, impart, 3. Mahākālāt – at a very ancient period. Here, Mahāryabha a Siddhānta: mentioned that this senior Âryabha a was of very ancient period, as the word Mahākālāt (in superlative degree) definitely denote a period of more than thousnds of years. Thus, this senior Âryabha a was much ancient in time than the author of Mahāryabha a Siddhānta: and Âryabha îyam. Besides, the author of both Âryabha îyam and Mahāryabha a Siddhānta: was one and the same Âryabha a and it can be shown by the following analysis. 110 Bhâskara’s writings In his commentary on Âryabha īyam (Dasagîtikā-Sûtra- Vyākya and Âryabha a- Tantra-Bhā ya) under the heading Jyoti aśāstraprādurbhāve Vyākhyākāramatam, on explaining 1st and 2nd śloka of Gîtikapāda: (1st adhyāya:), Bhâskara mentioned clearly as,50 +lÉ EòlɨɺªÉÉiÉÒÊxpªÉÉhÉÉÆ º¡Ö ]OÉ®½ MÉiªÉlÉÉÇxÉÉÆ |ÉÉnÖ¦ÉÉÇ´É: ? ¥ÉÀhÉ: |ɺÉÉnäxÉäÊiÉ * B´É¨ÉxÉÖ¸ÉÚªÉiÉä - +xÉäxÉÉSÉɪÉæhÉ ¨É½nÂʦɺiÉ{ÉÉäʦɥÉÇÀÉ%%®ÉÊvÉiÉ:* +iÉÉä%ºªÉ iÉi|ɺÉÉnäxÉ º¡Ö ]õOÉ®½ MÉiªÉlÉÉÇxÉÉÆ |ÉÉnÖ¦ÉÉÇ´É <ÊiÉ*+ɽSÉ - +iÉÒÊxpªÉÉlÉÉÇ´É MÉiÉäºiÉ{ÉÉäʦÉ: {É®Éä{ÉEòÉ® IÉ¨É EòÉ´ªÉ o¹] ä ä ä : * ªÉÉä%±ÉRÂóEÞiÉä®´ªÉªÉ¨Éx´ÉªÉºªÉ {ɮɶɮºªÉÉxÉÖEÞÊiÉÆ SÉE É® ** Atha kathamasyātîndriyā ām sphu agraha gatyarthānām prādurbhāva ? Brahma a prasādeneti * Evam anusrûyate - anenācārye a mahadbhistapobhir Brahmā%%rādhita * Ato%sya tatprasādena sphu agraha gatyarthnām prādurbhāva iti * Âha ca - Atîndriyārthāva gatestapobhi paropakāra k ama kāvya d e * Yo%lañk teravyayamanvayasya Parāśarasyānuk tim cakāra ** Here Bhāskara mentioned, “This is what one hears said: This Âcārya Âryabha a worshipped Brahma,* by severe penance. Thereby, the true knowledge of the subjects 111 pertaining to the true motion of the Graha was revealed to him, by the grace of Brahma. It is said, Âryabha a, who followed into the footsteps of Parāśara,* the ornament among the men and who came in the lineage of Brahma, acquired the knowledge of the subjects beyond the reach of senses.” Thus, it is very clear that Âryabha a was a worshipper of Brahma and the follower of Parāśara. This was as exactly revealed by Âryabha a himself in his two texts, Âryabha īyam and Mahāryabha a Siddhānta:. In Âryabha īyam, in the 1st śloka of Gîtikapāda and that of Ga itapāda (1st and 2nd adhyāya ),106 Âryabha a mentioned that he set forth his text only after having paid obeisance to Brahma. Further, in the 13th śloka of the Gîtikapāda he mentioned that one can attain the Supreme Brahma, by knowing the Daśagîtika- sûtram.107 In the 49th śloka of the Golapāda , he mentioned that because of Brahma a prasādena (by the grace of Brahma), he brought forth the true knowledge on Astronomy.108 In Mahāryabha a Siddhānta: in the 1st śloka of the Pārāśaryamatāntarādhikāra (2nd adhyāya ),95 Âryabha a mentioned that he wrote his Siddhānta: based on Parāśara’s matam (Pārāśaryam matam) and Pārāśaryam matam was best, famous and praised much in Kaliyuga and his Siddhānta: was similar to Pārāśaryam matam, on mean motions of Graha. The śloka is, EòʱɺÉÆYÉä ªÉÖMÉ{ÉÉnä {ÉɮɶɪÉÈ ¨ÉiÉÆ |ɶɺiɨÉiÉ: * ´ÉIªÉä iÉn½Æ iÉx¨É¨É ¨ÉiÉiÉÖ±ªÉÆ ¨ÉvªÉ¨ÉÉxªÉjÉ ** 112 Kalisamjñe yugapāde Pārāśaryam matam praśastamata * Vak ye tadaham tanmama matatulyam madhyamānyatra ** Thus, it is very much obvious that Âryabha a started writing Âryabha īyam by paying obeisance and bowing with reverence to Brahma and wrote Mahāryabha a Siddhānta: based on Parāśara’s text. This was exactly proclaimed by Bhāskara in his commentary on Âryabha īyam, as seen above. There Bhāskara mentioned in a very clear way that Âryabha a got the true knowledge of the subjects pertaining to the true motion of the Graha by worshiping Brahma and followed into the footsteps of Parāśara, who came in the lineage of Brahma. This proves that the author of Âryabha īyam and that of Mahāryabha a Siddhānta: was one and the same Âryabha a and not of two different persons. Varāhamihira’s Pañca Siddhāntikā As shown before, in the 20th śloka of 15th adhyāya (Jyauti opani ad) of Pañca Siddhāntikā, Varāhamihira mentioned 3 that Âryabha a maintained that the beginning of the day is to be reckoned from midnight at Lańka and he again said that the day begins from the Sunrise at Lańka. The Âryabha a’s method of reckoning of days from midnight at Lańka is mentioned by Bhāskara, in his Mahābhāskarîyam (Mahāryabha a Karma Nibandha:),60 in the śloka 21st to 35th of the 7th chapter which deals with astronomical constants. These astronomical constants of this midnight day-reckoning are exactly similar to that of Sûrya Siddhânta:, as given in 113 Varāhamihira’s Pañca Siddhāntikā in the 16th adhyāya (Sûrya Siddhānte Madhyagati ),61 dealing with the mean motions of Graha. Here, Sûrya Siddhānta: adopted the midnight day- reckoning, as mentioned in the 1st śloka of this 16th adhyāya .61 Thus, because of these common features between these two texts, the view that the text of Âryabha a with the midnight day-reckoning was based on Sûrya Siddhānta: was enhanced further. However, this text of Âryabha a with the midnight day-reckoning is not yet traceable and it is mentioned as (Laghu) Âryabha a Siddhānta: or Laghu Âryabha îyam. G.Thibaut mentioned as109 “Now, Âryabha a’s rules are known to us from the Laghu Âryabha îya, and we observe they agree in all essential points with the corresponding rules of Sûrya