Pancha Sid Dan Tika

P.P.S.T. SCIENCE SERIES NO. 1

PANCASIDDHANTIKA OF VARAHAMIHIRA WITH TRANSLATION AND NOTES

BY

T.S. KUPPANNA SASTRY

C R I T I C A L L Y EDITED

WITH INTRODUCTION AND APPENDICES BY

K.V. SARMA Adyar Library and Research Centre, Madras

P.P.S.T. F O U N D A T I O N ADYAR, MADRAS 1993

Published by : P P S T Foundation, P O B 2080, Adyar, Madras 600 020 (India)

ALL RIGHTS RESERVED First Edition 1993

Printed i n India By V i p i n Sachdev, Printers Plates, , Royapettah H i g h Road, Madras 600 014

PREFACE T h e Pancasiddhantika of the sixth century astronomer Varahamihira is a major work on mathematical/astronomy of early India. T h e work is particularly significant for the fact that, besides providing an insight into the level of contemporary development i n the discipline, it forms also a resume, though uneven, of five astronomical schools, to wit, the Vasistha, Paitdmaha, Romaka, Paulisa and Saura, that were i n vogue i n India d u r i n g the early centuries of the ChrisUan era, but whose original texts have not came down to us and are lost on account of improved astronomical systems having been developed in course of time. There have appeared two earlier edidons of this cryptic technical text, the first by G . Thibaut and Sudhakar Dvivedi (Banaras, 1889) and second by O . Neugebauer and D . Pingree (Copenhagen, 1970-71). But both these editions have limitations and imperfections, even as their editors themselves have indicated in their Introductions to the said editions. T h e main difficulty in gaining a proper understanding, let alone producing a correct edition, of the Pancasiddhantika has been confounded on account of all the available manuscripts having descended from a single corrupt archetype. This aspect of the matter cannot be better expressed than i n the words of G . Thibaut i n the Preface (p.v.) to his edition of that work. H e says : " I m p e r f e c t a n d f r a g m e n t a r y as (the) text a n d (the) t r a n s l a t i o n are, we m a y assert, at a n y rate, that i n o u r e n d e a v o u r s to o v e r c o m e the q u i t e u n u s u a l obstacles w h i c h the c o r r u p t a n d b a r e text o f the P a n c a s i d d h a n t i k a o p p o s e s to the i n t e r p r e t e r , we have s p a r e d n o t r o u b l e . T h e t i m e a n d t h o u g h t d e v o t e d to the present v o l u m e w o u l d , I m a y say w i t h o u t e x a g g e r a t i o n , have a m p l y sufficed f o r the e d i t i n g a n d e x p l a i n i n g o f twenty times the a m o u n t o f text p r e s e n t i n g o n l y n o r m a l difficulties." Hence the need for a further attempt for a better edition and interpretation o f this important text on early Indian astronomy. T h e present edition which is based o n all the available manuscripts of the text and also external testimonia and which takes into consideration the work o f interpretation attempted i n the two previous editions, presents as critical and readable a text as is possible on the basis of the above-said material. T o this is added a literal translation with explanatory words added as necessary. This is followed by detailed explanatory notes i n terms inclusive of modern mathematics, and adumbrated with tables and diagrams. Whenever computations are involved, illustrative examples are given and worked out. T h e r e again, most of the chapters are provided with explanatory introductions indicating the general contents and method o f approach of the matter contained i n the chapters.

T h e above work has been a labour of love pursued by the late P r o f T . S . K u p p a n n a Sastry, formerly Professor i n the Sanskrit College, Madras. A scholar i n Sanskrit, a student of modern mathematics and one fully conversant with Jyotissastra, Prof. Sastry was an ideal combination of Indian and Western schools o f astronomy. A n d , as such, he was best fitted for the task of expounding a difficult text on Indian astronomy like the Pancasiddhantika.

