PREFACE VII by supplying copies of the manuscripts of Pañcasiddhāntikā available with them. For the beautiful printing and nice get-up, thanks are due to Ms. Printers Plates, one of the leading presses of Madras. The PPST Foundation, Madras, an organisation set up for the popularisation of Indian sciences, has kindly undertaken the responsibility for the distribution of this publication. Last but not least, my grateful thanks are due to Prof. K.S. Shukla and Shri. S. Hariharan, who, besides making their personal contribution to the volume, had been available for reference and advice at all stages of the work on the present edition of the Pañcasiddhāntikā. Madras, January 4, 1993 K.V. SARMA

CONTENTS Page PREFACE V CONTENTS IX INTRODUCTION XIII Introductory – Source Material – Presentation of the Text – Translation – Notes – Division of Pañcasiddhāntikā – Ch. XVIII of Pañcasiddhāntikā – The Five Siddhāntas in PS : Their distribu- tion – Content analysis of the Pañcasiddhāntikā – Depiction of the Siddhāntas in the PS – Compara- tive study of the Siddhāntas -- Varāhamihira : His life and works. Page Ch.I. INTRODUCTION OF THE WORK Aim of the Work (verses 1-2) 1 The Five Schools of Astronomy (3-4) 4 Contents of the Work (5-7) 5 Days from Epoch : Romaka (8-10) 6 Days from Epoch : Pauliśa (11-13) 11 Yuga of the Sun and the Moon: Romaka and Saura (14-16) 15 Lord of the year (17-18) 18 Lord of the Month (19) 20 Lord of the Horā etc. (20-25) 20 Names of the 30 days of the Parsi months 24 Ch.II. VĀSIṢṬHA-SIDDHĀNTA : PLANETARY COMPUTATIONS ETC. Introductory 25 True Sun (1) 25 True Moon (2-4) 27 Nakṣatra and Tithi (7) 33 Day-time (8) 34 Gnomonic Shadow (9-10) 35 Lagna from shadow and vice versa (11-13) 37 Ch.III. PAULIŚA-SIDDHĀNTA : PLANETARY COMPUTATION ETC. Introductory 40 True Sun (1-3) 40 True Motion of Moon (5) 45 Equation of the centre (5-9) 47 Cara or Oblique ascension (10) 48 Day-time (11-12) 50 Deśāntara (13-14) 51 Page Local Sunset time (15) 53 Nakṣatra computation (16) 54 Sun’s daily motion (17) 56 Karaṇas (18-19) 57 Vyatīpāta and Vaidhṛta (20-22) 58 Ṣaḍaśīti-puṇyakāla (23-24) 64 Solstices (25) 65 Saṅkrānti-kāla (26) 65 Tridinaspṛg-yoga (27) 66 Rāhu (Node) (28-29) 67 Moon’s latitude (30-31) 69 Defect in Bhadraviṣṇu (32) 71 Defect in Pādāditya (33) 71 Defect in Romaka (34-37) 71 Ch.IV. THREE PROBLEMS : TIME, PLACE AND DIRECTION Introductory 76 Table of R Sines (1-15) 76 Declination of the Sun and the Moon (16-18) 87 Gnomonic shadow (19) 90 Latitude from Shadow (20-21) 91 Sine zenith distance (22) 95 Sine Co-latitude and Day-diameter (23-25) 96 Cara or Oblique Ascension (26) 98 Latitude from Cara (27-28) 100 Rt. ascensional difference (29-30) 102 Rising Signs (31) 104 Time to reach the Prime vertical (32-34) 106 Great gnomon (Sama-śaṅku) and its shadow (35) 110

X CONTENTS Page Page Astronomer's qualifications (36-37) 112 True Sun (1-3) 181 Gnomonic shadow and the prime True Moon (4-6) 183 vertical (38) 113 Daily motion of the Sun and the Moon (7) 185 Agrā : Sine amplitude (39) 113 Rāhu (8) 186 Latitude from Agrā (40) 114 Parallax in longitude (9) 187 Shadow at desired time (41-44) 115 Declination of the Nonagesimal (10-12) 187 Time after sunrise (45-47) 118 Parallax correction and orbital Time for Sunset (48) 121 diameter (13-14) 189 Shadow from time (49) 122 True diameter of the orbs (15) 191 Moon's shadow (50-51) 123 Moment of the eclipse (16) 192 Directions from shadow (52-54) 126 Eclipse diagram (17-18) 192 Sun from shadow (55-56) 132 Ch.V. PAULIŚA-SIDDHĀNTA : Ch.IX. SAURA-SIDDHĀNTA : MOON'S CUSPS SOLAR ECLIPSE Introductory 137 Introductory 197 Time of Moon's visibility (1-3) 137 Mean Sun (1) 197 Diagram of the Moon's cusps (4-7) 143 Mean Moon (2-4) 198 Daily rising and setting of the Rāhu : Maximum latitude (5-6) 201 Moon (8-10) 147 True Sun and Moon (7-9) 203 Epicyclic theory 206 Ch.VI. (VĀSIṢṬHA-) PAULIŚA- Bhujāntara correction 209 SIDDHĀNTA : LUNAR ECLIPSE Udayāntara correction 209 Introductory 152 Deśāntara correction (10) 209 Sun and Moon of equal longitude (1) 152 Mean motion of the Sun and the Moon (11) 210 Probability of an eclipse (2) 154 Motion of Moon's anomaly (12) 211 Duration of the eclipse (3-4) 156 True motion of Sun and Moon (13-14) 211 Total obscuration (5) 160 Kakṣā of the Sun and the Moon (15) 214 Direction of the eclipse (6-8) 162 Measure of the orbs (16) 215 Moment of the eclipse and its Sin Zenith Distance of Meridian colour (8-10) 165 point (17-18) 216 Diagrammatic representation (11-13) 168 Dṛkṣepa of the Sun (19-20) 219 Lunar and Solar eclipses – Gnomon (21) 220 Differences (14) 171 Parallax-corrected New Moon (22-23) 221 Parallax in latitude (24-25) 223 Ch.VII. (PAULIŚA-SIDDHĀNTA) : Duration of the eclipse (26-27) 225 SOLAR ECLIPSE Introductory 172 Ch.X. SAURA-SIDDHĀNTA : Parallax of longitude (1) 172 LUNAR ECLIPSE Parallax in latitude (2-4) 176 Eclipse computation (5-6) 178 Introduction 228 Diameter of the Shadow (1-2a) 228 Ch.VIII. ROMAKA-SIDDHĀNTA : Duration of the Eclipse (2b-4) 230 SOLAR ECLIPSE Obscuration at any desired moment (5-6) 232 Introductory 181 Time of total obscuration (7) 235