Siddhānta,” in his introduction to the book, Pañca Siddhāntikā of Varāhamihira, in the page xxvii. Thus, this text was available during 1890s. However, why, where and how it vanished is the unanswered mystery now. The Âryabha a’s method of reckoning of days at Sunrise at Lańka is mentioned in Mahāryabha a Siddhānta: in the 47th śloka of the Madhyamādhyāya (1st adhyāya ).110 The śloka states that the revolutions of the Graha are to be calculated from the Sunrise at Lańka, which means that the days are to be reckoned from Sunrise at Lańka. Âryabha îyam also mentions it in the same way in the 4th śloka of Gîtikapāda.111 Thus, Âryabha a used the midnight day- 114 reckoning from Lańka in (Laghu) Âryabha a Siddhānta: and this text may be based on Sûrya Siddhānta:. He also used Sunrise day-reckoning from Lańka in Mahāryabha a Siddhānta: and Âryabha îyam and these two texts mentioned it in a very similar way. However, to mask the similarity in the names of (Laghu) Âryabha a Siddhānta: and Mahāryabha a Siddhānta:, the name of Mahāryabha a Siddhānta: was altered into Mahā Siddhānta:. Thus, the name of the author itself was omitted, though the name of the text was mentioned as Mahāryabha a Siddhānta: at the end of first four adhyāyā:, by the author Âryabha a himself. For example, at the end of 1st and 2nd adhyāyā , Âryabha a mentioned as, #it mhayR-” isXdaNte mXygitnaRm àwmae=Xyay> , Iti Mahāryabha a Siddhānte Madhyagatirnāma 112 Prathamo%dhyāya , #it ïImhay-”R isXdaNt e parazymtaNtraixkaraR e iÖtIy>, Iti Śrîmahāryabha a Siddhānte Pārāśaryamatāntarādhikāro 112 Dvitîya , In spite of this, the name Mahā Siddhānta: was preferred, there by masking the similarity in the names between these two texts. This is to prevent us from the correct understanding of Bharat’s ancient history. Accordingly, Mahāryabha a Siddhānta: was mentioned as Mahā Siddhānta: and Laghu Âryabha a Siddhānta: (Laghu 115 Âryabha îyam) as Ârya Siddhānta: or Âryabha a Siddhānta: The proofs and evidences discussed so for clearly shows that the date of Mahāryabha a Siddhānta: was at the very early years of Kaliyuga and the author of the texts, Mahāryabha a Siddhānta:, Laghu Âryabha a Siddhānta: and Âryabha îyam was one and the same Âryabha a. Since both Âryabha îyam and Mahāryabha a Siddhānta: were written by the same author and the date of Mahāryabha a Siddhānta: was at the early years of Kaliyuga, then the date of Âryabha îyam should also be at the very early years of Kaliyuga. Thus, the date of Âryabha îyam at 360 Kali (2741 B.C.E.) seems to be proper and it favours the date of Âryabha a at 337 Kali (2764 B.C.E.). Besides, it definitely strenthens the acceptability of the word a bhi in the first line of 3-10th śloka of Âryabha îyam, which is correct grammatically, as shown before. 116 CONCLUSION From the evidences numbered 1 to 10, it is clearly found that the date 476 C.E. creates much controversy and paradoxical problems and it is not all in harmony and congruent with the contemporary or just posterior historical dates and events. Further, it creates much confusion and distortion in the chronology also. On the other hand, the date 2764 B.C.E. not only does not create any paradoxes but also is coherent and reasonable with other dates and events. Beyond that, with the date 2764 B.C.E., the correct chronology can be arrived without any distortions and inconsistency. Besides, the grammatical and the syntactical analysis of the tenth śloka of Kālakriyāpāda (3rd Adhyāya ) of Âryabha īyam (especially of the word ‘Vyatītā ’ with K idanta “Ni hā ” affix “ta”), clearly proves a bhi is the correct word syntactically and grammatically whereas a i is wrong, thus favouring the date 2764 B.C.E. Further, the analysis of the date of the text ‘Mahāryabha a Siddhānta:’ also favours 2764 B.C.E. as the correct date. Thus, the above evidences show that the date of Âryabha a at 337 Kaliyugābdam i.e. 2764 B.C.E. and the date of Âryabha īyam at 360 Kali i.e. 2741 B.C.E. are more agreeable. Further, they also support that the author of Âryabha īyam and Mahāryabha a Siddhānta: is one and the same Âryabha a of 337 Kali i.e. the early years of Kaliyugābdam. I humbly request the esteemed scholars and experts to 117 go through this book fully and thoroughly and to derive the correct chronology of Bhārat, especially of the astronomical part, based on the evidences and proofs discussed here and got elsewhere. As such now, the chronology of Bhārat has to be re-examined, as there are newer findings, development and proper understanding. These include newer and recent archeological excavations, epigraphy, copper plates, numismatics, the proper and correct understanding of astronomical and literary evidences, the development of the most modern marine archeology and other evidences obtained recently, thanks to the recent excellent scientific developments with high quality equipment, approach and computer skills and simulations. 