History of Science in South Asia A journal for the history of all forms of scientific thought and action, ancient and modern, in all regions of South Asia Al-Bīrūnī’s India, Chapter 14: an Account of Indian Astronomical, Mathematical and Other Literature Noémie Verdon and Michio Yano Kyoto University and Kyoto Sangyo University style citation form: Noémie Verdon and Michio Yano. “Al-Bīrūnī’s India, Chapter 14: an Account of Indian Astronomical, Mathematical and Other Literature.” History of Science in South Asia, 8 (2020): 57–76. DOI: 10.18732/hssa.v8i.54. MLA Online version available at: http://hssa-journal.org HISTORY OF SCIENCE IN SOUTH ASIA A journal for the history of all forms of scientific thought and action, ancient and modern, in all regions of South Asia, published online at http://hssa-journal.org ISSN 2369-775X Editorial Board: • • • • • • • Dominik Wujastyk, University of Alberta, Edmonton, Canada Kim Plofker, Union College, Schenectady, United States Dhruv Raina, Jawaharlal Nehru University, New Delhi, India Clemency Montelle, University of Canterbury, Christchurch, New Zealand Fabrizio Speziale, School of Advanced Studies in the Social Sciences (EHSS), Paris, France Michio Yano, Kyoto Sangyo University, Kyoto, Japan Gudrun Bühnemann, University of Wisconsin-Madison, USA Publisher: History of Science in South Asia Principal Contact: Dominik Wujastyk, Editor, University of Alberta Email: ⟨wujastyk@ualberta.ca⟩ Mailing Address: History of Science in South Asia, Department of History and Classics, 2–81 HM Tory Building, University of Alberta, Edmonton, AB, T6G 2H4 Canada This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. Copyrights of all the articles rest with the respective authors and published under the provisions of Creative Commons Attribution-ShareAlike 4.0 License. The electronic versions were generated from sources marked up in LATEX in a computer running GNU/LINUX operating system. PDF was typeset using XƎTEX from TEXLive. The base font used for Latin script and oldstyle numerals was TEX Gyre Pagella developed by GUST, the Polish TEX Users Group. Al-Bīrūnī’s India, Chapter 14: an Account of Indian Astronomical, Mathematical and Other Literature Noémie Verdon and Michio Yano Kyoto University and Kyoto Sangyo University INTRODUCTION A of information for various aspects of Indian culture. Since al-Bīrūnī’s main L-BĪRŪNĪ’S KITĀB TAḤQĪQ MĀ LI-L-HIND (hereafter Taḥqīq, ca. 1030 CE) is a mine interest was in astronomy and astrology, it is natural that he devoted many pages of this book – in fact, half of it – to these two sciences. Much of its content that is related to these scientific fields is extremely precious to Indologists who study the history of science, because this testimony sheds light on Indian texts and authors who are otherwise not extant or unknown within Sanskrit literature. Today, our understanding of al-Bīrūnī’s works, from the perspective of history of Indian astronomy and mathematics, mostly relies on studies done by Carl Edward Sachau, David Pingree, N. A. Baloch and E. S. Kennedy. There is, however, no monograph dedicated to this question, and information which can be drawn from these important studies is still fragmentary. In this article we would like to offer an English translation of Chapter 14, in which al-Bīrūnī gives very rich information on Indian astronomy and astrology. Sachau published the Arabic edition of the Taḥqīq in 1887, with a valuable introduction. Later, he translated the work into English (1888) with rich annotations.1 Sachau laid the essential foundations for the study of al-Bīrūnī’s book. 1 We base our translation on the Hyderabad edition of the Taḥqīq, referred to as Taḥqīq (1958), and indicate when its reading di- verges from that of Sachau’s edition: Taḥqīq (1887). HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 DOI: 10.18732/HSSA.V8I.54 58 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 Even though he was not a Sanskritist, many of his identifications of Indian texts, authors and concepts remain valid today. A peculiarity of Sachau’s translation, however, is that it is rather liberal, mostly when the Arabic original is obscure and intricate, and thus it can at times be misleading. Further, more than a century has passed since Sachau’s publications. In the last hundred years, many works on Indian astronomy, astrology and mathematics have appeared. For instance, whereas Sachau knew about the existence of a manuscript of the Brāhmasphuṭasiddhānta (hereafter BSS), which he names Brāhmasiddhānta, probably following al-Bīrūnī’s designation, he also writes that it had “not yet been completely edited or translated” at the time (Sachau 1888: II, 303). In 1973, N. A. Baloch edited and translated al-Bīrūnī’s translation of the Karaṇatilaka (Baloch 1973). Baloch’s introduction to the translations offered interesting insights into al-Bīrūnī’s knowledge of Indian astronomy and the context in which he had prepared his translation. Baloch also discussed the transmission of Sanskrit astronomical works to the Abbasid caliphate in the middle of the eighth century CE. Lastly, especially important are David Pingree’s works. His Census of Exact Sciences in Sanskrit (hereafter CESS) is one of the most significant contributions to Indology and history of science in the twentieth century.2 Pingree’s studies on the Pauliśasiddhānta and on the author Balabhadra have also been particularly helpful (Pingree 1969; 1983). With Pingree’s works at hand we are in a position offer numerous additions and corrections to Sachau’s translation. This paper offers some examples. We begin by providing below an updated translation of Chapter 14 of the Taḥqīq and – to the extent possible – we contextualize it in the footnotes. In this chapter, al-Bīrūnī gives the table of contents of the work which he calls Brāhmasiddhānta. In the appendix of the present article, we compare this list with the table of contents found in S. Dvivedin’s edition of the Brāhmasphuṭasiddhānta (BSS). 