CONTENTS XI Page Ch.XI. ECLIPSE DIAGRAM Introduction 236 Marking the ecliptic etc. (1-3) 236 Marking of points of contact etc. (4-5) 238 Conversion of minutes into angles (6) 240 Ch.XII. PAITĀMAHA SIDDHĀNTA Introduction 241 Days from Epoch (1-2) 241 Tithi, Nakṣatra etc. (3) 243 Vyatīpāta (4) 244 Duration of a day (5) 246 Ch.XIII. SITUATION OF THE EARTH: COSMOGONY Situation of the earth (1-4) 248 Rotation of the earth (5-8) 249 Situation of the Gods and Asuras (9-13) 250 Signs and Yojanas (14-16) 252 Position of Laṅkā and Ujjayinī (17) 253 Measures of the earth etc. (18-19) 253 Visibility of the Sun (20-29) 253 Astronomical observation (30-34) 258 Moon’s visibility (35-38) 258 The Planets and their situation (39-41) 259 Lords of the Months, Days and Year (42) 260 Ch.XIV. GRAPHICAL METHODS AND ASTRONOMICAL INSTRUMENTS Introductory 261 Ascensional differences of the zodiacal signs (1-4) 261 R sine of the Sun’s zenith distance for the given time (5-6) 264 Right ascensions of the signs (7) 266 Gnomon (8) 267 Local latitude (from the equinoctial midday shadow) (9-10a) 267 Sun’s longitude (10b-11) 268 V-Shaped yaṣṭi (12) 269 Moon’s longitude (13) 269 Cardinal directions (by means of a gnomon (14-16) 270 Page The Celestial Sphere (17-18) 270 Hemispherical Bowl and its use (19-20) 271 Hoop and its use (21-22) 272 Armillary Sphere (23-25) 273 Sun’s northward and southward journeys (26) 273 Instruments for measuring time (27-28) 274 Local longitude in terms of time (29-30) 274 The Nādī or Ghaṭī (31-32) 275 Conjunction of the Moon with a Star (33) 276 Positions of certain Junction- Stars (34-37) 277 Digits between the Moon and a Star in Conjunction and Time of Conjunction (38) 277 Heliacal Rising of Canopus (39-41) 278 Ch.XV. SECRETS OF ASTRONOMY Eclipses (1-10) 282 Situation at the Poles (11-16) 286 Weekday (17-18) 288 Day-reckoning (19-29) 289 Ch.XVI. SAURA SIDDHĀNTA : MEAN PLANETS Introductory 292 Mean positions of the Star-planets (1-19) 293 VM’s Bīja corrections (10-11) 298 Ch.XVII. SAURA-SIDDHĀNTA : TRUE PLANETS Epicycles of the planets (1-3) 300 True planets (4-9) 301 Special work for Mercury and Venus (10-11a) 307 Retrograde motion (11b) 309 Heliacal rising (12) 309 Latitudes of planets (13-14) 310 Ch.XVIII. VĀS.-PAU. SIDDH.: RISING AND SETTING OF PLANETS Venus (1-5) 312 Jupiter (6-13) 316 Saturn (14-20) 322 Mars (21-35) 339

XII CONTENTS Page Page Mercury (35-36) 341 True Saturn (79-81) 363 Hints (57-60) 351 General (61-63) 353 APPENDICES I. Verse Index 367 SPURIOUS SUPPLEMENT : II. Index of PS verses quoted by later TRUE PLANETS astronomers 371 III. Bhūtasaṅkhyā used in the PS 372 Introduction (64-66) 355 IV. Index of Places, Persons and Texts True Mars (67-69) 357 quoted in the PS 373 True Mercury (70-72) 359 V. Bibliography 374 True Jupiter (73-75) 361 VI. Subject Index 377 True Venus (76-78) 362 VII. Śaka and Samvatsara , time of Varāhamihira etc 383

INTRODUCTION

1. Introductory The Pañcasiddhāntikā (PS) of Varāhamihira (VM), (6th cent. A.D.), occupies an important place in the history of early Indian astronomy, for, herein we have been given certain aspects of five sys- tems of Indian astronomy current during the first centuries of the Christian era. The work supplies also considerable additional material on the astronomical concepts, computational methods and instruments used during the times of the author. VM makes mention of the objectives of the work towards its commencement: pūrvācāryamatebhyo yad yad śreṣṭhaṁ laghu sphuṭaṁ bījam | tat tad ihāvikalam aham rahasyam udyato vaktum || I.1 || Pauliśa-Romaka-Vāsiṣṭha-Saura-Paitāmahās tu pañca siddhāntāḥ || 2 || ‘Here, I shall state in full the best of the secret lore of astronomy extracted from the different schools of the ancient teachers so as to be easy and clear. ‘The five siddhānta-s, of which this work is a compendium, are the Pauliśa, the Romaka, the Vāsiṣṭha, the Saura and the Paitāmaha. Following the above statement, VM specifies also how he is intending to deal with the said five astronomical schools : yat tat param rahasyaṁ bhavati matir yatra tantrakārāṇām | tad aham apahāya matsaram asmin vakṣye grahaṁ bhānoḥ || dik-sthiti-vimarda-karṇa-pramāṇa-velā grahāgrahāv indoḥ | tārāgrahasaṁyogam deśāntarasādhanaṁ cā ‘smin || samamaṇḍala-candrodaya-yantra-cchedyāni śaṅkavacchāyā | upakaraṇādy akṣajyā-‘valambakā-’ pakramādyāni || I.5-7 || ‘I shall tell in this work, avoiding all jealousy, the computation of the solar eclipse which is guarded as a great secret and in which the mind of the astronomer reels. I shall also tell the occurr- ence or non-occurrence of the lunar eclipse, the directions of the first and last contacts, the dura- tion, the total phase, the ‘hypotenuse’ at any moment with related quantity of obscuration and time, and also the mutual conjunctions of the stars and the planets and the computation of difference in longitude as also the prime vertical, moonrise, astronomical instruments and other requirements, graphical representations, the gnomonic shadow, the sines of latitude, co-latitude and declinations and such other matters.’ While the importance of the work in the reconstruction of early Indian astronomy would be apparent from the above statement, the paucity of reliable manuscripts of the work makes the pre- paration of a correct edition of the work a formidable task, affecting, in its turn, a proper under- standing, translation and interpretation of the work. The gravity of the problem could be gauged from what G. Thibaut has stated in the Preface to the first edition of the work (TS), issued in 1889. He says:

1. The Pañcasiddhāntikā, the astronomical work of Varāha Mihira. The Text edited with an original commentary in Sanskrit and an English translation, by G. Thibaut and Mm Sudhakara Dvivedi, Leipzig : Varanasi, 1889; Rep. Lahore, 1930; Rep. Varanasi, 1968. (Page references made are to this reprint.)