VI

PREKAC.E

When Prof. Sastry passed away in 1982, he left behind his handwritten manuscript which was in different states of perfection. While the earlier chapters were in their final form, chapter X I V had been left untouched and so also were verses 35 to 55 of chapter X V I I l . T h e later chapters, portions of which had been issued in the form of articles, were in their rough draft form. T h e above-said material was placed in my hands by Dr. T . K . Balasubramanian, Scientist, Bhabha Atomic Research Centre, Bombay, Prof. Sastry's son, with the suggestion that the same might be duly processed and perfected and made pressworthy and placed before the world of scholars in printed form. As an academic associate of Prof. Sastry for nearly three decades, I accepted the challenge and set to work on it without delay. In this matter I had the cooperation of two eminent scholars in astronomy. Prof. K . S . Shukla of Lu( know and Shri. S. Hariharan of Bangalore. Work on Prof. Sastry's manuscript was twofold. T h e first related to the perfection of the existing Translation and Notes and the supply of the same for the sections which were left out by Prof. Sastry. Prof. Shukla translated C h . X I V with notes and diagrams and Shri. Hariharan supplied the Translation and Notes for the verses left out i n C h . X V I I I . While the above was done at Lucknow and Bangalore, respectively, in Madras, the end chapters were put in proper form. Alongside, the endre manuscript, r u n n i n g to about 500 pages, was duly perfected. T h i s revision work included also such matters as the crosschecking of entries, supply of diacritical marks to Sanskrit expressions, marking off of paragraphs, making the presentation uniform, and several other allied matters. The manuscript, revised as above, had also to be typed out and checked again. The large number of diagrams occurring in the work were also drawn to scale with the use of geometrical instruments and added at appropriate places. T h e second task related to the critical editing of the textual verses. A draft press copy was prepared on the basis of the readings adopted by Prof. Sastry. Copies of all manuscripts of Poncasiddhdntikd available at different repositories were procured and collated with the draft press copy. T h e text in the two printed editions and in the external tcstimonia, which had also been assembled, was collated similarly and the variants recorded. A n d , on the basis of the above, the final press copy of the critical text was prepared. Varied typograph) for the half a dozen different items of the edition was also selected to setoff the same distinctly in print. T h e resultant edition, provided with an Introduction and necessary Appendices including a Subject Index, is now placed before scholars. It is to be hoped that this edition of Pancasiddhantika will contribute, in some measure, to the furtherance of the study and appraisal of early Indian mathematics and astronomy. T h e publication of this volume had been made possible by the generous contribution of friends and patrons of academic studies. T h e Birlas made a gracious donation of Rs. 20,000/- and Dr. T . K . Balasubramanian, of Rs. 5,000/-. T h e Rashtriya Veda Vidya Pratishthan, New Delhi, has extended the major financial assistance in the form of purchasing copies of the book amounting to about rupees one lakh. T h e most profound thanks are due to the above named patrons for their kind gesture. Thanks are due to the Bhandarkar Oriental Research Institute, Poona, Oriental Institute, Baroda, and National Library, Calcutta, for their kind cooperation

\

PREFACE

VII

by supplying copies of the manuscripts of Pancasiddhantika 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. T h e P P S T 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 Pancasiddhantika. Madras, January 4, 1993

K.V. S A R M A

i

CONTENTS

Page

V

PREFACE

IX

CONTENTS

XIII

INTRODUCTION

Introductory - Source Material - Presentation o f the Text - Translation - Notes - Division of Paricasiddhandka - C h . X V I I I of Paiicasiddhantika - T h e Five Siddhantas in PS ; T h e i r distribution - Content analysis of the Pancasiddhantika - Depiction of the Siddhantas in the PS - Comparative study of the Siddhantas - Varahamihira : His life and works. Page Ch.I. I N T R O D U C T I O N OF T H E W O R K 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 E p o c h : Paulisa (11-13) 11 Yuga of the Sun and the M o o n : Romaka and Saura (14-16) 15 Lordoftheyear(17-18) 18 L o r d of the M o n t h (19) 20 L o r d o f the H o r a etc. (20-25) 20 Names of the 30 days of the Parsi months 24 Ch.II.

53 54 56 57 58 64 65 65 66 67 69 71 71 71

VASISTHA-SIDDHANTA:

PLANETARY COMPUTATIONS

ETC.

Introductory T r u e Sun (1) T r u e M o o n (2-4) NaksatraandTithi(7) Day-dme (8) Gnomonic Shadow (9-10) Lagnafrom shadow and vice versa (11-13) Ch.III.

Page Local Sunset time (15) Naksatra computation (16) Sun's daily motion (17) Karanas (18-19) Vyatlpata and Vaidhrta (20-22) Sadasiti-punyakala (23-24) Solstices (25) Sankranti-kala (26) Tridinasprg-yoga (27) R a h u (Node) (28-29) Moon's latitude (30-31) Defect i n Bhadravisnu (32) Defect i n Padaditya (33) Defect in Romaka (34-37)

25 25 27 33 34 35 37

FAULISA-SIDDHANTA:

PLANETARY COMPUTATION

Introductory T r u e Sun (1-3) T r u e Motion of M o o n (5) Equation of the centre (5-9) Cara or Oblique ascension (10) Day-time (11-12) Desantara (13-14)