118 Name of Âryabha a: G.Thibaut’s preface to Pañca Siddhāntikā of Varāhamihira (Explanation for the discrepancy is in the next page) 119 On the discrepancy in the name of Âryabha a: 10th to 12th lines from top Scanned copy of G.Thibaut’s Preface, Dated 15th December 1888 120 Pañca Siddhāntikā of Varāhamihira edited by G.Thibaut and Sudhakara Dvivedi 20th śloka of 15th Adhyāya (Jyauti opani ad) 16th line from top, Discrepancy in the name of Âryabha a: Compare right and left columns 121 Pañca Siddhāntikā of Varāhamihira edited by G.Thibaut and Sudhakara Dvivedi, Printed by E.J.Lazarus and Co., at Medical Hall Press, Benares, 1889 & Chowkhamba Sanskrit Series Office Varanasi, 1968, 8th śloka of 1st Adhyāya , Discrepancy on Varāhamihira’s date, Compare right and left columns, 8th line from top 122 Front page of the book “Kalasaka Vinjānamu Prathama bhāgamu, Jyoti Siddhāntula Kāla-nir ayam” (Telugu) written by Śrî Kota Venkatachelam of Vijayawada in 1949 C.E. 123 Chapter ‘Âryabha u Kālapraśamsa’ in page 56 to 60 of the above book showing 3-10th śloka with the word ‘ a bhi ’ in the first sentence of the śloka (in telugu script) 5th line from top. 124 Some of the amazing contributions of Aryabhatta in Astronomy and Mathematics 1. Earth’s rotation on its own axis from west to east, causing day and night Aryabhatta explained the rotation of the Earth on its own axis, which is thought to be a modern understanding. He mentioned it in the ancient past itself, as found in the 9th sloka of 4th adhyaya (Goladhyaya) of Aryabhattiyam. English translation of the verse is, “Just a person in a boat, moving forward sees the stationary objects (like trees etc. on the banks of the river) as moving backward, the stationary stars are seen at Lanka (on the equator) as moving westward, in the same way.” This verse thus clearly mentioned that the Earth is rotating from west to east, on its own axis and it is the cause of the day and night, as mentioned by modern science. Thus, Aryabhatta mentioned clearly that the stars are stationary, as far as the Earth is concerned and the Earth rotates from west to east. Stars though stationary, appears to move westward, due to the Earth’s eastward rotation, on its own axis 125 2. Velocity of Earth’s revolution around the Sun and its rotation on its own axis Aryabhatta, in the 1st and 2nd sloka of 3rd adhyaya of Aryabhattiyam, mentioned the divisions of time and angles of a circle. A day consists of 60 nadi. A nadi consists of 60 vinadika. A vinadika is equal to (the time taken by a man in normal conditions in pronouncing) 60 long syllables (with moderate flow of voice) or (in taking) six respirations. This is the division of time. The division of a circle (the ecliptic) proceeds in a similar manner from the revolution. Thus in 24 hours, a man takes 60 X 60 X 6 respirations i.e. 21,600 respirations in 24 X 60 minutes i.e. 15 respirations per minute. The modern Medical Text Books confirms this value of Aryabhatta. 1. Review of Medical Physiology – William F. Ganong, University of California, 12 -15/minute. 2. Hutchison’s Medical Text Book, 14 -18/ minute. 3. Text Book of Human Physiology – Sarada Subramanium, 14-20 respirations/minute. Further, Aryabhattiyam reveals, the respiratory rate of men – 15 / minute (6 per Vinadika; 2½ Vinadika = 1 minute) & correlated it with the Natural event i.e. the revolution of the Earth round the Sun in the Ecliptic. Aryabhattiyam reveals, the time limit of pronouncing of alphabets in our Nation is based on the natural event i.e. the time span of Earth’s revolution round the Sun in the Ecliptic. One Gurvakshara – the time limit for pronouncing one long syllable is the duration of time in which the Earth travels one Tatpara (third ) of angular distance in the Ecliptic around the Sun. Further, Aryabhatta, in the 6th sloka of 1st adhyaya of Aryabhattiyam, mentioned during the time taken for one respiration, the Earth rotates on its own axis, one minute of angle. Rate of respiration 15 per minute i.e. 1 respiration in every 4 seconds. The 126 Earth rotates on its own axis 360° in 24 hours i.e. 360 X 60 minutes of angles in 24 X 60 X 60 seconds. Hence in 4 seconds i.e. the duration of one respiration, the Earth rotates (4 X 360 X 60) ÷ (24 X 60 X 60) = 1 minute of angle. SUN EARTH In the time of pronouncing During the time of one full one long syllable, the Earth respiration, the Earth rotates revolves the Sun in the on its own axis by one ecliptic by 1 third (tatpara) minute (Kala) of angle of angular distance in latitude co-ordinate 127 3.Facts about Solar and Lunar Eclipse Aryabhatta in his Aryabhattiyam, in the 37 and 38th sloka of 4th Adhyaya ( Goladhyaya) explained the cause of Solar and Lunar Eclipse in a very scientific way and also explained the role of Rahu and Ketu (The Ascending and Descending Nodes of Moon) in causing these eclipses scientifically. In the 37th sloka, he mentioned that the Moon eclipses the Sun and the shadow of the Earth eclipses the Moon. In the 38th sloka, he explained that when at the end of a Lunar month i.e. at the end of a New Moon (Amavasya), the Moon, lying very nearer to its Nodes (Rahu or Ketu), enters (in between the Earth and) the Sun, causing the Solar Eclipse. At the end of the lunar fortnight, i.e. end of Full Moon (Pournami), the Moon, lying very nearer to its Nodes (Rahu or Ketu), enters into the shadow of the Earth, causing the Lunar eclipse. This is exactly as what is taught by modern science. The ascending (Rahu) and descending (Ketu) nodes of the Moon, lies in the same horizontal plane of Earth’s revolution around the Sun i.e. ecliptic. Hence in this plane and only at the nodes (Rahu and Ketu), the Sun, the Earth and the Moon will lie in the same horizontal plane. This is one of the two mandatory that should be satisfied to cause Eclipse. The second mandatory is that the Sun, the Earth and the Moon should be in the same vertical plane, i.e. in the same celestial longitude or 180° apart. This will be satisfied only at the end of the New Moon for Solar Eclipse and at the end of Full Moon for Lunar Eclipse. These scientific facts are well explained by Aryabhatta on par with 128 modern science itself. Besides the connection between the Eclipse and Rahu and Ketu is not superstition, if you go with Aryabhatta’s scientific explanation. 