XIV PAÑCASIDDHĀNTIKĀ “There is some reason to fear that the feeling of any one who may examine in detail this edi- tion and translation of Varāha Mihira’s astronomical work will, in the first place, be wonder at the boldness of the editors. I am fully conscious that on the imperfect materials at our dis- posal an edition in the strict sense of the word cannot be based, and that what we are able to offer at present deserves no other name but that of a first attempt to give a general idea of the contents of the Pañcasiddhāntikā. It would, in these circumstances, possibly have been wiser to delay an edition of the work until more correct Manuscripts have been discovered. Two considerations, however, in the end, influenced us no longer to keep back the results, how- ever imperfect, of our long continued endeavours to restore and elucidate the text of the Pañcasiddhāntikā. In the first place, we were encouraged by the consideration that texts of purely mathematical or astronomical contents may, without great disadvantages, be submit- ted to a much rougher and bolder treatment than texts of other kinds. What interests us in these works is almost exclusively their matter, not either their general style or the particular words employed, and the peculiar nature of the subject often enables us to restore with nearly absolute certainty the general meaning of passages the single words of which are past trustworthy emendation. And, in the second place, we feel convinced that even from that part of the Pañcasiddhāntikā which we are able to explain more is to be learned about the early his- tory of Sanskrit Astronomy than from any other work which has come down to our time.” (p.v.).

About the manuscript material available to him and the editorial criteria adopted by him Thibaut says in his Introduction to the edition:

“The present edition of the Pañcasiddhāntikā is founded on two Manuscripts, belonging to the Bombay Government. The text of the better one of those two Manuscripts is reproduced in the left hand columns of our edition, while the foot notes give all the more important different readings from the other Manuscript. A comparison of the traditional text with the emended one, as given in the right hand columns of the edition, will show that the former had, in many cases, to be treated with great liberty. Not unfrequently, the emended text is merely meant as an equivalent in sense of what we suppose Varāha Mihira to have aimed at expressing, while we attach no importance to the words actually employed in the emendation.” (p.lx).

The Pañcasiddhāntikā has again been edited recently by O. Naugebauer and D. Pingree, (NP)². And Pingree too observes, on the state of the manuscript material: “The present edition of the Pañcasiddhāntikā does not solve all the remaining problems connected with this text. We suspect that much will never be understood unless better manuscripts material becomes available.” (Vol. I, Intro., p. 19)

It, however, so happens that during the hundred years that have passed by since the publication of its first edition in 1889 no ‘really’ new manuscript of the work has come to light. A few manus- cripts that have become available,³ all go back to the two manuscripts used in the first edition, as shown by the commonality in them of omissions and corruptions which occur in the newly available manuscripts.

2. The Pañcasiddhāntikā of Varāhamihira. Pt. I. Text and Translation by D. Pingree; Pt. II. Notes by O. Neugebauer, Cobenhavn, Munksgaard, 1970.
3. For details, See below under ‘Manuscript material’.

INTRODUCTION XV The edition of Pañcasiddhāntikā which is now issued is also based on the manuscripts used for the two above-said editions. The question that would naturally arise here would be: Why then is the need for another edition when no new source material is to be had? The answer is threefold: i. First, it was felt that in reconstructing the text from the corrupt manuscripts, which alone are available, both TS and NP have subscribed to an editorial principle voiced by Thibaut when he says: “What, in the attempt to reconstitute the text of an astronomical or mathematical work, has chiefly to be kept in view, is of course to arrive at rules which are capable of being proved mathematically. This consideration has, in more than one place, led us to introduce changes even where such appeared hardly to be required by the external form of the traditional text.” (Introduction, p.lxi), And, this they have done to an extent which seems to be hardly justified in editing a classical text. Then again, such emendations are often inserted without specific indication, especially in the edited text of NP, with the result that the reader takes the emended text as the ‘real’ manuscript text. The translation and interpretations that follow are, primarily, based on the emended text and not on the ‘real’ text. In fact, an editorial principle which has to be applied with the utmost caution and in as limited a manner as possible, seems to have been used rather extensively. In the present edition of Pañcasiddhāntikā, the principle of sthitasya gatiś cintanīyā, ‘justification of the extant reading should be thought of’, has been primarily adhered to, alongside the correction of the copyist’s errors by visualising the psychology of the scribe who is illiterate with reference both to the language and the subject of the text. ‘Real’ emendations have been comparatively small and far between. In all cases, however, when changes had to be made to the manuscripts readings, they have been specifically indicated by their being placed within curved brackets in the case of scribal errors and in square brackets in the case of editorial supplementation. And, whenever there has been an emendation, the reasons for suggesting the emendation have been given in the Notes that follow each verse. ii. Secondly, in a number of places, TS nor NP do not seem to have caught the correct import of the text and this has affected their Translation and Notes. All these have been attempted to be rectified. In many places, the untenability of the TS and NP readings, translations and notes have also been pointed out. iii. Thirdly, and what is most important, special effort has been made to digest the textual verses fully, and offer, in the case of knotty places and apparently vague passages, detailed interpretations and elucidations, adumbrated with tables and illustrations. Moreover, a number of examples have also been worked out to illustrate the rules enunciated by Varāhamihira. Under the circumstances, it is to be hoped that the present publication will form another step towards understanding and evaluating the principles and practices of early Indian astronomy. 2. Source Material A-B. The available manuscripts of Pañcasiddhāntikā, of which five have been collated for prepar- ing the present edition, fall into two recensions which have been designated as A and B. Common corruptions and omissions indicate that even these two recensions go back to a common original which too should have been far from perfect in the matter of accuracy. The technical nature of the work, brizzling with unusual terminology, have made the scribes commit all types of imaginable errors except in the case of well-known words and expressions. These errors include, as a reference to the footnotes recorded in the edition would show, wrong spellings, erratic sandhi-s and splitting