ETC,

40 40 45 47 48 50 51

Ch.IV. T H R E E P R O B L E M S : T I M E , PLACE A N D DIRECTION Introductory Table o f R Sines (1-15) Declinadon of the Sun and the M o o n (16-18) Gnomonic shadow (19) Latitude from Shadow (20-21) Sine zenith distance (22) Sine Co-latitude and Day-diameter (23-25) Cara or Oblique Ascension (26) Latitude from Cara (27-28) Rt. ascensional difference (29-30) Rising Signs (31) T i m e to reach the Prime vertical (32-34) Great gnomon (Sama-sartku) and its shadow (35)

76 76 87 90 91 95 96 98 100 102 104 106 110

c:oNrEN'rs

X

Page

Page Astronomer's qualifications (36-37) Gnomonic sfiadow and the prime vertical (38) Agra : Sine amplitude (39) Latitude from Agra (40) Shadow at desirea time (41 -44) Timeafter sunrise (45-47) T i m e for Sunset (48) Shadow from time (49) Moon's shadow (50-51) Directions from shadow (52-54) Sun from shadow (55-56) Ch.V.

112 113 113 114 115 118 121 122 123 126 132

137 137 143 147

PAULISA-

SIDDHANTA: LUNAR

ECLIPSE

Introductory Sun and M o o n of equal longitude (1) Probability o f a n eclipse (2) Duration ofthe eclipse (3-4) Total obscuration (5) Direction of the eclipse (6-8) Moment ofthe eclipse and its colour(8-10) Diagrammatic representation (11-13) L u n a r and Solar eclipses — Differences (14)

152 152 154 156 160 162 165 168 171

Ch.VII. ( P A U L i : § A - S I D D H A N T A ) : SOLAR ECLIPSE

Introductory Parallax of longitude (1) Parallax in latitude (2-4) Eclipse computation (5-6)

172 172 176 178

Ch.VIII. R O M A K A - S I D D H A N T A : SOLAR ECLIPSE

Introductory

189 191 192 192

SOLAR ECLIPSE

Introductory T i m e o f Moon's visibility (1-3) Diagram of the Moon's cusps (4-7) Daily rising and setting of the M o o n (8-10) (VASI§THA-)

181 183 185 186 187 187

Ch.IX. S A U R A - S I D D H A N T A :

PAULISA-SIDDHANTA:

MOON'S CUSPS

Ch,VL

T r u e Sun (I-3) T r u e M o o n (4-6) Daily motion of the Sun and the Moon (7) Rahu (8) Parallax in longitude (9) Declination of the Nonagesimal (10-12) Parallax correction and orbital diameter (13-14) T r u e diameterofthe orbs (15) Moment of the eclipse (16) Eclipse diagram (17-18)

181

Introductory M e a n Sun (1) Mean M o o n (2-4) R a h u : M a x i m u m latitude (5-6) T r u e Sun and M o o n (7-9) Epicyclic theory Bhujantara correction Udayantara correction Desantara correction (10) MeanmotionoftheSunandtheMoon(lI) M o t i o n o f Moon's anomaly (12) T r u e motion of Sun and M o o n (13-14) Kaksa of the Sun and the M o o n (15) Measure of the orbs (16) Sin Zenith Distance of Meridian point(17-18) Drksepa ofthe Sun (19-20) G n o m o n (21) Parallax-corrected New M o o n (22-23) Parallax in latitude (24-25) Duration of the eclipse (26-27)

197 197 198 201 203 206 209 209 209 210 211 211 214 215 216 219 220 221 223 225

Ch.X. S A U R A - S I D D H A N T A : L U N A R ECLIPSE

Introduction 228 Diameter of the Shadow (1-2a) 228 Duration ofthe Eclipse (2b-4) 230 Obscuration at any desired moment (5-6) 232 T i m e oftotal obscuration (7) 235

CONTENTS

Page

Page Ch.XI. ECLIPSE D I A G R A M Introduction Marking the ecliptic etc. (1-3) Markingof'p(jints of contact etc. (4-5) Conversion olminutes into angles (6)

236 236 238 240

Ch.XII. P A I T A M A H A S I D D H A N T A Introducuon Days from Epoch (1-2) T i t h i , Naksatra etc. (3) Vyatipata (4) Duration of a day (5)

241 241 243 244 246

Ch.XIII. S I T U A T I O N O F T H E EARTH: COSMOGONY Situation of the earth (1-4) Rotation of the earth (5-8) Situation of the Gods and Asuras (9-13) SignsandYojanas(14-16) Position of Lartka and L'jjayinI (17) Measures of the earth etc. (18-19) Visibility ofthe Sun (20-29) Astronomical observation (30-34) Moon's visibility (35-38) T h e Planets and their situation (39-41) Lords of the Months, Days and Year (42)