4.Value of π (pi) given by Aryabhatta π is defined as the ratio between the circumference of a circle to its diameter and is constant. It is an irrational number i.e. a real number that cannot be expressed as a ratio of integers. The modern value is 3.1415926535897932384626433832795…..… Aryabhatta mentioned in the 10th sloka of 2nd adhyaya the value of pi as 62,832 divided by 20,000 which give the value as 3.1416, almost very nearer to modern value. Astonishingly, here Aryabhatta mentioned that it is only an approximate value and not absolute. The Diagram of a circle Circumference Diameter Pi πCircumference of a circle ÷ diameter 129 5.Sine θ values of Aryabhatta Sineθ = opposite side ÷ hypotenuse. In the diagram, ABC is the right triangle, where ∠ ACB is 90° and the sine of angle BAC (α) = BC (opposite side) ÷ AB (hypotenuse). In the following diagram of a circle, ACB is the arc of the circle and is the bow (Dhanus), ADB is the chord of the circle and also the bowstring and is called as Jya in Bharatian Jyotpattiganita (Jyaganita or Trikonamiti, the modern equivalent is Trigonometry). AOB is the same bowstring in a backward stretch on shooting (as shown in 2nd diagram). OC, AO and OB are the radius of the circle, where OC is the arrow of the bow. AD is the half chord i.e. ardhajya which later on named as jya itself. OAD is the right triangle with ∠ ADO is 90° and hence sine θ is AD ÷ OA. Therefore, jya (AD) = sine θ X AO, and since AO is radius of the circle, Jya AD is sineθ X Radius (R) i.e. R sine θ. 130 Further, Radius = circumference ÷ 2π , as 2π R is circumference. The circumference of the circle in angular measurement is 360° = 21,600′. π = 3.1416 (Aryabhattiyam 10-2). Hence, 21,600′ ÷ 2 X 3.1416 = 3438′. These, R sine values for various angles from 03° 45′ up to 90° were given in the sloka 11 and 12 of 2nd Adyaya of Aryabhattiyam. These R sine values of Aryabhatta are almost equivalent in accuracy to their modern values. (See Table) 131 GLOSSARY 1. Abul-Fazl ibn Mubarak :- A vizier in the court of King Akbar, wrote Ayeen Akberi (Ain I Akbari), during the reign of Akbar. 2. Alberuni (Abu Raihan) :- The famous historian who accompanied Mahmud of Ghajni and came to Bhārat around 1025 C.E. He wrote a text on Bhārat, which is known as “Tahqiqma lil Hind” rendered English by Edward C.Sachau (Alberuni’s India). 3. Alexander Cunningham, Sir. (1814–1893):- Major General, Royal Engineers (Bengal) in Royal Indian Army, Archaeological surveyor to the government of India (1861 to 1865), Director-general of Archaeological Survey of India (1871 to 1885). 4. Amoghavar a N patuńga, King:- He belongs to Rā trakûta clan, whose period of reign was C.E. 814 – 878. 5. Âryabha a :- The ancient astronomer and mathematician of Bhārat. 6. Aśoka of Mauriya, King :- Ancient King of Magadha Kingdom in Bhārat. He won Kalinga Kingdom. He then followed Buddhism. 7. A ādhyāyī of Pā ini :- Ancient text on Sanskrit grammar written by Pā ini. 8. Asterisms :- These are the 27 divisions of the celestial space, above and below the ecliptic pathway of the Earth, 132 each one is of 13° 20'. They are of 27, starting from Aśvinī to Revatī. 9. Bhārat :- The old and traditional name of India. 10. Brahma :- The God and Creator of Universe in Hindu way of worship. 11. Bhāskarācārya :- Astronomer and great mathematician of Bhārat. 12. Bhāskara :- Bhārat’s astronomer and mathematician of Âryabha a tradition. 13. Brahmagupta :- Great astronomer and mathematician of Bhārat. 14. Divine years :- Equal to 360 years in Earth. 15. Equinoxes and Solstices :- The point of intersection of the celestial equator and the ecliptic are the equinoxes. They are shown as 0° (Vernal Equinox, the first point of Me a - Aries) and 180° (Autumnal Equinox, the first point of Tulā - Libra). The Solstices are 90° (Summer Solstice) and 270° (Winter Solstice) of the Ecliptic. These 4 are with reference to Northern Hemisphere of the Earth. For Southern Hemisphere, the climatic condition is opposite correspondingly. 16. Kālidāsa :- One of nine great scholars in the court of King Vikramāditya of Ujjainī. 17. Kotta Venkatachelam :- Great scholar in the History of Bharat, wrote history based on Purana, ancient 133 astronomical text, etc. of Bharat. Native of Vijayawada, Andhrapradesh. 18. Kusumapura :- It is a place of Sanskrit and other higher studies, including astronomy and mathematics. It is thought to be the present day Patna or some place nearer to it in Bihar state of Bhārat. 