XVI PAÑCASIDDHĀNTIKĀ of words, omission of vowel signs, verses made to stop short in the middle or to run into another, numbering of verses in the wrong places and so on. In several cases some of these corruptions are common to all the manuscripts, confirming that these errors have to be traced back to a common archetype of both the recensions. The said five manuscripts have been designated A1, A2 and B1, B2, B3, according to the two recensions and relative reliability of the manuscripts. All the manuscripts are in paper, written in Devanagari script. A₁. Ms. No. 338/1879-80 of the Bhandarkar Oriental Research Institute, Pune, described in A Catalogue of Collections of Mss. deposited in the Deccan College by S.R. Bhandarkar (Bombay, 1888), p. 143. It has 22 folios with 11 lines per page. It is complete and has been copied at Stambhatīrtha (modern Cambay in Gujarat) in Sam. 1673, Śaka 1538 (AD. 1616), by Śaṅkara son of Govinda. This manuscript is the 'better of the two manuscripts' used in the TS. edition of the PS. The manuscript is far from perfect and exhibits numerous scribal errors and some transpositions, but it is definitely better than the B manuscripts. A₂. Ms. No. 49, currently preserved in the National Library, Calcutta, but it originally belonged to the erstwhile Imperial Library, Calcutta. It is in 24 folios with 9 lines a page. It is incomplete and extends to a portion of XVIII. 90 d. The writing is very readable but is very much error-ridden. The readings are closely associated to A₁. Pingree suspects that it "agrees almost entirely with A (our A₁) of which it is most probably a copy." (see his edition of PS, Introduction, p. 20). This cannot be a copy of A₁ for the reason that there occur differences between the two, for which see I. 3c, 7d, 10a, 12a and a number of other contexts. Pingree doubts also that A₂ is "perhaps the copy utilized by Thibaut and Dvivedin" (Introduc- tion, p.20). This goes against Thibaut's statement that his "edition of PS is founded on two Manus- cripts belonging to the Bombay Government" (T's Introduction, p. LX). It is also to be noted that while A₁ is complete, A₂ is incomplete. It is again to be noted that minor over-writings and correc- tions above the lines occur in A₂ at several places obviously having been added by a modern user of the manuscript. These latter, being modern, have not been noted as variants in the footnotes to the present edition. B₁. Ms. No. 37/1874-75 of the Bhandarkar Ori. Res. Inst., Pune, described in A Catalogue of Col- lections of Mss. deposited in the Deccan College (Bombay, 1888). Copied in modern "Universal foolscap" paper, with a title page in Devanagari reading "number 37-Satra 1872 [A.D.] Pañcasiddhāntikā, patrāṇi 49-15-1930", it is in 49 pages, with 15 to 17 lines a page. This is the second of the two man- uscripts used by TS, from which they have documented only some of the variants, as recorded in the footnotes of their edition. Pingree states (Intro., p.20), that in the edition he has documented only those variants recorded by TS in their footnotes. In the present edition, however, the manuscript has been fully collated and all the variants therein recorded. This manuscript carries, through its entire length, correc- tions, obviously made by Thibaut. B₂. Ms. No. 64 of the National Library, Calcutta. It contains 108 pages numbered 7 to 114, and is incomplete, commencing only from I.22, the previous verses having been written on the folios 1-6, now lost. The manuscript is shapely and the writing readable, but the matter contained is extremely

INTRODUCTION XVII corrupt. The numbering of the verses is also erratic. Several verses are broken in their middle and verse numbers are interposed. At times the last line of a verse is continued with the beginning let- ters of the next verse, entailing at times, the beginnings and ends being half-words. (see III. 1 and 2). The manuscript seems to be the handiwork of a good-handed scribe from a highly corrupt orig- inal. Corrections by a modern hand in lighter ink is seen at places. Pingree suspects that "this manuscript seems to be a copy of B – perhaps that used by Thibaut and Dvivedin." (Introduction, p.20). B₃. Ms. No. 7165 of the Oriental Institute, Baroda. This manuscript in 33 folios contains the complete work. A post-colophonic statement says that it was copied in Saṁ,. 1928/śaka 1793 (A.D. 1872) by Uttamarāma Durlabharāma, a resident of Amadāvāda (Ahmedabad). The writing is read- able but corrupt readings persist. Verse numbers are written for the first chapter, but not for the later chapters. Numbers expressed in the verses are written also in digits in many places. A few more manuscripts of Pañcasiddhāntikā are known to exist (or to have existed) but could not be used for the present edition. They are :

1. Ms. No. 288 of the Bombay University. This is at present missing in the Library. Pingree has used this manuscript. In 32 folios it contains the full text of PS. It was copied in Saṁ. 1928, corres- ponding to AD. 1871, by Nāthurāma Pārika.
2. Ms. No. 6288 of the India Office, London, (Buhler 268) described in the A Catalogue of Skt. and Pkt. Mss. in the India Office Library, vol. II by A.B. Keith. This is a copy of our Ms. A₁, copied in Saṁ 1936, Śaka 1802 (A.D. 1879). We have not used it nor has Pingree. About still other manuscripts, Pingree states : "Besides these seven manuscripts, there existed in 1890 the manuscript belonging to J.B. Modak of Thāṇā which was copied from B (our B₁), and we know of a manuscript (no. 6674) of the Pañcasiddhāntikā in the Ānandāśrama in Poona. The man- uscripts, recorded as the property of Sjt. Pushpachandra Sarma Daloi of Helach in Assam and of the Arsha Library in Vijayanagara (no. 506), probably contain the Bhāsvatī of Śatānanda, which is sometimes confused with our text." (Introduction, p. 21). C. The emended text of Thibaut-Sudhakara Dvivedi, as printed in the right hand columns of their edition. On this Thibaut says (Introduction, pp. lx-lxi): "The present edition of the Pañcasiddhāntikā is founded on two manuscripts belonging to the Bombay Government. The text of the better one of these two Manuscripts is reproduced in the left hand columns of our edition, while the foot notes give all the more important diffe- rent readings from the other Manuscript... the emended one as given in the right hand col- umns of the edition. "What, in the attempt to reconstruct the text of an astronomical or mathematical work, has chiefly to be kept in view, is of course, to arrive at rules which are capable of being proved mathematically. This consideration has, in more than one place, led us to introduce changes even where such appeared hardly to be required by the external form of the traditional text." Notwithstanding the wild emendations which Thibaut-Sudhakar Dvivedi have made, at times, their emended readings have been recorded as C in the footnotes of the present edition. D. The edition, Translation and Notes of TS by O. Neugebauer and D. Pingree, (2 vols., Kopenhagen, 1970). Pingree edits and translates the PS, while Neugebauer offers the Notes. All