248 249 250 252 253 253 253 258 258 259 260

Ch.XIV. G R A P H I C A L M E T H O D S AND ASTRONOMICAL INSTRUMENTS Introductory Ascensional differences o f the zodiacal signs (1-4) R sine ofthe Sun's zenith distance for the given time (5-6) Right ascensions ofthe signs (7) Gnomon (8) Local latitude (from the equinoctial midday shadow) (9-1 Oa) Sun's longitude (lOb-11) V-Shapedyasti(12) Moon's longitude (13) Cardinal directions (by means of a gnomon (14-16)

XI

T h e Celestial Spfiere( 17-18) Hemispherical B o v l and its use (19-20) H o o p and its use (21-22) ArmiUary Sphere (23-25) Sun's northward and southward journeys (26) Instruments for measuring time (27-28) Local longitude i n terms of time (29-30) TheNadiorGhati(31-32) Conjunction ofthe M o o n w'th a Star (33) Positions of certain JunctionStars (34-37) Digits between the M o o n and a Star in Conjunction and T i m e of Conjunction (38) Heliacal Rising of Canopus (39-41)

270 271 272 273 273 274 274 275 276 277

277 278

Ch.XV. SECRETS O F A S T R O N O M Y Eclipses (1-10) Situationatthe Poles (11-16) Weekday (17-18) Day-reckoning (19-29)

282 286 288 289

Ch.XVI.SAURA SIDDHANTA: MEAN PLANETS Introductory Mean positions of the Star-planets (1-19) V M ' s B I j a corrections (10-11)

292 293 298

Ch.XVII. S A U R A - S I D D H A N T A : T R U E PLANETS 261 261 264 266 267 267 268 269 269 270

Epicycles ofthe planets (1-3) T r u e planets (4-9) Special work for Mercury and Venus (10-11 a) ' Retrograde motion ( l i b ) Heliacal rising (12) Latitudes of planets (13-14)

300 301 307 309 309 310

Ch.XVIII. V A S . - P A U . SIDDH.: RISING A N D S E T T I N G O F P L A N E T S Venus (1-5) Jupiter (6-13) Saturn (14-20) Mars (21-35)

312 316 322 339

XII

CONTENTS

Page Mercury (35-36) Hints (57-60) General (61-63)

341 351 353

SPURIOUS S U P P L E M E N T : T R U E PLANETS Introduction (64-66) T r u e Mars (67-69) T r u e Mercury (70-72) T r u e Jupiter (73-75) T r u e Venus (76-78)

355 357 359 361 362

Page T r u e Saturn (79-81)

363

APPENDICES I. Verse Index II. Index o f P S verses quoted by later astronomers III. Bhutasaiikhya used i n the PS I V . Index o f Places, Persons and Texts quoted in the PS V . Bibliography V I . Subject Index

367 371 372 373 374 377

INTRODUCTION 1. Introductory T h e Pancassiddhdntikd (PS) o f Varahamihira ( V M ) , (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 systems of Indian astronomy current d u r i n g the first centuries of the Christian era. T h e work supplies also considerable additional material on the astronomical concepts, computational methods and instruments used d u r i n g the dmes o f the author. V M makes mention ofthe objectives ofthe work towards its commencement: purvdcdryamatebhyo yad yad srestham laghu sphutam bijam \ tat tad ihdvihalam ahum rahasyam udyato vaktum 11 1.1 | Paulisa-Romaka-Vdsistha-Saura-Paitdmahds tuparkasiddhdntdh || 2 | 'Here, I shall state i n full the best of the secret lore o f astronomy extracted from the different schools of the ancient teachers so as to be easy and clear. 'The five siddhdnta-s, of which this work is a compendium, are the Paulisa, the Romaka, the Vasistha, the Saura and the Paitdmaha. Following the above statement, V M specifies also how he is intending to deal with the said five astronomical schools : yat tatparam rahasyam bhavati matiryatra tantrakdrdridm \ tad aham apahdya matsaram asmin vaksye graham bhdnoh \ \ dik-sthiti-virmrda-karna-prarndna-veld grahdgrahdv indoh tdrdgrahasarnyogam desdntarasddhanam cd 'smin 11 sarmmandala-candrodaya-yantra-cchedydni sdhhavacchdyd \ upakaranddy aksajyd-'valambakd-'pakrarriddydni \ \ 1.5-7 | 'I shall tell i n this work, avoiding all jealousy, the computation o f the solar eclipse which is guarded as a great secret and i n which the m i n d of the astronomer reels. I shall also tell the occurrence or non-occurrence of the lunar eclipse, the directions of the first and last contacts, the duration, 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 i n 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 i n the reconstruction of early Indian astronomy would be apparent from the above statement, the paucity of reliable manuscripts of the work makes the preparation of a correct edition o f the work a formidable task, affecting, i n its turn, a proper understanding, translation and interpretation of the work. T h e gravity o f the problem could be gauged from what G . Thibaut has stated in the Preface to the first edition ofthe work (TS), issued in 1889. He says: 1. The Pancasiddhantika, the astronomical work of Varaha 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