19. Lańka :- The 0° Longitude and 0° Latitude, in the ancient period and is of the same longitude of Ujjainî. (At present it is 75° 46' 38" due to 0° Longitude was fixed at Greenwich). This Lańka was situated south-east of Maldives in Indian Ocean, at the top of the Malaya Mountain. In the ancient period, it was submerged in the sea and it is different from the present day Srī Lańka. 20. Lā adeva :- Direct pupil of Âryabha a. Astronomer and mathematician of Bhārat. 21. Mahābhārata war :- The famous war fought in 3138 B.C.E. at Kurukshetra, a place now in Hariyana state of Bhārat and Yudhi hira of Pā ava won the war. 22. Mahāyuga or Yuga, K ta (Satya), Tretā, Dvāpara and Kaliyuga:- One Mahāyuga or Yuga is the length of time equal to 43,20,000 years. It has 4 parts (Yugapāda) namely K ta (Satya), Tretā, Dvāpara and Kaliyuga of 17,28,000, 12,96,000, 8,64,000 and 4,32,000 years respectively. 23. Navagraha:- Nava – nine, Grah - to seize, lay hold of, eclipse etc. Graha and Planet are not synonymous. Graha denotes any celestial body that has attractive force on 134 other celestial bodies and it can include Star, Planet and Satellite. Navagraha, the nine Solar celestial bodies, have attracting force over the Earth, well above the minimum level and thus they alone can alter the Nature, environment and the life of living beings on the Earth. This can be verified quantitatively from the value of the gravitational and tidal forces of the Sun, Moon, Mercury, Venus, Mars, Jupiter and the Saturn and the resultant vector force from the Ascending and the Descending nodes of Moon (Rāhu and Ketu). 24. Parameśvara:- Mathematician and astronomer of 1380 C.E. period. Wrote many commentaries on ancient astronomical texts of Bhārat. 25. Parāśara:- The ancient i of Bhārat, who wrote Pārāśaryamatam, an astronomical text, based on which Âryabha a wrote Mahāryabha a Siddhānta: a treatise on astronomy. 26. Patanjali i’s Vyākara a Mahābhā ya :- The ancient text of detailed commentary on A ādhyāyī of Pā ini, written by Patanjali i. 27. Precession or Oscillation of equinoxes :-The points of equinoxes, are not fixed. They retrograde due to the rotation of the Earth around the axis joining the ecliptic poles and is known as precession of equinoxes. The modern estimation is 50.29" per year. The ancient astronomical texts like Sûrya Siddhānta mention it as 135 oscillation between 27 ° Me a to 3° Mīna, i.e.27° on either side of 0°. 28. Rāśi:- Starting from Me a (Aries) to Mīna (Pisces), these are the 12 zodiac signs of the celestial space, above and below the elliptical pathway of the Earth around the Sun (Ecliptic) and each one is of 30° longitude (12 x 30° = 360° one full circle). 29. Śālivāhana, King:- The great grandson of King Vikramāditya, whose capital was the famous Ujjainī. He started his era known as Śālivāhana Śaka, at 78 C.E. (Kali 3179 completed). 30. Siddhānta Kaumudī :- Sanskrit grammar text. 31. Srîdharācārya :- Mathematician of Bhārat. 32. ŚrīMahāvîrācārya :- Mathematician of Bhārat who lived around 850 C.E. 33. ŚrīŚvetavarāha Kalpa :- The present Kalpa. It is of 1000 Mahāyuga. Hence, it is of 432,00,00,000 years. 34. ŚrīVyāghramukha, King:- He is the King of ŚrīCāpavamśa (ŚrīCāpa clan). His period of reign and region of rule have not been derived absolutely, till date. 35. Sudhākara Dvivedī, M.M. (1855–1910) :- .The Sanskrit and mathematics scholar of Bhārat. He translated many ancient astronomical texts. He served in the Government College of Sanskrit at Vāranāsi and also as the head of mathematics department in Queen’s college, Vāranāsi. 36. Sumatihar a (1621 C.E.):- Mathematician and 136 astronomer of medieval period, who wrote commentaries on various ancient astronomy texts. 37. Sûrya Siddhānta , Romaka (Lomaka) Siddhānta and Pauliśa Siddhānta :- Very ancient astronomical texts of Bhārat. 38. Thibaut. G. (1848–1914) :- An Indologist, famous for his contributions to the understanding of ancient Bhāratian mathematics and astronomy. He was born in Germany. He translated many of ancient astronomical texts of Bhārat, the important one is ‘Pañca Siddhāntikā’ of Varāhamihira. In 1875, he became Professor at Government Sanskrit College Vāranāsi (Banaras) in Bhārat. 39. Ujjainī:- The capital of Mālva Kingdom. It is now in the western part of Madhyapradesh state, Bhārat. It was also the capital of King Vikramāditya and King Śālivāhana. It is a place of Sanskrit and other higher studies. 40. Vaivasvata Manvantara :- The present (7th) Manvantra. One Manvantra is of 71 Mahāyuga and one Sandhi period equal to the time of Satya yuga (17,28,000 years), totally making in to 30,84,48,000 years. 14 Manvantra with one Sandhi period of 17,28,000 years make one Kalpa period. 41. Vanavāsa:- One of the 4 ways of leading life in Bhārat. Here one has to go to forest and lead a simple and spiritual life without concentrating on worldly matters. 137 42. Varāhamihira :- Ancient astronomer of Bhrat. 43. Vāranāsi (Banaras) :- The very ancient, famous, holy and religious city, in Uttharapradesh state of Bhārat. 44. Vedāńga Jyoti am :- Ancient text detailing LuniSolar cycle of Sage Lagadha’s tradition. 45. Vikramāditya, King:- He ruled almost whole of Bhārat, with his capital at Ujjainī. He started his era known as Vikrama Samvat, at 57 B.C.E. (Kali 3044 completed). 