XVIII PAÑCASIDDHĀNTIKĀ our manuscripts are used in this edition too. Herein occur a number of emendations which are sometimes put within brackets, but sometimes without brackets. Often the emendations are wilder than those of Thibaut-Sudhakar Dvivedi. E. External testimonia. About 125 Pañcasiddhāntikā verses have been identified as quoted in later texts, the largest number thereof, 117 being in the commentary of Utpala of Kashmir (A.D. 966) on the Bṛhatsaṃhitā of Varāhamihira. Other authors who quote from the PS are Pṛthūdaka- svāmin (A.D. 854), Makkibhaṭṭa (14th cent.), Parameśvara of Kerala (1360-1460), Nīlakaṇṭha Somayāji, (b. 1443), again of Kerala, and Sūryadevayajvan (b. 1191) of Tamilnadu, in South India. These PS quotations are taken as External Testimonia and the variants found in such readings have been noticed in the footnotes with 'E' prefixed to the abbreviations of authors/works which quote the verses. These sources are : E. Jy. Jyotirmīmāṃsā of Nīlakaṇṭha Somayāji. E.M. Makkibhaṭṭa's Com. on the Siddhāntaśekhara of Śrīpati. E.N. Nīlakaṇṭha Somayāji's Bhāṣya on the Āryabhaṭīya. E.Pa. Parameśvara's com. on the Āryabhaṭīya. E.Pr. Pṛthūdakasvāmin's com. on the Brāhmasphuṭasiddhānta of Brahmagupta. E.S. Sūryadevayajvan's com. on the Āryabhaṭīya. E.U. Utpala's com. on the Bṛhatsaṃhitā of Varāhamihira. Pingree has adopted this method of referring to external testimonia, and we have followed him in the matter. In fact, we have been much benefitted by his identifications and our labour relates only to texts which have not been noticed by him. On the provenance of PS, Pingree states that : "So far there is no indisputable evidence that the Pañcasiddhāntikā was known outside of an area roughly corresponding to the modern states of Madhya Pradesh, Gujarat, Rajasthan, the Punjab, Kashmir, and West Pakistan. "However, some verses from the text are quoted by fifteenth century Kerala astronomers of the dṛggaṇita school in their commentaries on the Āryabhaṭīya. Thus Parameśvara (c. 1380-1460) cites a verse, and Nīlakaṇṭha (b. 1443) several others. It is noteworthy that all four verses that they quote are also found in Utpala's commentary on the Bṛhatsaṃhitā, which was known in Kerala; it is not proved, then that they had a copy of the Pañcasiddhāntikā." (Intro- duction p. 17). Pingree's assertion as above is not correct for the reason that Kerala and South Indian astronom- ers quote not only the said four verses occurring in Utpala's commentary, but five more PS verses which do not occur in Utpala's commentary, they being PS, I.3, 4 by Nīlakaṇṭha in his Jyotir- mīmāṃsā, the verses saṅkhyā tu teṣām and yāny ataḥ prati again by Nīlakaṇṭha in his Āryabhaṭīya-bhāṣya IV.10 and PS XIII.36 by Sūryadevayajvan in his Āryabhaṭīyavyākhyā. (See below App. II: Index of PS verses quoted by later astronomers). This would mean that PS should have been prevalent in South India also. Recording of Variant readings Textual variants recorded in footnotes in the present edition are restricted to be above-said mate- rial listed under A, B, C, D and E. Some of the PS verses have, indeed been studied by scholars but emendations and variants occurring in these studies have not been recorded here mainly for the

INTRODUCTION XIX reason that they have mostly been documented by Pingree in his edition of the PS and so can be referred to therefrom.¹ 3. Presentation of the Text While the generally accepted conventions of critical editing of Indic texts are duly followed in the present edition, attention might be drawn to certain methodologies which are stressed herein, in view of the technical nature of the text, the defective nature of the manuscripts and the tentative- ness of many of the emendations and textual changes effected in the two earlier editions. i. On account of the inadequacies of the copyists of the parent manuscripts and also due to deficiencies in the parent manuscripts themselves, some emendations have to be done in the edited text. However special care has been taken in this edition to indicate such emendations by placing them within curved brackets; square brackets are used to enclose fillings of apparent omissions or newly suggested readings. Doubtful suggestions are marked by an interrogation mark.

1. Studies mentioned in this footnote have mostly been identified by Pingree and on pages 18-19 of his edition of PS and variants. i. G. Thibaut, 'Notes from Varāha Mihira's Pañcasiddhāntikā', Jl. of Asiatic Society of Bengal, 53 (1884) 259-93. ii. S.B. Dikshit, 'The Original Sūrya-siddhānta', Indian Antiquary, 19 (1890) 45-54. iii. S.B. Dikshit, 'The Romaka Siddhānta', Indian Antiquary, 19 (1890), 133-42. iv. S.B. Dikshit, 'The Pañcasiddhāntikā', Indian Antiquary, 19 (1890) 439-40. v. J. Burgess, 'The Romaka Siddhānta', Indian Antiquary, 19 (1890) 284-85. vi. J. Burgess, 'The sines and arcs in the Pañcasiddhāntikā', Indian Antiquary, 20 (1891) 228. vii. M.P. Kharegat, 'On the interpretation of certain passages in the Pañcha Siddhāntikā of Varāhamihira, an old his- torical work' Jl. of the Bombay Branch of the Royal Asiatic Society, 19 (1895-97) 109-41. viii. K.S. Shukla, 'On three stanzas from Pañcasiddhāntikā,' Gaṇita, 5 (1954) 129-36. T.S. Kuppanna Sastri ix. 'The Vāsiṣṭha Sun and Moon in Varāhamihira's Pañcasiddhāntikā', Jl. of Or. Research, Madras, 25 (1955-56) 19-41. x. 'Some misinterpretations and omissions in Thibaut and Sudhakara Dvivedi in the PS of VM', Vishweshvaranand Indological Journal, 11 (1973) 107-18. xi. 'The epoch of the Romaka Siddhānta in the PS and the epoch longitudes of the Sun and Moon the Vāsiṣṭha Siddhānta', Indian Jl. of Hist. of Science, 13 (1978) 151-58. xii. 'The Vāsiṣṭha-Pauliśa Venus in the PS of VM', Collected Papers of T.S. Kuppanna Sastry, Tirupati, 1989, pp. 141-47. xiii. 'The Vāsiṣṭha-Pauliśa Jupiter and Saturn in the PS', Collected Papers, pp. 148-68. xiv. 'The Vāsiṣṭha-Pauliśa Mars in the PS of VM', Collected Papers, pp. 169-87. xv. 'The epoch-constants of the Vāsiṣṭha-Pauliśa star-planets', Collected Papers, pp. 201-5. xvi. 'Saurasiddhānta of PS : Planetary constants and computation', Collected Papers, pp. 206-40. xvii. 'Pañcasiddhāntikā XVIII. 68-81 : An interpolation', Collected Papers, pp. 241-54.