2 Since CESS is incomplete, we also referred to his book Jyotiḥśāstra (Pingree 1981). HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 59 CHAP TER 1 4 : O N THE RECO RD O F THEIR BO O K S IN THE OTHER S CIENCES 3 Sciences are many, and by the periodic change of ideas about them, they increase when their time is favourable. The characteristic of such [time] is the desire and respect of people for [sciences] and its practitioners. And those who are more entitled to this (i.e., the growth of science) are those who rule over the [people], because their (i.e., the rulers’) work is to unload the hearts overwhelmed by worldly stress and to stimulate4 inclination to increase praise and favour, because hearts are disposed to the love of this and to the hate of its opposite. Our time is not of this described characteristic. But on the contrary, if that is necessarily the case, when does a [new] science appear, or [when] does what has appeared progress?5 But what is found now is a residue and a remnant of the time which used to be of this characteristic. When something spreads all over the earth, all [groups of people] on [earth] receive their share. India is one of them. Their (i.e., Indians’) belief in [cyclic] change of time agrees with visual observation.6 The science of stars is most famous among them, because the matters of religion are dependent on it. The title of astrologer and astronomer does not occur by mere computation to those who do not understand the judgements [of stars]. That which our authors know as “Sindhind” is [their] “Siddhānta” or “upright,” not crooked and not changeable. This name refers to each science of 3 In the preceding two chapters of the Taḥqīq, al-Bīrūnī discusses religious, grammatical and poetic literature. In chapter 14, he chiefly deals with astronomical, astrological and mathematical literature, while briefly mentioning the Carakasaṃhitā and the Pañcatantra. (On the Carakasaṃhitā in the Taḥqīq, see also Sachau 1888: I, 162–3, 382– 3.) In his translation of this title, Sachau adds elements absent in the Arabic original. His translation is as follows: “Hindu literature in the other sciences, astronomy, astrology, etc.” (Sachau 1888: I, 152). In general, in the Taḥqīq al-Bīrūnī very rarely uses a specific adjective referring to the Indians. When he does so, the Arabic term is either the collective noun al-hind ( YJêË@), i.e., India or Indian, or a derived adjective al-hindī ( ø YJêË@), i.e., Indian. Sachau constantly translates these Arabic terms as “Hindu,” and regularly adds the adjective, even when the term does not occur in the Arabic text.  4 Taḥqīq (1887): 73, line 4: QîE., Taḥqīq  (1958): 118, line 1: QîE. 5 The Arabic passage is rather idiomatic. Sachau translates in the following way: “The present times, however, are not of this kind. They are the very opposite, and therefore it is quite impossible that a new science or any new kind of research should arise in our days” (Sachau 1888: I, 152). 6 This sentence appears a little out of context, but it simply serves as a transition sentence between the discussion on the developments of ideas and sciences and the actual topic considered hereafter in the chapter, science of stars. At any rate, alBīrūnī appears to consider (cyclic) change of time as true. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 60 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 computation of stars that rises to the highest rank for them, even though for us they fall short of our Zīğes, and they are five: (1) Sūryasiddhānta related to the sun, which Lāṭa composed. (2) Vasiṣṭhasiddhānta related to one of the stars of the Great Bear 7 and which Viṣṇucandra composed.8 (3) Pulisasiddhānta, related to Paulisa,9 who was a Greek [man] from the city of Sayntara which I think is Alexandria10 and Pulisa composed [this text]. (4) Romakasiddhānta, related to Byzantium and which Aŝrīkhīn composed.11 (5) Brāhmasiddhānta12 related to Brāhma and which Brahmagupta, the son of Jiṣṇu, composed in the city of Bhillamāla, which is between Multān and Anhilwāra,13 by [a distance of] 16 yojanas. All of them are based on the book of Paitāmaha which is related to the first father who is Brahmā.14 Varāhamihira composed a small-sized Zīğ, which he calls Pañcasiddhāntikā. The title implies that it contains what are in the [afore-mentioned] five, but it is not [just] like that. And this [book] is not superior to them, so as to call it better than the five. But the name is established as five because of their number.15 Then, Brahmagupta says16 that the Siddhāntas are many. One of them is 7 Vasiṣṭha is 𝜁 Ursae Majoris. Cf. Bṛhatsaṃhitā 13.5-6. 8 For Viṣṇucandra, see CESS: A5, 704. His name is found in BSS XI, 31, 50 and 55. 9 Pulisa/Paulisa is Pauliśa in Varāhamihira’s Pañcasiddhāntikā (PS). Pingree (1969) discusses the later Pulisa known to al-Bīrūnī. 10 The two Arabic editions read sayntra  ( QJƒ). According to al-Bīrūnī, this corresponds to Alexandria. There are several cities known as Alexandria (Dey 1927: 4; Bhattacharyya 1991: 56–7). 11 Sachau identifies this name as Śrīsheṇa, i.e., Śrīṣeṇa, which is possible since the interchange of /ṣ/ and /kh/ is a common phenomena in north Indian writing systems. See below where Ṣat- of Ṣatpañcaśika is written Khatt-. Śrīṣeṇa is mentioned in BSS XI, 31, 46 and 55. 12 Actually, there exists a Brahmasiddhānta which is different from Brahmagupta’s Brāhmasphuṭasiddhānta, edited by S. Dvivedin (Benares, 1901–1902, abbreviated BSS). The Brahmasiddhānta is included in the compendium Jyotiṣasiddhāntasaṃgraha edited by V. P. Dvivedin (Benares, 1912). See the Appendix to this article (p. 68 below) for a commented comparison of the division into chapters of the Brahmasiddhānta with that found in S. Dvivedin’s edition of the Brāhmasphuṭasiddhānta. 13 Anhilwāra ( èP@ñÊîE@), also known as Nahrvāra, corresponds to the Sanskrit toponym Anahilapurapattana and today’s Pattan/Patan (23∘ 52’N, 72∘ 10’E) in Gujarat (Dey 1927: 6; Bhattacharyya 1991: 67, 227; Bosworth and Minorsky 1937: 88, 238, 245). Anhilwāra was ruled by a king known as Balla-ray (i.e., Vallabha-rāja of the Rāṣṭrakūṭa dynasty) in Arabic and Persian sources. 14 Pingree (1969: 177–9) discusses this passage. 15 This remark is not easy to understand. Al-Bīrūnī perhaps means that the title only refers to the number of the five well-known Siddhāntas, but that Varāhamihira’s work differs from them in content. Anyway the Pañcasiddhāntikā al-Bīrūnī used might have been different from what we have today. 16 We cannot find the relevant passage of this statement. Therefore it is difficult to determine where exactly the quotation ends. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 61 “Sūrya,” one of them is “Indu”,17 one of them is “Pulisa,” one of them is “Romaka,” one of them is “Vasiṣṭha,” and one of them is “Yavana”,18 namely Greek. In spite of their abundance, they don’t differ [from each other]; only the wording [differs], not the meaning. [A man] who looks at them with a right attention will find their [points of] agreement. By now I do not have any copy [of them], except the ones by Pulisa and by Brahmagupta. Its translation by me is still not complete, but I record the list of the chapters of the Brāhmasiddhānta, because this would be helpful for [its] understanding.19 1. On the conditions of the sphere and the shape of heaven and earth.20 2. On the rotations of the planets and the study of time, the derivation of mean [longitude of] planets, and computation of the Sines (ğuyūb) of arcs. 3. On the equation of planets. 4. On three questions which are the shadow [of gnomon], the time passed in the day, and the ascendant and derivation of one from the other. 5. On the appearance of the planets from the sun’s ray and their disappearance in it. 6. On the sight of the new moon (hilāl) and the condition of moon’s horns. 7. On the lunar eclipse. 8. On the solar eclipse. 9. On the shadow of the moon. 10. On the conjunction of the planets and their meeting. 11. On the latitudes of the [fixed] stars. 12. On the criticism of the books and the Zīğes and on the distinction between the true and the false. 13. On mathematics and its study of plane geometry and others. 14. On the correction (uttara) of the mean planets.21 15. On the correction of the equation the planets. 16. On the correction of the three questions. 17 Since indu means the Moon, al-Bīrūnī might be referring to the Somasiddhānta, which is contained in the Jyotiṣasiddhāntasaṃgraha mentioned in footnote 12. 18 Yavana is mentioned again later as one of the books on astrology. We do not know any book on astronomy called Yavana. 19 See Appendix, p. 68 below. 20 In S. Dvivedin’s edition this is the 21st chapter titled Golādhyāya. See Appendix. The text known to al-Bīrūnī is different from that of S. Dvivedin’s twentieth-century edition. 21 The word uttara has several meanings. Brahmagupta uses this word in the title of the second half of his Khaṇḍakhādyaka where he gives the ‘’correction” of the first part. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 62 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 17. On the deviation (deflection) of eclipses. 18. On the correction of the sight of the new moon (hilāl) and its horns. 19. On kuṭṭaka, which means “pounding,” i.e. the endeavour to search for minute [things], from which oil is extracted. This is about al-ǧabr wa-l-muqābala,22 by putting together in search of other numbers. 20. On the matters of shadows. 21. On the computation of the metrics of poetry and its prosody. 22. On the rings and instruments.23 23. On the time and four measures, namely solar, civil, lunar, and of the nakṣatra. 24. On the signs of the numbers and numerals in metrical treatises.24 In this way are 24 chapters, as Brahmagupta said, while the 25th chapter is Dhyānagrahādhyāya in which emerges25 the search for reflection (fikra)26 without the study of mathematics.27 I did not record it here (i.e., in the above enumeration of chapters), because I would depart from mathematics. I think that what he alluded to, with it, was the proofs of operations, otherwise how [can a man] draw something from this art [of astrology] without mathematics.28 All [texts] which are below the rank of siddhānta are mostly called either tantra or karaṇa. As for tantra, its meaning is to act in the hand of a governor (i.e., to be subordinate or secondary). As for karaṇa, it means secondary, namely to siddhānta. In addition its experts are ācāryas, or learned ascetics who are followers of Brahmā.29 Āryabhaṭa and Balabhadra30 each has a famous tantra 22 The expression al-ǧabr wa-l-muqābala means “perfective addition and compensative subtraction” according to Lane’s Lexicon (Lane 1863–93). The two words are technical terms of mathematical operation. The former is the origin of the modern term “algebra.” 23 The word “ring” means armillary sphere. 24 This is al-Būrūnī’s misunderstanding. See Appendix.  25 The two editions read éJ¯ h. Qm' ø YË@ (Taḥqīq (1887): 74, l. 13; Taḥqīq (1958): 120,  ll. 7–9). The MS reading is éJÓ h. Qm' ø YË@ according to Sachau’s edition (Taḥqīq (1887): 74, fn. 3). 26 This is al-Bīrūnī’s understanding of dhyāna. 27 Actually Dhyānagrahopadeśādhyāya is full of highly mathematical computations. We think that this chapter could constitute a bridge between the Siddhānta of S. Dvivedin (BSS) and Karaṇa of the Khaṇḍakhādyaka. However, it seems that al-Bīrūnī did not understand this chapter. 28 Cf. The beginning of Wright 1934: 1. 29 The Arabic term ʿāmilūna ( àñÊÓA«), translated here as “experts,” literally means doers, workers, while also referring to the person in charge of an administrative office. Sachau for his part interprets the term as referring to the “governors,” as follows: “Under governors they understand the Ācāryas, i.e., the sages, anchorites, the followers of Brahman.” (Sachau 1888: v. 1, 155). 30 In the Taḥqīq, al-Bīrūnī makes abund- HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 63 and Bhānurajas31 has a book Rasāyana tantra and rasāyana is explained in his book.32 As for the karaṇa related to its name (i.e., rasāyana?), it is Brahmagupta’s Khaṇḍakhādyaka. This name refers to a sweet type [of food] among the [Indians]. I heard, concerning the reason of this [title], that Sugrīva, a Buddhist,33 composed a Zīğ called Dadhisāgara, namely the ocean of sour milk.34 His disciple composed a Zīğ called Kūrababaya,35 namely “the mountain of rice.” Then Indu composed Lavaṇamuṣṭi, namely “a handful of salt.” And therefore, Brahmagupta called his book “candy” in order to make complete the meal and its ingredients. This [book] was based on the view of Āryabhaṭa and therefore he continued it with the book which he calls Uttarakhaṇḍakhādyaka, namely “its correction’. Then, another book follows – I do not know whether it belongs to him (i.e., Brahmagupta) or to someone else – which is called Khaṇḍakhādyakatappā36 in which the reasons of the numbers used in it (i.e., Uttarakhaṇḍakhādyaka) are given and which, as I think, belongs to Balabhadra. Vijayanandin,37 the commentator from the city of Vārānasī, wrote a Zīğ known by [the name] Karaṇatilaka, namely Ġurra al-tawābiʿ.38 Vaṭeśvara, the son of Mahadatta39 from the city of Nāgpūr ant references to Balabhadra, chiefly when the discussion deals with astronomical and cosmological subjects. Sachau hypothesizes that Balabhadra could be the commentator of the Kitāb Pātanǧal (Sachau 1888: v. 2, 264). This position is however not supported by evidence (Verdon 2020). On Balabhadra in al-Bīrūnī’s work, see Pingree 1983. 