46. Yudhi hira Dharma Rāja of Pañca Pān ava :- Very Ancient King of Bhārat, who won the Mahābhārata war in 3138 B.C.E. at Kurukshetra, north of Delhi. His capital was Indraprastha (Delhi). These words are marked with *mark in the book 138 REFERENCES 1. ‘Âryabha îyam,’ Âryabha a, 10th śloka of 3rd adhyāya (Kālakriyā pāda ) 2. ‘Kalasaka Vinjānamu Prathamabhāgamu, Jyoti Siddhāntula Kāla-nir ayam,’ (Telugu) Âryabha u Kālapraśamsa, pages 56 to 60, Śrî Kota Venkatachelam, 1949, Vijayawada 3. ‘Pañca Siddhāntikā’ Varāhamihira, 20th śloka of 15th adhyāya (Jyauti opani ad), Text, Sanskrit commentary and English translation, G.Thibaut and M.M. Sudhakara Dvivedi, Printed by E.J.Lazarus and Co., at the Medical Hall Press, Benares, 1889 & Chowkhamba Sanskrit Series Office Varanasi, 1968, pages Text -45 Translation – 88 4. Ibid., 3rd śloka of the 1st Adhyāya (Kara āvatāra ) pages Text 1, Translation 3 5. ‘Bhāskara’s commentary on Âryabha îyam,’ (Dasagîtikā-Sûtra-Vyākya and Âryabha a-Tantra- Bhā ya) ‘Âryabha īya of Âryabha a with the commentary of Bhāskara 1 and Someśvara,’ edited by K.S.Sukla, Indian National Science Academy New Delhi, 1976, page Text 202, under 10th śloka of Kālakriyā pāda (3rd adhyāya ) 6. ‘Pañca Siddhāntikā’ Varāhamihira, op.cite., 10th śloka 139 of the 1st adhyāya , (Kara āvatāra ) pages Text – 2, Translation - 4 7. ‘Bhāskara’s commentary on Âryabha îyam,’ (Dasagîtikā-Sûtra-Vyākya and Âryabha a-Tantra- Bhā ya) ‘Âryabha īya of Âryabha a with the commentary of Bhāskara 1 and Someśvara,’ op.cite., pages 45 and 46, under 1st śloka of Ga itapāda (2nd adhyāya ) 8. ‘Pañca Siddhāntikā’ Varāhamihira, 8th śloka of the 1st adhyāya (Kara āvatāra ), op.cite., pages Text - 2, Translation – 4. 9. Ibid., 2nd śloka of 12th adhyāya (Paitāmaha Siddhānta:) pages Text 31, Translation 67 10. ‘Chronology of Kashmir History Reconstructed’ of Srî Kota Venkatachelam, 1955, Vijayawada, pages 241 to 255 11. ‘B hat Samhitā’ Varāhamihira, 3rd śloka of 13th adhyāya Text & English Translation, M.Ramakrishna Bhat, Motilal Banarsidass Publishers, Delhi, 1997, Part I, page 161. 12. ‘B hat Samhitā’ Varāhamihira with Bha otpala commentary, 2nd & 3rd śloka of 13th adhyāya , edited by Dr.K acandra Dvivedī, Sampurnanand Sanskrit University, Varanasi, 1996, Volume 1 page 255 13. ‘Kalha a’s Rājataranginî A Chronicle of the Kings of Kaśmīr’ First Taranga 56th śloka, Edited by M.A.Stein, 140 Motilal Banarsidass Publishers Private Ltd, Delhi, 1892 (2003), Volume 1 page 12 (Translation) and Volume 3 page 4 (Text) 14. ‘Âryabha îyam,’ Âryabha a, 5th śloka of 1st adhyāya (Gītikapāda ), ‘Âryabha îya of Âryabha a’ Kripa Shankar Shukla and K.V.Sharma, Indian National Science Academy, New Delhi, 1976, page 9 15. ‘Ayeen Akberi (Ain i Akbari)’ Abul-Fazl ibn Mubarak, English translation from Persian by Francis Gladwin and published in London, 1800 C.E. (printed by G.Auld Greville Street), First volume, Third part, page 263 16. ‘Book of Indian Eras with Tables for calculating Indian Dates,’ Sir. Alexander Cunningham, Indological Book House Varanasi, 1970, (first edition 1883 C.E.) page 7 17. ‘Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bháscara,’ Henry Thomas Colebrooke, (Age of ÁRYABHA A), published in London (John Murray, Albemarle Street), 1817 C.E., pages xliii (xli to xlv) 18. ‘Indian Eras,’ pages 50, 10 -16, 24 – 40 and 48 – 52, Srî Kota Venkatachelam, 1956, Vijayawada 19. Ibid., pages 13 to 15 20. ‘A Sanskrit-English Dictionary,’ Sir. Monier Monier - Williams, page 1045, Motilal Banarsidass Publishers, Delhi, 2002 141 21. ‘Jyotirvidābhara am,’ Srî Kālidāsa, 21st śloka of the 22nd adhyāya Text, Sanskrit commentary and Hindi Translation, Dr.Ramachandra Pandeya:, Motilal Banarsidass, Delhi, 1988, page 660 22. Ibid., 10th śloka of 22nd adhyāya , page 656 23. ‘The Patiganita of Sridharacarya with an Ancient Sanskrit Commentary’ Kripa Shankar Sukla, Department of Mathematics and Astronomy, Lucknow University, 1959, pages Introduction xi to xiv 24. ‘The Goladīpikā by Parameśvara’ K.V.Sarma, The Adayar Library and Research Centre Adayar, Madras-20, India, May 1956 &1957, pages 6 to 8 25. Jyotirvidābhara am’, Srî Kālidāsa, 110 and 111 śloka of 10th adhyāya (Rājasattādhyāya ), op.cite., pages 283 and 284 26. ‘Kalha a’s Rājatarańginī A Chronicle of the Kings of Kaśmīr’ 125th and 128th śloka of 3rd Tarańga , op.cite., Volume 1 page 83 (Translation) & Volume 3 page 28 (Text) 27. Ibid., 129 to 290 śloka of 3rd Tarańga , Volume 1 pages 83 to 95 (Translation) & Volume 3 pages 28 to 34 (Text) 28. Ibid., 5th and 6th śloka of 2nd Tarańga , Volume 1 page 56 (Translation) & Volume 3 page 17 (Text) 29. ‘Alberuni’s India’ (Tahqiq ma lil Hind), Alberuni (Abu Raihan), Edited by Edward C.Sachau, London Trubner & 142 Co., Ludgate Hill, 1888 & Munshiram Manoharlal Publishers, 2001, pages 6 & 7 of 2nd Volume 30. ‘Book of Indian Eras with Tables for calculating Indian Dates,’ Sir. Alexander Cunningham, op.cite., pages 52 &49 31. ‘Ancient India as described by Ptolemy’ John W.McCrindle, edited in 1885 at Edinburgh (Munsiram Manoharlal, 2000) pages 154 & 155 32. ‘Esoteric Buddhism’ A.P.Sinnett, Indological Book House, Varanasi, 1972, page 151 33. ‘The Asiatic Researches’ 4th volume page xiv, published 1798 C.E. London & ‘The Works of Sir William Jones’ volume 3, page 220, published in 1807 C.E. London 34. ‘On