XX PAÑCASIDDHĀNTIKĀ ii. Thibaut and Dvivedi who print their emended text in the right hand column of their edition do not specifically indicate their emendations and one has to identify the emendations oneself. Pin- gree indicates his emendations in many places by angular brackets but in many other places prints the emended text without any indication. In the present edition, all their emendations are iden- tified and noticed in the footnotes denoting them by the sigla C and D. When these emendations are accepted in the present edition also, they are not separately marked as above. This procedure is expected to enable the comparison between the emendations of TS and NP and those made in this edition and evaluate the merit and appropriateness between the two. In fact, it is felt that many of the emendations of TS and NP, especially of the latter, are often far-fetched, ungrammatical, offending the metre or failing to give a cogent sense. See, for example, the TS/NP emendations in I.23; IX.5; XI.2, 4, 5; XII.5a, 5d; XIII.38d, 41d: XVII.1, 12; XVIII.2d, 3, 19, 24, 25. iii. In order that a discerning student of the text shall have before him, in full, what occurs in the several manuscripts, an attempt has been made to record all variants, right or wrong. This has been done for three reasons : (a) Correct forms of corrupt passages can be visualized only if all the rea- dings, as found in the manuscripts, are before one’s eyes; (b) Then alone would it be possible for an editor to vindicate the emendations suggested by him; (c) The corrupt and apparently meaning- less readings in the manuscripts which the editor could not correct or has wrongly emended can be corrected or better emendations suggested by other scholars if all the variants are given. However, obvious errors of a purely scribal nature, like separate words written jointly, using anusvāra for anunāsika and vice versa, using double consonants for single consonants and vice versa, giving the benefit of doubt for a letter that could be read rightly or wrongly, have been cor- rected silently and not noticed in the footnotes. 4. Translation The translation provided in the edition is as literal as possible without sacrificing readability and not going against the English idiom. Elucidatory expressions and words which are understood in the context are added within brackets, the ultimate aim being to make the matter dealt with clear and fully understood. Topical headings have been provided to verses or groups of verses with the same objective, again, towards the above-said objective. 5. Notes The notes added are generally detailed and self-contained. There again, they seek to elucidate the verses and the underlying ideas, primarily from the Indian standpoint. Tables and geometrical diagrams are provided wherever warranted. Quite often, the need for the emendations suggested in the text is explained. The emendations made by TS and NP are also examined and observations offered. An aspect of the Notes which deserves special mention is the addition of self-suggested mathematical or astronomical problems and working them out according to methods enunciated in the verses, and also by employing modern methods. Introductions are prefixed for several chap- ters, towards setting out the significance of the contents of the respective chapters. 6. Division of Pañcasiddhāntikā The colophons of the several Sections of PS, as found in the manuscripts, which all go back to a defective archetype, are uneven. Some of the colophons merely mention the topic treated in the respective sections but some others designate the sections as adhyāya-s (chapters) and also indicate the numbers thereof. The several colophons read :

INTRODUCTION XXI

1. Karaṇāvatāraḥ
2. Nakṣatrādicchedaḥ
3. Iti Pauliśasiddhāntaḥ
4. Iti Karaṇādhyāyaś caturthaḥ
5. Iti Śaśidarśanam
6. Candragrahaṇe ṣaṣṭhodhyāyaḥ
7. Pauliśasiddhānte ravigrahaṇam
8. Iti Romakasiddhānte 'rkagrahaṇam aṣṭamo 'dhyāyaḥ
9. Iti Sūryasiddhānte 'rkagrahaṇam navamo 'dhyāyaḥ
10. Candragrahaṇam daśamo 'dhyāyaḥ
11. A(nu)varṇanam ekādaśo 'dhyāyaḥ
12. Iti Paitāmahasiddhānte dvādaśo 'dhyāyaḥ
13. Trailokyadarśanam nāma trayodaśo 'dhyāyaḥ
14. Iti Chedyakayantrāṇi caturdaśo 'dhyāyaḥ
15. Jyotiṣopaniṣat pañcadaśo 'dhyāyaḥ
16. Sūryasiddhānte madhyagatiḥ
17. Tārāgrahasphuṭīkaraṇam ṣoḍaśo (? saptadaśo) 'dhyāyaḥ
18. Pauliśasiddhānte tārāgrahāḥ However, whether there be full chapter headings and chapter numbers or there be only the men- tion of the topics in the colophons, the commencement of a new subject helps to ascertain the beginnings of the chapters. The omission of the specification of the chapter headings and numbers has to be ascribed to the imperfections in the original archetype. This helps us to correct Pingree's edition where Chs. XVI and XVII are taken as a single chapter, which he numbers as XVI. Now, after eleven verses, here, there occurs the colophon 'Sūryasid- dhānte madhyagatiḥ', which is the subject of those eleven verses. After still another fourteen verses occurs in the colophon 'Tārāgrahasphuṭīkaraṇam ṣoḍaśo 'dhyāyaḥ', and an entirely different subject is treated in those fourteen verses. Ignoring the radical difference in the subjects dealt with in the two sets of verses and the colophon after the first set of verses and guided merely by the colophon at the end of the second set of verses, Pingree combines the two sets of verses, 11 plus 14 = 25, to con- stitute ch. XVI and takes ch. XVIII of TS and of the present edition as ch. XVII. 7. Chapter XVIII of Pañcasiddhāntikā The theme of Ch. XVIII is the heliacal rising and setting of the star-planets according to the Vāsiṣṭha and Pauliśa schools. Venus, Jupiter, Saturn, Mars and Mercury are treated, in that order, in verses 1-56, and certain allied matters in verses 57-60. In verse 61 the author states that he, Var- āhamihira, hailing from Avanti, has composed the PS for the benefit of students. In the next verse, 62, he asks astronomers dissatisfied with Pradyumna and Vijayanandi, to resort to his work. Having thus completed his treatise, couched entirely in the Āryā metre, following a convention, adopted by Sanskrit writers, of concluding works by a closing colophonic verse couched in a different metre, VM breaks into a different metre, the Vasantatilakā, for the purpose : āvantyakaḥ samāsāc chiṣyahitārtham sphuṭāṅkasamam | cakre Varāhamihiras tārāgrahakārikātantram || 61 || Pradyumna-bhūmitanaye jīve saure 'tha Vijayanandikṛte | budhe ca bhagnotsāhaḥ sphuṭam idam karaṇam bhajatām || 62 ||