31 CESS: A4, 294. Bhānurajas is entered as “the author of Karaṇapratilaka(?),” but no more information is given. 32 In the Taḥqīq, al-Bīrūnī describes rasāyana áK AƒP as a fourth path leading to liberation, basing himself on the Kitāb Pātañjal. He further defines it as “procedures involving drugs resembling alchemy in the obtainment of what is by nature impossible” ú¯ ZAJÒJºË@ øQm.× øQm.' éK ðX AK. QK. @YK ùë)  JJÒÒË@ ÉJ’m' (AîE. HAª Taḥqīq (1958): 61 ll. 4–6; Sachau 1888: v. 1, 80. See also Sachau 1888: v. 1, 188–93. 33 Śamanā, Skt. śramaṇa.  Ï @) is used here. 34 A Persian word ( IƒAÖ 35 The Arabic transliteration kūra-babaya is most probably from the Sanskrit kūraparvata (kūra: boiled rice; parvata: mountain). The Sanskrit phonemes /p/ and /v/ in parvata were transliterated into Arabic by a single sound /b/, in the same way as vihāra became bihār PAîE. in Arabic transliteration (Taḥqīq (1958): 349, l. 9). Further, the original /r/ disappeared under a Prakrit influence. Lastly, as the Arabic letter /t/ ( AK) and /y/ ( AK) differ only by the diacritical signs it is possible that these were interchanged in the transliteration of the term. 36 Pingree 1983. 37 For Vijayanandin, see CESS: A5, 625. His name is referred to in S. Dvivedin (BSS) XI, 49 and 58. 38 Literally, the title Ġurra al-tawābiʿ  ( ©K. @ñJË@ èQ«) means “ornament on the forehead of a dependency.” It seems to be a literal Arabic translation of the Sanskrit title Karaṇatilaka, the Arabic tawābiʿ (plural of tāʿiba) referring to something of minor importance and rendering the Sanskrit karaṇa, i.e., secondary. See also Baloch’s translation of this title (Baloch 1973: 7). The Arabic translation of the Karaṇatilaka by al-Bīrūnī has been edited and translated into English by Baloch (1973). The title of  .' QË@ H Q«. See the work in this edition is HAm Baloch’s translation of the two titles (Baloch 1973: 7). 39 Shukla 1985–6. See also CESS: A5, 555. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 64 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 wrote a Zīğ whose name is Karaṇasāra,40 namely the extract from the secondary (i.e., karaṇa). Bhānurajas composed a book [entitled] Karaṇapratilaka as an extract from it.41 They assumed that the aspects of the planets are related to each other.42 Utpala, the Kaśmīrian, composed the Rāhunrākaraṇa,43 namely “breaking of tawābiʿ” and the Karaṇapāta,44 namely “killing of tawābiʿ”.45 [Further, there is] the Karaṇacūḍāmaṇi. I do not know its author. Then, there are other books with other titles, such as the great Mānasa46 from the work of Manu47 and which Utpala commented on, and the small Mānasa,48 which Mañjula49 from the southern district composed. And the Daśagītikā of Āryabhaṭa and his Āryāṣṭaśata.50 Lokānanda51 by the name of its author, and the book by Bhattila52 the Brahmin, [titled] by his name. You will hardly count [the books] of this genre. As for their books on astrology (aḥkām al-nuğūm), each of the following [authors] Māndavya (?),53 Parāśara,54 Garga, 55 Brāhma, Balabhadra,56 Divyātattva57 composed, and Varāhamihira composed a book [called] [Bṛhat]Saṃhitā, whose definition is: a collection which contains in abundance a little bit of everything, such as report on travelling58 by the phenomena of the sky, matters 40 There is no entry for Karaṇasāra in CESS. 41 See footnote 31. 42 The meaning of this sentence is unclear. Sachau connects it to the previous sentence, as follows: “another one, by Bhāṇuyaśas (?), is called Karaṇaparatilaka, which shows, as I am told, how the corrected places of the stars are derived from one another” (Sachau 1888: I, 157). Sachau’s Bhāṇuyaśas should be Bānurajas. 43 CESS: A4, 283, Rā.h.t(?).ra karaṇa (Ārdharātrikakaraṇa?). 44 According to Pingree (CESS: A4, 283), Karaṇaghāta, or ‘Killing of karaṇa’ is Utpala’s work. 45 The meaning of “killing of tawābiʿ” is not clear. A similar idea may be found in the example of Mādhava, a Sāṃkhya teacher, who was referred to as sāṃkhyanāśaka, i.e., destroyer of Sāṃkhya, “because he deviated from the Sāṃkhya position” (Larson and Bhattacharya 2008: 147). 46 This is Bṛhanmānasa of Muñjāla (or Mañjula). See CESS: A4, 435. 47 This should be Mañjula. 48 See Shukla 1990, especially page 4. 49 Arabic text is Éj  JK which Sachau reads “Puñcala.” 50 Daśagītikā is the first chapter of Āryabhaṭīya, but sometimes it is regarded as an independent work. The rest of the Āryabhaṭīya, consisting of 108 Āryā verses, is called Āryāṣṭaśata as a work on its own. AlBīrūnī reflects the tradition which regards the Daśagītikā and the Āryāṣṭaśata as two separate works. 51 No information about this book or author is avalable in CESS. 52 No informatin is available in CESS. . YKAÓ. 53 Arabic text reads māndabba H 54 There are many Parāśaras. See CESS: A4, 194–202. 55 Garga is the author of the Gārgyajyotiṣa (CESS: A2, 116 f). Bill Mak organized an working group on Garga tradition. The recent result is: Geslani et al. 2017. 56 For Balabhadra see CESS: A4, 233. See also Pingree 1983: 353–60. 57 Pingree only gives his name (CESS: A3, 112). 58 yātrā in Sanskrit. Especially military expeditions. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 65 of dynasties59 and interrogation,60 then physiognomy,61 dreams,62 and zaǧr.63 Their learned people believe in it and they follow the prescription of the astrologers which they interpret from the knowledge of phenomena of the sky and cosmos by the Saṃhitā. Each one of [the authors] Parāśara, Satya,64 Maṇittha,65 Jīvaśarman,66 Mau67 the Greek, composed a book [known as] Jātaka, namely book on nativity. Varāhamihira composed two books on this [topic], small and large68 and Balabhadra commented on it. I translated the smaller of the two into Arabic.69 On the topic on nativity, they have a large book called Sārāvalī,70 that is an anthology like the Pazīdaǧ71 which Kalyānavarman the king composed, and which reflects scientific excellence. A book, larger than this [one], which brings together all subjects related to astrology, is known as Yavana72 , i.e., belonging to the Greeks. And Varāhamihira composed small books, among which [one is] Ṣaṭpañcasikā,73 i.e., 56 subjects on interrogations, a book Horāpañcahatarā (?) also on this topic. Concerning journeys, [he has] books [entitled] Yogayātrā and the Tikanikayātrā,74 concerning marriage and wedding, a book Vivāhapaṭala,75 and concerning architecture … (lacuna). Then on zaǧr,76 omen and the like, there is 59 This refers to a kind of astrology which developed in Persia. The famous historian Ibn Khaldūn discusses this topic in his Muqaddima. It offers the interpretation of historical events, especially that of dynasties. This kind of astrology is absent in India, although a book of this kind is ascribed to “Kanaka al-Hindī.” 