the chronology of the Hindus’ written in January 1788 published in ‘The Works of Sir William Jones’ volume 4 pages 40 & 43,1807, London 35. ‘Bhavi ya Mahāpurā am’ 14 to 24 śloka of Pratisarga Parva, Prathama Khā a, 7th Adhyāya (3-1-7-14 to 24) & 22nd śloka Pratisarga Parva, Caturtha Khā a, 1st Adhyāya (3-4-1-22) 36. Ibid., 10 to 13 śloka of Pratisarga Parva, Tritīya Khā a, 2nd Adhyāya (3-3-2-10 to 13) 37. Ibid., 47 & 48th śloka of Pratisarga Parva, Prathama Khā a, 6th Adhyāya (3-1-6-47 & 48), 1st to 14th śloka of Pratisarga Parva, Prathama Khā a, 7th Adhyāya (3- 1-7-1 to 14) and 12th to 15th śloka of Pratisarga Parva, Prathama Khā a, 4th Adhyāya (3-1-4-12 to 15) 143 38. Ibid., 7th & 8th śloka of Pratisarga Parva, Prathama Khā a, 7th Adhyāya (3-1-7-7 & 8) 39. Ibid., 9th to 33rd śloka Pratisarga Parva, Tritīya Khā a, 2nd Adhyāya (3-3-2-9 to 33) 40. ‘Siddhānta Śiromanī’ Śrîmad Bhāskarācārya, 28th śloka of Kālamānādhyāya Madhyamādhikāra Grahaga itādhyāya , Text with Svavāsanābhā ya and Vārttika, Dr.Muralidhara Caturvedī, Sampurnanand Sanskrit University, Varanasi, 1998, page 26 41. ‘A Sanskrit – English Dictionary,’ Monier Williams, Oxford Clarendon Press, London May 1872, page 1065 42. ‘Sûrya Siddhānta:’ Madhyamādhikāra (1st adhyāya) 47th śloka and 57th śloka, Dr.Ramachandra Pandeya:, Chaukhamba Surbharati Prakashan, Varanasi, pages 26 & 36 43. ‘Siddhānta Śiromanī’ Srîmad Bhāskarācārya, Golādhyāya Praśnādhyāya 58th śloka, op.cite., page 524 44. ‘Kara akutūhalam,’ 2nd śloka of 1st adhikāra (Madhyamādhikāra ), edited by Dr.Satyendra Mishra, Krishnadas Academy, Varanasi, 1991, pages 2 and 3 45. ‘Siddhānta Śiromanī’ Srîmad Bhāskarcārya, 2nd śloka of Kālamānādhyāya of 1st adhikāra (Madhyamādhikāra ) of Grahaga itādhāya , op.cite., page 6 144 46. ‘Brahma Sphu a Siddhānta:’ Brahmagupta 7th and the 8th śloka of Samjñādhyāya (23rd adhyāya ), edited by board of editors headed by Acharyavara Ram Swarup Sharma, Indian Institute of Astronomical and Sanskrit Research, New Delhi, 1966, pages Sanskrit Text 320 (in Volume 1) and 1519 and 1520 (in Volume 4) 47. ‘Jyotirvidābhara am,’ Srî Kālidāsa, 8th śloka of the 22nd adhyāya op.cite., page 655 48. ‘Brahma Sphu a Siddhānta:’ Brahmagupta 26 and 27th śloka of Madhyamādhikāra (1st adhyāya) op.cite., pages Sanskrit Text 9 and 10 (in Volume 1) and 54 to 57 (in Volume 2) 49. ‘Alberuni’s India’ (Tahqiq ma lil Hind), Alberuni (Abu Raihan), op.cite., page 7 of 2nd Volume 50. Bhâskara’s commentary on Âryabha īyam [Dasagîtikā- Sûtra-Vyākya and Âryabha a-Tantra-Bhā ya], Jyoti aśāstraprādurbhāve Vyākhyākāramatam, ‘Âryabha īya of Âryabha a with the commentary of Bhāskara 1 and Someśvara,’ op.cite., 1st and 2nd śloka of Gîtikapāda [1st adhyāya ]), pages Introduction xxii to xxv and 11 51. Ibid., Introduction, pages xix to xxii 52. ‘Laghu Bhāskarîyam,’ Bhāskara, 2nd śloka, Text with English Translation, K.S.Shukla, Dept. of Mathematics and Astronomy, Lucknow University, 1963, pages Text - 1, Translation -1 145 53. ‘Mahābhāskarîyam (Mahāryabha a Karma Nibandha:),’ Bhāskara 4th śloka of the 1st adhyāya , Text with English Translation, K.S.Shukla, Dept. of Mathematics and Astronomy, Lucknow University, 1960, pages Text 1, Translation 2 54. Ibid., 21st to 29th śloka of 1st adhyāya , pages Text 4 to 6, Translation 16 to 21 55. ‘Hindu Astronomy’ W.Brennand, Chas. Straker & Sons Ltd., London, 1896, pages xi, 137 to 139 56. ‘Pañca Siddhāntikā’ Varāhamihira, 20th śloka of 15th adhyāya: (Jyauti opani ad), op.cite., pages Preface vi, Text – 45 57. ‘Âryabha îyam,’ Âryabha a, 3rd śloka of 1st adhyāya (Gītikapāda ), op.cite., pages 6 to 8 58. ‘Âryabha a and Axial Rotation of Earth’ Sri Amartya Kumar Dutta, Resonance, Journal of Science Education, Indian Academy of Sciences, Bangalore, Volume 11- 4, April 2006, pages 67 and 68 (56 to 74) 59. James Q. Jacobs, The oldest exact astronomical constant and Astronomical Formulas, 1. http://www.jqjacobs.net/astro/aryabhata.html 2. http://www.jqjacobs.net/astro/xls/ epoch_calc_v2011.xls (J.Chapront, M.Chapront-Touse, & G.Francou, Astron.Astrophys 387, 700..709 (2002), p.704 Table 4, 700..709 (2002), p.704 Table 146 4 (from Hastro-L post, Tom Peters, Dec. 13, 2010): original sources) James Q. Jacobs Anthropologist, Archaeologist http://www.jqjacobs.net/ permission mail From: James Q. Jacobs 62. ‘Sûrya Siddhānta:’ 2nd, 23rd, 46th, 47th and 57th śloka of the Madhyamādhikāra (1st adhyāya ), with the commentary of M.M.Sudhākara Dvivedī, edited by Dr. Śrī K a Candra Dvivedī, Sampurnanand Sanskrit University, Varanasi, 1987, pages Text 2, 3, 11, 18, 23 and 24 63. ‘Sûrya Siddhānta:’ Dr.Ramachandra Pandeya: 23rd śloka of Madhyamādhikāraha (1st adhyāya ) op.cite., pages 14 to 16 64. Ibid., 46th śloka of Madhyamādhikāra (1st adhyāya ) pages 26 to 28 65. ‘Vedāńga Jyoti a of Lagadha,’ in its k and Yajus Recensions, with Translations and Notes of Prof.T.S.Kuppanna Sastry, Indian National Science Academy, New Delhi, 1985, pages 13, 23, 28, 45 and46 66. ‘Vedic Astronomy (‘Vedaanga Jyotisha) (A Prehistoric Puzzle)’ Prof. Prabhakar Vyankatesh Holay, Shri Babasaheb Apte Smarak Samitee, Nagpur, 1989, pages 78 to 82 67. Ibid., page 81 68. Ibid., pages 12 and 81 and ‘Vedāńga Jyoti a of Lagadha,’ op.cite., page 35 and Vedanga Jyotisham by Dr.Sureś Candra Miśra, Ranjan