XXII PAÑCASIDDHĀNTIKĀ dṛṣṭam Varāhamihireṇa sukhaprabodham | ... ... ... ... ... ... ... ... ... ... || 63 || The manuscripts are defective here, omitting the next three lines of the concluding verse, some exhibiting also a gap. In continuation of the above, the manuscripts commence another short work with a maṅgala- śloka ('verse of salutation') and then a second verse expressing a pratijñā ('resolve') to compose a 'better work' by 'Varāhamihira himself.' prastāve 'pi na doṣān jānann api vakti yaḥ parokṣasya | prathayati guṇāṁś ca tasmai sujanāya namaḥ parahitāya || aṣṭādaśabhir baddhāny ā tārāgraham etad āryābhiḥ | varam iti Varāhamihiro dadāti nirmatsaraḥ karaṇam || These verses end abruptly without any closing colophonic verse, as might be expected. Not taking into consideration the fact that VM had closed the PS most formally with all attendant paraphernalia, with verse 63, both TS and NP treat this short work, as the concluding part of Pañ- casiddhāntikā and as a work of Varāhamihira himself, and translate it and explain it as such. It is not noticed by TS and NP that computation according to these verses can give only rough results since the equation of the centre has been dispensed with, which makes them valueless. Further, there are mistakes in the computation of Venus and Mercury, which one cannot expect to be committed by VM. The prose colophon 'Pauliśasiddhānte tārāgrahāḥ evam' ('Thus the star-planets of the Pauliśasiddhānta') does not have any reality behind it since the computations therefrom do not accord with those of the Pauliśasiddhānta elucidated earlier. These points have been discussed in detail in the Notes, below, to these verses. Obviously, these verses are apocryphal and are the handi- work of an inferior astronomer who has ascribed them to VM. For this reason, in the present edi- tion, Pañcasiddhāntikā is formally closed with verse 63 and the verses following given as a prakṣepa (interpolation) by someone else who has moreover blacked out in the original archetype the three lines in verse 63, being the concluding verse of PS. 8. The Five Siddhāntas in PS : Their Distribution It had been mentioned earlier that VM's treatment of the five siddhāntās in the PS are uneven. It is not that each Siddhāntā is taken up one by one and a résumé of the same given fully or sys- tematically. Select topics are taken up, apparently arbitrarily, and are dealt with individually or jointly when the enunciations of two schools are similar. Alongside, chapters are devoted also to general astronomical topics which are applicable to all the schools. The assortment of the treatment of the subjects in the several chapters are as indicated below. 9. Content Analysis of the Pañcasiddhāntikā Ch.I. 1-7 General Introduction 8-10 Romaka Days from epoch (Ahargaṇa) 11-13 Pauliśa Days from epoch (Ahargaṇa) 14-16 Saura-Romaka Yuga of Sun and Moon, Lords of the year, month, and horā.

INTRODUCTION XXIII Ch.I. 17-25 Romaka Lords of the days of the month Ch.II 1-13 Vāsiṣṭha 1 " True Sun (Ravi-sphuṭa) 2-6 " True Moon (Candra-sphuṭa) 7 " Nakṣatra computation 7 " Tithi computation 8 " Day-time (Aharmāna) 9-10 " Gnomonic shadow (Śaṅkucchāyā) 11-13 " Lagna Ch.III 1-37 Pauliśa 1-3 " True Sun (Ravi-sphuṭa) 4 " True motion of Moon (Candragati) 5 " Equation of the centre (Mandaphala) 6-9 " Sense obscure 10 " Cāra 11-12 " Day-time (Aharmāna) 13-14 " Deśāntara 15 " Local time (Iṣṭadeśakāla) 16 " Nakṣatra computation 17 " Sun's daily motion (Ravi-gati) 18-19 " Karaṇa-s 20-22 " Vyatīpāta and Vaidhṛti 23-24 " Ṣaḍaśīti-kāla 25 " Solstices (Ayana) 26 " Saṅkrānti-kāla 27 " Tridinaspṛk-yoga 28-29 " Rāhu (Node) 30-31 " Moon's latitude (Candra-vikṣepa) 32 " Bhadraviṣṇu, defect in 33 " Pādāditya, defect in 34-35 " Romaka, defect in 36-37 General Astronomy, importance of Ch.IV 1-58 General Problems of Time, Space and Direction (Tripraśna) 1-15 " Table of R sines (Jyāḥ) 16-18 " Declination of Sun and Moon (Krānti) 19-22 " Gnomonic shadow and derivatives (śaṅkucchāyā) 23-25 " Sine colatitude and Day-diameter (Lambajyā and Dinamāna) 26-28 " Cara and derivatives

XXIV PAÑCASIDDHĀNTIKĀ Ch. IV. 29-30 " Rt. ascensional difference (Laṅkodaya-rāśimāna) 31-34 " Rising of signs (Rāśyudaya) 35-36 " Gnomonic shadow (Śaṅkucchāyā) 37-38 " Astronomer's qualifications 39-40 " Sine amplitude (Agrā) 41-49 " Gnomonic shadow at required time (Iṣṭacchāyā) 50-51 " Moon's shadow (Candracchāyā) 52-54 " Directions from shadow (Diksādhana) 55-58 " Sun from gnomonic shadow (chāyātaḥ raviḥ) Ch. V 1-10 Paulīśa Moon's horns (Candraśṛṅgonnati) Ch. VI 1-14 Vāsiṣṭha and Lunar eclipse (Candragrahaṇam) Paulīśa Ch. VII 1-6 Paulīśa Solar eclipse (Ravi-grahaṇa) Ch. VIII 1-18 Romaka Solar Eclipse (Ravi-grahaṇa) Ch. IX 1-27 Saura Solar eclipse (Ravi-grahaṇa) Ch. X 1-7 Saura Lunar eclipse (Candra-grahaṇa) Ch. XI 1-6 General Eclipse diagram (Grahaṇaparilekhā) Ch. XII 1-6 Paitāmaha 1-2 " Days from epoch (Ahargaṇa) 3-4 " Tithi, Nakṣatra etc. 4 " Vyatīpāta 5 " Day-time (Aharmāna) Ch. XIII 1-42 General Situation of ther worlds (Trailokyasaṁsthānam) Ch. XIV 1-41 General Astronomical instruments (Chedyaka-yantrāṇi) Ch. XV 1-29 General Jyotiṣopaniṣat Ch. XVI 1-11 Saura Mean planets 1-9 " Mean planets (Graha-madhya) 10-11 " Bīja correction by VM

INTRODUCTION XXV Ch. XVII. 1-14 Saura True planets 1-11a " True planets (Graha-sphuṭa) 11b " Retrograde motion (Vakragati) 12 " Heliacal rising (Grahāstodaya) 13-14 " Planetary latitudes (Graha-vikṣepa) Ch.XVIII 1-60 Vāsiṣṭha-Pauliśa Heliacal rising and setting of planets (Grahāstodaya) 1-5 " Venus (Śukra) 6-13 " Jupiter (Guru) 14-20 " Saturn (Śani) 21-35 " Mars (Kuja) 36-56 " Mercury (Budha) 57-60 " Hints 61-63 General Conclusion of PS 64-81 Spurious Supplement True planets 64-66 " Introduction 67-69 " True Mars 70-72 " True Mercury 73-75 " True Jupiter 76-78 " True Venus 79-81 " True Saturn 10. Depiction of the Siddhāntas in PS The above Content Analysis of the PS would enable the identification of the extent of selective depiction of the different siddhāntas by VM in the work, as shown below. PAULIŚA-SIDDHĀNTA Ṣaḍaśītikāla III.23-24 Candra-vikṣepa III.30-31 Ahargaṇa I.11-13 Rāhu III.28-29 Nakṣatra III.16 Candra-grahaṇa VI.1-14 Mandaphala III.5 Ravi-grahaṇa VII.1-6 Ravigati III.17 Candraśr̥ṅgonnati V.1-10 Raviphuṭa III.1-3 Grahāstodaya XVIII.1-60 Candra-sphuṭa III.4 Ayana III.25 Saṅkrānti III.26 ROMAKA-SIDDHĀNTA Tridinaspr̥kyoga III.27 Deśāntara III.13-14 Ahargaṇa I.8-10 Cara III.10 Yuga I.14-16 Aharmāna III.11-12 Lord of the year I.17-18, 21 Iṣṭadeśakāla III.15 Lord of the month I.19, 21 Karaṇa III.18-19 Lord of the Horā I.20, 21 Vyatīpāta III.20-22 Lord of the Days I.23-25 Vaidhṛti III.20-22 Ravi-grahaṇa VIII.1-18