60 This genre is called praśna (lit. question) in Sanskrit. According to Pingree 1981: 101 ff it corresponds to the “catarchic astrology.” 61 For physiognomy (puruṣalakṣaṇa), see Zysk 2016. 62 On dream (svapna) Michio Yano has prepared an English translation, which has not been published yet, of the svapna chapter of the Atharvavedapariśiṣṭa. 63 This word corresponds to Sanskrit śākuna (literally omen), a prognostication by the behaviour of animals. According to Steingass (Arabic-English dictionary), the term zaǧr (Qk. P) refers to an omen based on the flight of birds, from the verbal root, zaǧara meaning “to take omen from birds’ flight.” 64 Satya is frequently quoted in Utpala’s commentary on the Bṛhajjātaka. See Pingree 1981: 83–84. 65 CESS: A4, 343. Maṇittha is a Greek. 66 Cf. CESS: A3, 70. Jīvaśarman is quoted by Varāhamhira in the Bṛhajjātaka 7.9 and 11.1. 67 Probably Maya who was regarded as the author of the Sūryasiddhānta. 68 Laghujātaka and Bṛhajjātaka, respectively. 69 In chapter 80 of the Taḥqīq, al-Bīrūnī offers translations of passages drawn from the Laghujātaka. See Arabic text, Taḥqīq (1958): 529–35 and Taḥqīq (1887): vol. 2, 225– 34. 70 For the Sālāvalī of Kalyānavarman, see CESS: A2, 26. 71 Persian word? h. YK Q.Ë@ 72 This is the Yavanajātaka, edited and translated by Pingree (1978). 73 Al-Bīrūnī is mistaken here. The author of Ṣaṭpañcasikā is Pṛthuyaśas, the son of Varāhamihira. See CESS: A4, 277 f; A5, 219 ff, and Pingree 1981: 110–11. 74 Both Yogayātrā and Tikanikayātrā are Varāhamihira’s works on expedition. It is surprising that al-Bīrūnī does not mention Bṛhadyātrā. 75 For Varāhamihira’s Vivāhapaṭala, see CESS: A5, 573. See also Sugita (2001). 76 See footnote 63. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 66 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 a book [entitled] Surūdava77 and it exists in three copies.78 One the them is attributed to Mahādeva.79 The author of the second [one] is Vimalabuddha,80 while that of the third [copy] is Baṅgāla.81 There [exists] a book, Cūḍāmaṇi,82 i.e., the science of the supernatural, composed by a Buddhist, an author who is a śramaṇa wearing a red garment, and a book, Praśna Cūrāmaṇi, i.e., questions on the science of the supernatural, which Utpala composed.83 Among their savants whose names are not handed down with [their] books, are: Pradyumna,84 Sangahil,85 Divākara,86 Pareśvara,87 Sārasvata,88 Pīruvāna,89 Devakīrti,90 and Pṛthūdakasvāmin.91 The science of medicine is like the science of stars except that it (i.e., astral science) is entangled with religion. And they have a book, known by [the name of] its author who is Caraka,92 and which they prefer among their books on medicine. [They] believe about him that he was a ṛṣi in the last Dvāpara [yuga] and that his name was Agniveśa. Later on, he was named Caraka, that is the intelligent [one], after he obtained medicine from the best children of Sūtra, who were ṛṣis. These [ṛṣis] received it from Indra and Indra received it from Aśvinī,93 one of the two physician devas, who received it from Prajāpati, who is Brahman the first father.94 This book was translated into Arabic for the Baramakids family.95 They have variety of several other sciences. You [can] hardly count [their] books, but I could not comprehend them by [my] knowledge. I wish I could translate the book Pañcatantra, which is known among us as the book Kalīla wa-Dimna. It moved to and fro between Persian and Indian [languages] and later on Arabic. The Persian [version comes] from the mouth of people whose alternation is not faithful to it (i.e., original version?), such as ʿAbd al-lāh ibn al-Muqaffaʿ by his addition of the chapter on “Barzūya” in [his version], aiming at awakening doubt 77 CESS: A4, 283, S.rū.dh.w (Sūtradhāra?).  K; Taḥqīq 78 Taḥqīq (1887): 75, l. 19 IÊ  K. (1958): 122, l. 14 HC 79 It is difficult to idenfity this person. 80 There is no entry for this person in CESS. 81 Nothing is known about Baṅgāla. 82 See CESS: A3, 52; Pingree (1981: 88). 83 CESS: A4, 283, where Praśnacūrāmaṇi = Āryasaptati which is again = Praśnajñāna = Bhuvanadīpikā = Jñānamālā (CESS: A4, 282). 84 Pradyumna is attested in S. Dvivedin (BSS) XI, 46 and 58. 85 There is no entry for Sangahil in CESS. 86 Divākara before al-Bīrūnī is not known. 87 There is no entry for Pareśvara in CESS. 88 Nothing is known about Sārasvata. 89 There is no entry for Pīruvāna in CESS. 90 There is no entry for Devakīrti in CESS. 91 For Pṛthūdakasvāmin, see CESS: A4, 221. His full name is Caturveda Pṛthūdakasvāmin (fl. 864). His commentary on S. Dvivedin (BSS) Chapter 21 (Chapter 1 according to al-Bīrūnī) was studied by Ikeyama (2003). Pṛthūdakasvāmin’s commentary on the Khaṇḍakhādyaka is edited and translated by Sengupta (1934). 92 For Caraka in the Islamic world, see Meulenbeld (1999–2002: 1A, 116).  ). 93 The Arabic text reads Aśvinī ( úGñƒ@ Aśvins are twins and regarded as the physicians of gods. 94 This episode is described in Caraksasaṃhitā 6.1.4.4. 95 On the Barmakids see van Bladel (2011). See also Sachau (1888: I, xxxi–xxxii; II, 313.). HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 67 of [people who are] weak in religious beliefs and at their breaking in order to call [them] up to the Manichean creed. If he is suspect regarding what he added, he is not free from the same regarding what he translated.96 96 The Sanskrit collection of fables, known as Pañcatantra, was translated into Pahlavi and Syriac in the mid-sixth century CE. It was transmitted into Arabic during the eighth century under the title Kalīla waDimna, which reflects the Sanskrit names of two important protagonists of the original stories, i.e., Karaṭaka and Damaṇaka. As al-Bīrūnī notices, the book Kalīla wa-Dimna was neither literal nor direct translation of the Pañcatantra. ‘Abd Allah Ibn al-Muqaffa฀ (ca. 720–756), on the basis of the Pahlavi text, made some modifications in his Arabic translation of it (Brockelmann 2012; Gabrieli 2012). HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 68 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 AP P ENDIX : CO NTENTS O F THE BRĀHMASPHUṬASI DDHĀNTA Al-Bīrūnī’s Taḥqīq Dvivedin’s edition  È@ñk @ ú¯ (1) PB@ð ZA҂Ë@ éJJëð èQºË@  QÓð I» @ñºË@ P@ð X @ ú¯ (2) h. @QjJƒ@ @ éJÓPB@ éËð@ .   @ ú愮Ë@ H. ñJm.Ì '@ð I.»@ñºË@ HAƒð   I.»@ñºË@ Õç' ñ®K ú¯ (3)       úæ•AÖÏ @ð É¢Ë@ ùë úæË@ IKCJË@ éË@ñƒ B@ ú¯ (4) ‘ªK. áÓ AîD”ªK. h. @QjJƒ@ð ©ËA¢Ë@ð PAîDË@ áÓ  ¨Aªƒ áÓ I.» @ñºË@ Pñê£ ú¯ (5) éK. AîEA®Jk@ð Ò‚Ë@ éJKQ¯ ÈAgð ÈCêË@ éK ðP ú¯ (6)  ¬ñ‚» ú¯ (7) QÒ®Ë@  ¬ñ‚» ú¯ (8) Ò‚Ë@  É £ ú¯ (9) QÒ®Ë@ AîE@Q¯@ ð I.»@ñºË@ ¨AÒJk. @ ú¯ (10) I.» @ñºË@ ðQ« ú¯ (11)    Õ殂Ë@ áÓ iJj’Ë@ QJÖßð HAm.' QË@ð I.JºË@ ú¯ AÓ XA® JK@ ú¯ (12)  Ï @ ú¯ éJËð@QÓð H. A‚mÌ '@ ú¯ (13) AëQ«ð HAgA‚Ö I.»@ñºË@ Aƒð @ ‡J ®m ' ú¯ (14) I.»@ñºË@ Õç' ñ® K ‡J ®m ' ú¯ (15)  éJËAJË@ éËñƒB@ ‡J ®m ' ú¯ (16)  ¯@Qm' @ ú¯ (17) ¬ñ‚ºË@ HA  ÈCêË@ éK ðP ‡J ®m ' ú¯ (18) éJKQ¯ð     . B@ éJ.‚  úæªÓ úΫ †YË@ †YK ñëð ½J» ú¯ (19) . I.Ê¢Ë@ ú¯ XAîDk  A®Ö Ï @ð QmÌ '@ ú¯ ñëð áëYË@ éJÓ h QjJ‚ AÓ  KQ®Ö Ï AK. éÊK HA . .. . éK XY« Qk @ IËA¢Ó ú¯ð .  É¢Ë@ PñÓ@ ú¯ (20)  à@Pð @ HAK  . A‚k ú¯ (21) é“ðQ«ð Qª‚Ë@  HBB@ QK@ð YË@ ú¯ (22) éªK P B@ QK XA®Ö Ï @ð àAÓP B@ ú¯ (23) .   ¢JÖÏ @ ÈCg ú¯ ÐA¯P B@ð X@Y« B@ HAÓC« ú¯ (24) HAÓñ  Aë XAëQÂJëX (25) (21) golādhyāya (1) madhyamādhikāra (2) spaṣṭādhikāra (3) tripraśnādhikāra (6) udayāstādhikāra (7) candraśṛṅgonnatyādhikāra (4)candragrahaṇādhikāra (5) sūryagrahaṇādhikāra (8) candracchāyādhikāra (9) grahayutyadhikāra (10) bhagrahayutyadhikāra (11) tantraparīkṣādhyāya (12) gaṇitādhyāya (13) madhyagatyuttarādhyāya (14) sphuṭagatyuttarādhyāya (15) tripraśnottarādhyāya (16) grahaṇottarādhyāya (17) śṛṅgonnatyuttarādhyāya (18) kuṭṭakādhyāya (19) śaṅkucchāyādijñānādhyāya (20) chandaścityuttarādhyāya (22) yantrādhyāya (23) mānādhyāya (24) saṃjñādhyāya (25) dhyānagrahopadeśādhyāya HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 69 GENERAL COMMENTS The sequence of the chapters found in al-Bīrūnī’s work differs from that of Dvivedin’s edition. His chapter 1 corresponds to chapter 21 in Dvivedin. His chapters 2 to 4, correspond to chapters 1 to 3 of Dvivedin’s. His chapters 5 and 6 correspond to chapters 6 and 7 in Dvivedin respectively, while his chapters 7 and 8 are Divedin’s chapters 4 and 5. From al-Bīrūnī’s chapters 9 to 21, the chapter numbers correspond to Dvivedin’s 8 to 20. Chapters 22 to 25 in Arabic and Sanskrit exactly correspond. In chapter 14 of the Taḥqīq, al-Bīrūnī explains that he did “not have any copy [of them] (i.e., Siddhānta), except the ones by Pulisa and by Brahmagupta.” The extent to which he could actually access Brahmagupta’s work or parts of it is uncertain. Indeed, in the preceding chapter of the Taḥqīq, dealing with grammar and metrical science, al-Bīrūnī states the following:97 I have not studied a thing about them (i.e., books on metrical science), nor about most of the chapter in the Brāhmasiddhānta which deals with the calculation of [metrical science]  ®Ö Ï @ áÓ QJ» úΫ Bð AîDÓ Zúæ úΫ ©Ê£ @ ÕËð  éËA ú¯ YKAëYƒ Ñë@QK. ú¯ úæË@ AîE. A‚k He also makes this striking comment:98 I have only read one leaf of the afore-mentioned chapter (i.e., in the Brāhmasiddhānta) and this [chapter] most certainly contains precious things, as principles related to numbers  J‚Ó  × B ùëð èYg@ð é¯Pð  B @ èPñ»YÖÏ @ éÊ ®Ö Ï @ áÓ ©ËA£ @ ÕËð  éËAm úΫ éÊÒ éK XYªË@ Èñ“B@ áÓ A®K The discrepancy in the arrangement of chapters may be due to a difference of textual transmission, but if al-Bīrūnī did not read the whole manuscript, then the oral commentary by his Indian informants may also account for this difference. Whereas there is evidence that he frequently adapted his Sanskrit sources when rendering them into Arabic, in case of enumerations he adds explanations but does not generally change the sequence of listed items.99 97 Taḥqīq (1958): 106, 1888: I, 137–38. 98 Taḥqīq (1958): 117, 1888: I, 150–51. ll. 14–15, Sachau ll. 12–14, Sachau 99 See Maas and Verdon (2018: 315–28) on al-Bīrūnī’s interpretative choices and Verdon (2020) on his way of dealing with lists. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 70 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 Thus, there is little chance that this difference results from al-Bīrūnī’s own reworking. Further, so far, only one manuscript and one edition of Sanskrit exist of the Brāhmasphuṭasiddhānta.100 This difference, then, may imply that the text which he accessed was different in some respects from that which has been transmitted to us. In addition to this main discrepancy, al-Bīrūnī complemented some chapters’ titles with explanations of their content. On the whole, however, his translation is rather true to the original subject matter. We provide below specific comments on al-Bīrūnī’s wording, as compared to the Sanskrit list: Taḥqīq 1: Al-Bīrūnī paraphrases the original title by explaining that sphere (Skt.   ) is both celestial and terrestrial. gola; Ar. èQ» Taḥqīq 2: Al-Bīrūnī provides more details about the content of the chapter. Taḥqīq 3: Al-Bīrūnī does not give a literal translation but refers in his title to the mathematical operation through which the mean planet becomes its apparent position. Taḥqīq 4 and 5: Al-Bīrūnī provides with a paraphrase. Taḥqīq 11: Al-Bīrūnī uses the term latitude ( ðQ«) in the title; which shows that he understood its content, because the conjunction of planet and nakṣatra implies this calculation. This title also indicates the two possible translations of the Arabic term kawākib ( I . » @ñ») as planets or stars. Taḥqīq 12: Al-Bīrūnī paraphrases here the original Sanskrit title and differen  .' P). tiates between books ( I . J») and astronomical tables, or Zīğes ( HAm The Sanskrit titles, from this chapter onward, contain the word adhyāya (chapter) instead of adhikāra (section). The reasons for this change are unclear. Taḥqīq 13: Al-Bīrūnī refers to the Sanskrit kṣetragaṇita (lit. calculation of plane  Ï @). figures), by the term plane geometry HAgA‚Ö   Taḥqīq 14: Al-Bīrūnī translates uttara by the Arabic ‡J®m'. The Sanskrit term signifies either “second part” or “correction” in different contexts. In the Sanskrit corresponding chapter (Dvivedin 13), Brahmagupta provides a correction of the computation of mean planets which was given in his chapter 1 (Taḥqīq 2; Dvivedin 1).   