Publications, New Delhi, 2005, page 43 69. ‘Sûrya Siddhānta:’ 9th and 10th śloka of 3rd adhyāya 148 (Tripraśnādhikāra , Digdeśakālajñānam) ‘Sûrya Siddhānta: with the commentary of Paramesvara’ Dept. of Mathematics and Astronomy, Lucknow University, 1957, pages 42 to 44 70. ‘Sûrya Siddhānta:’ with the commentary of M.M.Sudhākara Dvivedī, op.cite., page 78 71. ‘Sûrya Siddhānta: with the commentary of Paramesvara’ op.cite., page 43 72. Ibid., 11th and 12th śloka of the 3rd adhyāya (Tripraśnādhikāra ), pages 43 and 44 73. ‘The Student’s Sanskrit-English Dictionary’ Vaman Shivram Apte, Motilal Banarsidass, 2nd Edition, reprint 2000, page 505 & “A Sanskrit – English Dictionary,” Monier Williams, Oxford Clarendon Press, London May 1872, page 908 74. Ibid., page 9 & Ibid., page 12 75. Ibid., page 92 & Ibid., page 137 & “Dhāturūpa Mañjarī, An Easy Text on Sanskrit Verbs” K.L.V.Sastri and L.Anantharama Sastri, R.S.Vadhyar & Sons, Palghat, 2001, page 39 & “Prakriya Bhasyam” Fr. John Kunnapally, Malayalam, Translated into English by Prof.K.V.R.Pai, page 361 76. ‘The A ādhyāyī of Pā ini’ 1-1-26, Srīsa Chandra Vasu, Motilal Banarsidass, Delhi, 1st Edition, reprint 2003, Volume 1 pages 21 & 22 149 77. Ibid., 3-2-102, Volume 1 pages 450 & 451 78. Ibid., 3-4-69 and 70, Volume 1 pages 584 to 586 79. Ibid., 3-4-71 and 72, Volume 1 pages 586 & 587 80. ‘Siddhānta Kaumudī’ of Bha oji Dīk ita, Jnanendra Sarasvati and Jayakish a, Pā ini 2-3-12, pages 142 and 143, Tukārām Jāvajī, Jāvajī Dādājī’s Nirnayasāgar Press, Bombay, 1908 81. ‘The A ādhyāyī of Pā ini’ 2-3-12, op.cite., Volume 1 page281 82. ‘The Siddhānta Kaumudī’ of Bha oji Dīk ita, Srīsa Candra Vasu, Pā ini 2-3-12, Number 585, Volume 1, page 355, Motilal Banarsidass, Delhi, Second Edition Reprint, 2003 83. ‘The Student’s Sanskrit English Dictionary,’ Vaman Shivram Apte, op.cite., page 537 & ‘A Sanskrit – English Dictionary,’ Monier Williams, Oxford, op.cite., page973 84. Ibid., page 180 & Ibid., page 283 85. ‘The A ādhyāyī of Pā ini’ 3-2-187 and 3-2-188, op.cite., Volume 1 pages 481 & 482 86. ‘Samskrita Vyakarana Pravesika,’ Pandit L.Anantarama Sastri, R.S.Vadhyar & Sons, Palghate, 1999, pages 75-76 87. ‘The Siddhānta Kaumudī’ of Bha oji Dīk ita, Srīsa Candra Vasu, op.cite., Number 539, Volume 1 page 330 150 88. ‘Sūrya Siddhānta Text with English Translation’ 1- 55 śloka, E.Burgees & S.Jain, Oriental Book Centre, Delhi, 2005, page 54 89. ‘Âryabha îyam,’ Âryabha a 22nd śloka of 2nd Adhyāyā (Ga itapāda ) 90. ‘The A ādhyāyī of Pā ini’ 1-4-51 op.cite., Volume 1 pages 187 & 188 91. ‘Siddhānta Kaumudī’ of Bha oji Dīk ita, Jnanendra Sarasvati and Jayak ish a, Pā ini 1-4-51 and 7-1-69, op.cite., pages 129, 130, 445 & 446, 92. ‘The Siddhānta Kaumudī’ of Bha oji Dīk ita, Srīsa Candra Vasu, Pā ini 1-4-51 and 7-1-69, op.cite., Numbers 539 & 2765, Volume 1 pages 329 to 331 & Volume 2 Part 1 pages 672 and 673 93. Patanjali i, ‘Vyākara a Mahābhā ya’ Text and Commentary, Pā ini 1-4-51 and 7-1-69, Kaiya a Upādyāya & Nāgeśa Bha a, edited by M.M.Pandit Shivadatta Sharma, volume 2 pages 263 to 273 and edited by Pandit Dadhiram Sharma, volume 6 page 61, Chaukhamba Sanskrit Pratishtan, Delhi, Reprint Edition 1991 94. ‘Mahāryabha a Siddhānta:’ Âryabha a, 2nd śloka of the Pārāśaryamatāntarādhikāra (2nd adhyāya ), Sudhakara Dvivedi, Chaukhamba Sanskrit Pratishtan, Delhi, page 43 151 95. Ibid., 1st and 2nd śloka of 2nd adhyāya (Pārāśaryamatāntarādhikāra ), page 43 96. Ibid., Madhyamādhyāya (1st adhyāya ) 25, 35, 36, 48th and 51st śloka, pages 12, 20, 21, 35 and 37 97. Ibid.,19th śloka of Madhyamādhyāya (1st adhyāya ), page 9 98. Ibid., 17th śloka of the Pārāśaryamatāntarādhikāra (2nd adhyâya ), page 53 99. Ibid., 7th and 13th śloka of the Madhyamādhyāya (1st adhyāya ), pages 4 and 6 100.‘Ga itasārasangraha:’ ŚrīMahāvîrācārya, 3rd to 8th śloka of Samjñādhikāra (1st Chapter) and 50th śloka of K etraGa ita Vyavahâra (7th Chapter), Dr.Padmavathamma and M.Rangācārya, ŚrîSiddhāntakîrthi Grantha māla, Śrî Hombuja Jain Math, 2000, pages 2, 3, 454 and 455 101.‘Pā îga itam,’ Srîdharācārya, with ancient Sanskrit commentary, 117 and 115th śloka, Kripa Shankar Shukla, Dept. of Mathematics and Astronomy, Luknow University, 1959, pages 175 and 161 (90 and 88 English Translation) 102. ‘Mahāryabha a Siddhānta:’ Âryabha a, 78th and 70th śloka of Pā yadhyāya: (15th adhyāya:) op.cite., page 167 & 165 152 103. ‘Pā îga itam,’ Srîdharācārya, with ancient Sanskrit commentary, op.cite., pages Introduction 41, 42 and 38 to 40 104. ‘Mahāryabha a Siddhānta:’ Âryabha a, 92nd śloka, Pā yadhyāya: (15th adhyāya:) op.cite., page 172 105. Ibid.,, 14th śloka of 13th adhyāya (Pātādhikāra ), pages 128 &129 106. ‘Âryabha îyam,’ Âryabha a, 1st śloka of Gîtikapāda and that of Ga itapāda (1st and 2nd adhyāyā ) 107. Ibid., 13th śloka of the Gîtikapāda (1st adhyāya ) 108. Ibid., 49th śloka of the Golapāda (4th adhyāya ) 109. ‘Pañca Siddhāntikā’ Varāhamihira, op.cit., page Introduction xxvii 110. ‘Mahāryabha a Siddhānta:’ Âryabha a, 47th śloka of the Madhyamādhyāya (1st adhyāya ), op.cite., page 34 111. ‘Âryabha îyam,’ Âryabha a, 4th śloka of Gîtikapādā (1st adhyāya ) 112. ‘Mahāryabha a Siddhānta:’ Âryabha a, at the end of Madhyamādhyāya (1st adhyāya ) and Pārāśaryamatāntarādhikāra (2nd adhyāya ), op.cite., pages 41 and 53. UUU