XXVI PAÑCASIDDHĀNTIKĀ SAURA-SIDDHĀNTA Candra-sphuṭa II.2-6 Nakṣatra II.7 Yuga I.14-16 Tithi II.7 Lord of the year I.17-18, 21 Aharmāna II.8 Lord of the month I.19, 21 Śaṅkucchāyā II.9-10 Lord of the Horā I.20, 21 Lagna II.11-13 Graha-madhya XVI.1-11 Candra-grahaṇa VI.1-14 Graha-sphuṭa XVII.1-11 Grahāstodaya XVIII.1-60 Graha-vikṣepa XVII.13-14 Candra-grahaṇa X.1-7 PAITĀMAHA-SIDDHĀNTA Ravi-grahaṇa IX.1-27 Ahargaṇa XII.1-2 Grahāstodaya XVII.11-12 Nakṣatra XII.3 Tithi XII.3 VĀSIṢṬHA-SIDDHĀNTA Vyatīpāta XII.4 Ravi-sphuṭa II.1 Aharmāna XII.5 With regard to the Chapters and verses not included in the above table, some, like chapters XI to XV, and several verses, are of a general nature, applicable to all the siddhāntas and in the case of the others it is difficult to identify positively the siddhāntas to which they pertain. 11. Comparative Study of the Siddhāntas It can be seen from the above Table that several of the topics selected by VM from the different siddhāntas for depiction in the PS are common. This should enable a comparative study of the common topics, the more important of which are noticed in the Table below. In this connection it is necessary to point out, an erroneous view current, to the effect, that the Pauliśa siddhānta is accurate, the Romaka is equally accurate, the Saura is still more accurate and that the Vāsiṣṭha and Paitāmaha highly inaccurate. This view has been brought into vogue through two unwarranted emendations introduced by TS and NP into the text of the following verse in the PS: Pauliśatithis sphuṭo 'sau tasyāsannas tu Romaka-proktaḥ | spaṣṭataraḥ sāvitraḥ pariśeṣau dūravibhraṣṭau || PS. I.4 ‘The tithi resulting from Pauliśa is tolerably accurate and that of the Romaka approximate to that. The tithi of the Saura is very accurate. But that of the remaining two (viz., the Vāsiṣṭha and the Paitāmaha) have slipped far away (from the real).’ Here VM speaks only about the tithi, (lunar day), as computed during his time according to the different siddhāntas; He is not making a relative estimate of the siddhāntas as such or in respect of the various other computations. As elucidated in the Note to this verse in the body of this book (p.5) : “The five Siddhāntas are compared here with reference to their tithi alone because that is the chief of the five aṅgas, viz., tithi, vāra, nakṣatra, yoga and karaṇa; that is most useful not only for religous purposes but also for civil purposes; that is independent of the origin of reference in the ecliptic and can be examined for correctness by observation of eclipses and heliacal rising; and that is used in finding the days from Epoch, the sine qua non of all astronomical computation. “This being the case, the change of tithi into kṛta by the late Dr. G. Thibaut and M.M. Sudhakara Dvivedi (TS for short), especially when the manuscripts read only tithi or titha, is unwarranted, to say the least. Doing this, they have condemned the Vāsiṣṭha Siddhānta beyond

INTRODUCTION XXVII the author’s intention and become blind to its merits and peculiarities, which otherwise they could have easily seen. Equally off the mark is the emendation of tithi into stvatha by Neugebauer and Pingree (NP for short). See below, Explanatory Notes, for the real reason for this ‘slipping away from the real’.” On this subject might be advantageously referred to the section ‘The place of the Vāsiṣṭha in the his- tory of Hindu astronomy’ in T.S.K. Sastry’s paper ‘The Vāsiṣṭha Sun and Moon’ in the Jl. of Or. Research, Madras, 25 (1955-56) 19-41, reprinted in his Collected Papers on Jyotiṣa (Tirupati, 1989, pp.1-28) Table of Common topics Ahargaṇa Vāsiṣṭha II.8 Paulīśa I.11-13 Paitāmaha XII.5 Romaka I.8-10 Paitāmaha XII.1-2 Vyatīpāta-Vaidhṛti Paulīśa III.20-22 Nakṣatra-Tithi Paitāmaha XII.4 Paulīśa III.16 Candra-grahaṇa Vāsiṣṭha II.7 Vāsiṣṭha-Paulīśa VI.1-14 Ravi-sphuṭa Saura X.1-7 Paulīśa III.1-3 Ravi-grahaṇa Vāsiṣṭha II.1 Paulīśa VII.1-6 Candra-sphuṭa Romaka VIII.1-18 Paulīśa III.4 Saura IX.1-27 Vāsiṣṭha II.2-6 Grahāstodaya Aharmāna Vāsiṣṭha-Paulīśa XVIII.1-60 Paulīśa III.11-12 Saura XVII.11-12 12. Varāhamihira : His Life and Works One of the foremost early Indian astronomer and astrologer, Varāhamihira belongs to the sixth century A.D. In the Pañcasiddhāntikā (I.8) he takes the cut-off date or epoch for computations using the Paulīśa Siddhānta as Śaka 427, which corresponds to A.D. 505. Since the practice in Indian astronomical manuals (Karaṇa-grantha-s) is to take a contemporary date, as near to the composition of work, answering to certain specifications, as the cut-off date, it is reasonable to presume that PS was composed some time after A.D. 505. Regarding his demise there is a statement by Āmarāja in his commentary on Brahmagupta’s Brāhmasphuṭasiddhānta, which reads : navādhika-pañcasamkhyā- śake Varāhamihirācāryo divam gataḥ. “In śaka 509 Varāhamihira attained to the heavens.’ This would mean that VM passed away in A.D. 587. This date is corroborated by VM’s mention in PS XV.10, of Āryabhaṭa who composed his Āryabhaṭīya in A.D. 499, which work should have become well known by the time that VM composed his PS.