Taḥqīq 17: Al-Bīrūnī does not translate the term correction by ‡J®m' here, which raises the question of whether this difference in the titles reflects a difference in the chapter’s content. Taḥqīq 19: It is the only place in this list where al-Bīrūnī transliterates the Sanskrit term into Arabic. However, he could not provide an Arabic translation of this title, which refers to a specific algorithm developed by Indian mathematicians/astronomers. Instead, he explains it as meaning, 100 There is a printed edition by Śarmā et al. (1966), but it is totally based on the edition by S. Dvivedin (BSS). HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 71 pounding, i.e., the endeavour to search for the minute [things],   from which oil is extracted. This is about algebra ( éÊK. A®ÖÏ @ð Q.m.Ì '@, by “putting together in search of other numbers.” Al-Bīrūnī appears to first provide his readers with an etymological explanation, and subsequently with a mathematical one. Taḥqīq 21: The content of this chapter in Sanskrit dealing with chandas, or metrical science, is very obscure and difficult to understand. Al-Bīrūnī deals with chandas in chapter 13 of the Taḥqīq.101 Taḥqīq 22: Rings ( QK@ð X) or armillary spheres were used for demonstrations,  ) for observations. while instruments ( HB@ Taḥqīq 23: Al-Bīrūnī lists the four measures of time as follows: solar, civil, lunar, and of the mansions ( úÍ PAJÓ), i.e., of the nakṣatras. He knew well about them, as he discussed them separately in Al-āṯār al-bāqiya,102 the Tafhīm103 and the Taḥqīq.104 Taḥqīq 24: The title of this chapter in the edition of S. Dvivedin (BSS) is Saṃjñādhyāya, or “Chapter on the technical terms.” But in this chapter, consisting of only 13 verses, Brahmagupta gives a summary of the second part of the Brāhmasphuṭasiddhānta and therefore this chapter is a kind of colophon. Thus al-Bīrūnī’s title is misleading. 101 Taḥqīq (1958): 105, l. 17–117 l. 18, Sachau 1888: I, 136–52. 102 Sachau 1878: 13, ll. 4–10; 1879: 15. 103 Wright 1934: 169. 104 Taḥqīq (1958): 297, l. 9–299 l. 17, Sachau 1888: I, 353–56. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 72 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 ABBREVIATIO NS Brahmasiddhānta Dvivedin, V. P. (1912) (ed.), Brahmasiddhānta in Jyautiṣasiddhāntasaṃgrahaḥ tatra Pitāmahasiddhāntaḥ, Vṛddhavasiṣṭhasiddhāntaś ca (Benares Sanskrit Series, 154; Benares: Braj Bhushan Das & Co.), 1–79, http://n2t.net/ark:/13960/ t6353t221; the last work in the compendium. BSS Dvivedin, S. (1901–2) (ed.), Brāhmasphuṭasiddhānto Dhyānagrahopadeśādhyāyaś ca, GaṇakacakracūḍāmaṇiSrīBrahmaguptaviracitaḥ = Brāhmasphuṭasiddhānta and Dhyānagrahopadeśādhyāya by Brahmagupta (The Pandit, New Series, 23 and 24; Benares: Medical Hall Press), http://n2t.net/ark:/13960/ t9f50913n. CESS Pingree, D. E. (1970–94), A Census of the Exact Sciences in Sanskrit, 5 vols. (Philadelphia: American Philosophical Society), http://n2t.net/ark:/13960/t4dp0cq1z, (on 9 Mar. 2018). Taḥqīq (1887) Sachau, C. E. (1887), Albêrûni’s India: An Account of the Religion, Philosophy, Literature, Geography, Chronology, Astronomy, Customs, Laws and Astrology of India about A.D. 1030. Edited in the Arabic Original (London: Trübner & Co.), https://gallica .bnf.fr/ark:/12148/bpt6k8538742. Taḥqīq (1958) Bureau of Osmania Oriental Publications (1958) (ed.), Kitāb al-Bīrūnī fī taḥqīq mā li-l-Hind min maqūla maqbūla fī l-ʿaql aw marḏūla = Kitāb fī Taḥqīq-ī-Mā li’l-Hind or Al-Bīrūnī’s India (Arabic Text) … Revised by the Bureau from the Oldest Extant MS. in the Bibliotheque Nationale, Paris [Schefer 680] (Da’irat al-Ma’arif il-Osmania Publications, 11; Hyderabad: Da’irat al-Ma’arif il-Osmania Publications, Osmania University), http://n2t.net/ark:/13960/t5w66sf79, (on 9 Jan. 2020). REFERENCES Ācārya, Y. T. (1941) (ed.), Maharṣiṇā Punarvasunopadiṣṭā, Tacchiṣyeṇāgniveśena Praṇītā, Carakadṛḍhabalābhyāṃ Pratisaṃskṛtā Carakasaṃhitā, Śrīcakrapāṇidattaviracitayā Āyurvedadīpikāvyākhyayā Saṃvalitā (3rd edn., Mumbayyāṃ: Nirnaya Sagara Press), http://n2t.net/ark:/13960/t48q2f20n, (on 1 Jan. 2018). HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 73 Baloch, N. A. (1973), Ghurrat al-Zijat or Karana Tilaka. A Handbook of Astronomy by Bijayanand of Benares. Translated from the Original into Arabic with an Exposition of the underlying Principles by Abu Raihān Muhammad b. Ahman al-Beruni (University of Sind: Sind). Bhattacharyya, N. N. (1991), The Geographical Dictionary of Ancient and Early Medieval India (1999 reprint, Delhi: Munshiram Manoharlal). Boilot, J.-D. (1955), ‘L’oeuvre d’al-Beruni: essai bibliographique’’, Mélanges de l’institut dominicain d’études orientales du Caire, 2: 161–256. Bosworth, C. E. and Minorsky, V. (1937), Ḥudūd al-ʿālam, The Regions of the World. A Persian Geography. 372 A.H. (982 A.D.). Translated and explained by V. Minorsky (1970 reprint, London: Luzac & Co.). Brockelmann, C. (2012), ‘Kalīla Wa-Dimna’, Encyclopaedia of Islam, Second Edition, ed. P. Bearman, T. Bianquis, C. Bosworth, E. van Donzel, and W. P. Heinrichs (Leiden: Brill), ISBN: 9789004161214. DOI: 10.1163/1573-3912_islam_COM _0427, (on 1 Nov. 2019). Bureau of Osmania Oriental Publications (1958) (ed.), Kitāb al-Bīrūnī fī taḥqīq mā li-l-Hind min maqūla maqbūla fī l-ʿaql aw marḏūla = Kitāb fī Taḥqīq-ī-Mā li’lHind or Al-Bīrūnī’s India (Arabic Text) … Revised by the Bureau from the Oldest Extant MS. in the Bibliotheque Nationale, Paris [Schefer 680] (Da’irat al-Ma’arif il-Osmania Publications, 11; Hyderabad: Da’irat al-Ma’arif il-Osmania Publications, Osmania University), http://n2t.net/ark:/13960/t5w66sf79, (on 9 Jan. 2020). Dey, N. L. (1927), The Geographical Dictionary of Ancient and Mediaeval India (Calcutta Oriental Series, 21.E.13; 2nd edn., London: Luzac & Co.), http://n2t .net/ark:/13960/t6c28s09f. Dvivedin, S. (1895–7) (ed.), Bṛhatsaṃhitā Śrī 6 Varāhamihirapraṇītāṃ. Śrī Bhaṭṭotpalakṛtavivṛtisahitā (Vizianagram Sanskrit Series, 12; Kāśı ̄: E. J. Lazarus & Co.), http://n2t.net/ark:/13960/t6xw9sc33, (on 13 Oct. 2019); Vol. 2 at: http://n2t.net/ark:/13960/t9m382x4s. — (1901–2) (ed.), Brāhmasphuṭasiddhānto Dhyānagrahopadeśādhyāyaś ca, GaṇakacakracūḍāmaṇiSrīBrahmaguptaviracitaḥ = Brāhmasphuṭasiddhānta and Dhyānagrahopadeśādhyāya by Brahmagupta (The Pandit, New Series, 23 and 24; Benares: Medical Hall Press), http://n2t.net/ark:/13960/t9f50913n. Dvivedin, V. P. (1912) (ed.), Brahmasiddhānta in Jyautiṣasiddhāntasaṃgrahaḥ tatra Pitāmahasiddhāntaḥ, Vṛddhavasiṣṭhasiddhāntaś ca (Benares Sanskrit Series, 154; Benares: Braj Bhushan Das & Co.), 1–79, http :// n2t . net / ark :/ 13960 / t6353t221; the last work in the compendium. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 74 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 Gabrieli, F. (2012), ‘Ibn al-Muḳ affaʿ’, Encyclopaedia of Islam, Second Edition, ed. P. Bearman, T. Bianquis, C. Bosworth, E. van Donzel, and W. P. Heinrichs (Leiden: Brill), ISBN: 9789004161214. DOI: 10.1163/1573-3912_islam_SIM _3304, (on 1 Nov. 2019). Geslani, M., Mak, B., Yano, M., and Zysk, K. G. (2017), ‘Garga and Early Astral Science in India’, History of Science in South Asia, 5/1: 151–91. DOI: 10.18732/ h2nd44. Ikeyama, S. (2002), ‘Brāhmasphuṭasiddhānta Ch. 21 with the Commentary of Pṛthūdaka’, PhD (Brown University). — (2003), ‘Brāhmasphuṭasiddhānta (Ch. 21) of Brahmagupta with the Commentary of Pṛthūdaka. Critically Edited with English Translation and Notes’, Indian Journal of History of Science, 38: 38(1), 1–74, 38(2), 75–152, 38(3), 153– 236, 38(4), 237–308; Supplement. Kennedy, E. S. (1956), ‘A Survey of Islamic Astronomical Tables’, Transactions of the American Philosophical Society, 46/2: 123–77. DOI: 10.2307/1005726. — (1970), ‘Al-Bīrūnī’, in C. C. Gillispie, F. L. Holmes, et al. (eds.), Dictionary of Scientific Biography, ii (New York: Charles Scribner’s Sons), 147–58. Lane, E. W. (1863–93), An Arabic-English Lexicon, 8 vols. (reprint 1968, Beirut: Librarie du Liban), http://n2t.net/ark:/13960/t60585z2s, (on 16 Apr. 2020). Larson, G. J. and Bhattacharya, R. S. (2008), Yoga: India’s Philosophy of Meditation (Encyclopedia of Indian Philosophies, 12; Delhi: Motilal Banarsidass), ISBN: 9788120833494, http://n2t.net/ark:/13960/t6f27jv0n, (on 14 May 2020). Maas, P. A. and Verdon, N. (2018), ‘On al-Bīrūnī’s Kitāb Pātaǧal and the Pātañjalayogaśāstra’, in K. Baier, P. A. Maas, and K. Preisendanz (eds.), Yoga in Transformation: Historical and Contemporary Perspectives (Göttingen: Vienna University Press through V & R Press), 283–334, ISBN: 384710862X. DOI: 10.14220/ 9783737008624. Meulenbeld, G. J. (1999–2002), A History of Indian Medical Literature, 5 vols. (Groningen: E. Forsten), ISBN: 9069801248. Neugebauer, O. and Pingree, D. E. (1970–1), The Pañcasiddhāntikā of Varāhamihira, trans. D. Pingree (Det Kongelige Danske Videnskabernes Selskab; København: Munksgaard), https://archive.org/details/pancasiddhantika1 _1970, (on 16 Apr. 2020). Pingree, D. E. (1969), ‘The Later Pauliśasiddhānta’, Centaurus, 14/1: 172–241. DOI: 10.1111/j.1600-0498.1969.tb00142.x. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 NOÉMIE VERDON AND MICHIO YANO 75 — (1970–94), A Census of the Exact Sciences in Sanskrit, 5 vols. (Philadelphia: American Philosophical Society), http://n2t.net/ark:/13960/t4dp0cq1z, (on 9 Mar. 2018). — (1981), Jyotiḥśāstra: Astral and Mathematical Literature (A History of Indian Literature, 6.4; Wiesbaden: Harrassowitz), http://n2t.net/ark:/13960/ t9h49pm8x, (on 16 Apr. 2020). — (1983), ‘Brahmagupta, Balabhadra, Pṛthūdaka and Al-Bīrūnī’, Journal of the American Oriental Society, 103/2: 353–60. DOI: 10.2307/601457. Pingree, D. E. (1978) (ed.), The Yavanajataka of Sphujidhvaja (Harvard Oriental Series; Cambridge, MA: Harvard University Press), ISBN: 9780674963733, https://archive.org/details/PingreeYJ, (on 21 Aug. 2018). Sachau, C. E. (1878) (ed.), Al-āṯār al-bāqiya ʿan il-qurūn al-ḫāliya. Taʾlīf Abī al-Rayḥān Muḥammad ibn Aḥmad al-Bīrūnī al-Khawārizmī. Chronologie orientalischer Völker von Alberuni herausgegeben von Dr. C. Eduard Sachau (Leipzig: F. A. Brockhaus). — (1879), The Chronology of Ancient Nations. An English Version of the Arabic text of the Athâr-ul-Bâkiya of Al-Bîrûnî or “Vestiges of the past” (London: W. H. Allen & Co.), http://n2t.net/ark:/13960/t3zs37k3b. — (1887), Albêrûni’s India: An Account of the Religion, Philosophy, Literature, Geography, Chronology, Astronomy, Customs, Laws and Astrology of India about A.D. 1030. Edited in the Arabic Original (London: Trübner & Co.), https://gallica .bnf.fr/ark:/12148/bpt6k8538742. — (1888), Alberuni’s India: An Account of the Religion, Philosophy, Literature, Geography, Chronology, Astronomy, Customs, Laws and Astrology of India about AD 1030. An English Edition with Notes and Indices, 2 vols. (London: Trübner and Co.), http://n2t.net/ark:/13960/t8hf2hw55, (on 9 Jan. 2020). Śarmā, R. et al. (1966) (eds.), Śrībrahmaguptācārya-viracita Brāhmasphuṭasiddhāntaḥ (Delhi: Indian Institute of Astronomical and Sanskrit Research), https:// tinyurl.com/sharma1966, (on 18 Apr. 2020). Sengupta, P. (1934), ŚrīmadBrahmaguptakṛtaṃ Khaṇḍakhādyakaṃ Karaṇam = The Khaṇḍakhādyaka, an Astronomical Treatise of Brahmagupta with the Commentary of Caturveda Pṛthūdaka Svāmin (Calcutta: University of Calcutta). Shukla, K. S. (1985–6), Edition and English Translation of the Vaṭeśvara-Siddhānta and Gola of Vaṭeśvara Critically Edited with English Translation and Commentary, New Delhi, http://n2t.net/ark:/13960/t33227612; Vol. 2 at http://n2t.net/ ark:/13960/t7kq0931s. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 76 AL-BĪRŪNĪ’S INDIA, CHAPTER 14 Shukla, K. S. (1990), A Critical Study of the Laghumānasa of Mañjula (New Delhi: Indian National Science Academy); Also published as a supplement to the Indian Journal of History of Science 1990 (25). Sugita, M. (2001), ‘Varāhamihira’s Vivāhapaṭala – An attempt of Reconstruction from the Cintāmaṇi and its Translation’, ZINBUN 35: 73–120. Van Bladel, K. T. (2011), ‘The Bactrian Background of the Barmakids’, in A. Akasoy, C. Burnett, and R. Yoeli-Tlalim (eds.), Islam and Tibet: Interactions along the Musk Routes (Farnham: Ashgate), chap. 3, 43–88, https://academia.edu/5857685. Verdon, N. (2020), Al-Bīrūnī’s Kitāb Sānk and Kitāb Pātanğal: A Historical and Textual Study (Vienna: De Nobili Research Library) (forthcoming). Wright, R. R. (1934) (trans.), The Book of Instruction in the Elements of the Art of Astrology by Abū’l-Rayḥān Muḥammad ibn Aḥmad al-Bīrūnī. Written in Ghaznah, 1029 A.D.. Reproduced from Brit. Mus. MS. Or. 8349 (London: Luzac & Co), http://n2t.net/ark:/13960/t4nk85m6q. Zysk, K. G. (2016), The Indian System of Human Marks, 2 vols. (Leiden: Brill), ISBN: 978-90-04-29982-5. DOI: 10.1163/9789004299825. HISTORY OF SCIENCE IN SOUTH ASIA 8 (2020) 57–76 Please write to ⟨wujastyk@ualberta.ca⟩ to file bugs/problem reports, feature requests and to get involved. The History of Science in South Asia • Department of History and Classics, 2–81 HM Tory Building, University of Alberta, Edmonton, AB, T6G 2H4, Canada.