PANCASIDDHANTIKA

"There is some reason to fear that the feeling of any one who may examine in detail this edition and translation of Varaha 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 disposal an edition i n 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 ofthe Paiicasiddhantika. It would, in these circumstances, possibly have been wiser to delay an edition o f the work u n d l more correct Manuscripts have been discovered. T w o consideradons, however, i n the end, influenced us no longer to keep back the results, however imperfect, of our long continued endeavours to restore and elucidate the text of the Paiicasiddhantika. I n the first place, we were encouraged by the consideration that texts of purely mathematical or astronomical contents may, without great disadvantages, be submitted 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. A n d , i n the second place, we feel convinced that even from that part of the Paiicasiddhantika which we are able to explain more is to be learned about the early history of Sanskrit Astronomy than from any other work which has come down to our time." (p.v.). About the manuscript material available to h i m and the editorial criteria adopted by him Thibaut says in his Introduction to the edition: " T h e present edition o f the Pancasiddhantika is founded on two Manuscripts, belonging to the Bombay Government. T h e text ofthe better one o f 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 o f the traditional text with the emended one, as given i n the right hand columns of the edition, will show that the former had, in many cases, to be treated with great liberty. Not unfrequendy, the emended text is merely meant as an equivalent in sense of what we suppose Varaha M i h i r a to have aimed at expressing, while we attach no importance to the words actually employed i n the emendadon." (p.lx).

T h e Pancasiddhantika has again been edited recently by O . Naugebauer and D . Pingree, (NP)^. A n d Pingree too observes, on the state of the manuscript material: "The present edition of the Pancasiddhantika 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 d u r i n g the hundred years that have passed by since the publication of its first edition i n 1889 no 'really' new manuscript of the work has come to light. A few manuscripts that have become available,^ all go back to the two manuscripts used i n the first edition, as shown by the commonality in them of omissions and corruptions which occur in the newly available manuscripts.

2. The Pancasiddhantika of Varahamihira. 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

T h e edition of Pancasiddhantika which is now issued is also based on the manuscripts used for the two above-said editions. T h e question that would naturally arise here would be: W h y then is the need for another edition when no new source material is to be had? T h e answer is threefold: i. First, it was felt that in reconstructing the text from the corrupt manuscripts, which alone are available, both T S and N P have subscribed to an editorial principle voiced by Thibaut when he says: "What, i n the attempt to reconstitute the text of an astronomical or mathematical work, has chiefly to be kept i n view, is of course to arrive at rules which are capable of being proved mathematically. This consideration has, i n more than one place, led us to introduce changes even where such appeared hardly to be required by the external form o f the traditional text." (Introduction, p.lxi). A n d , this they have done to an extent which seems to be hardly justified i n editing a classical text. T h e n again, such emendations are often inserted without specific indication, especially i n the edited text of N P , with the result that the reader takes the emended text as the 'real' manuscript text. T h e translation and interpretations that follow are, primarily, based o n the emended text and not on the 'real' text. In fact, an editorial principle which has to be applied with the utmost caution and i n as limited a manner as possible, seems to have been used rather extensively. In the present edition of Pancasiddhantika, the principle oisthitasya gatis cintaniyd, justification of the extant reading should be thought o f , 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 i n the case of scribal errors and i n square brackets i n the case of editorial supplementation. A n d , whenever there has been an emendation, the reasons for suggesting the emendation have been given in the Notes that follow each verse. ii. Secondly, i n a number of places, T S nor N P do not seem to have caught the correct import of the text and this has affected their Translation and Notes. A l l these have been attempted to be rectified. In many places, the untenability o f the T S and N P 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, i n 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 Varahamihira. U n d e r the circumstances, it is to be hoped that the present publication will form another step towards understanding and evaluating the principles and practices o f early Indian astronomy. 2. Source Material A-B. T h e available manuscripts of Pancasiddhantika, of which five have been collated for preparing the present edition, fall into two recensions which have been designated as A and B . C o m m o n corruptions and omissions indicate that even these two recensions go back to a common original which too should have been far from perfect i n the matter of accuracy. T h e technical nature of the work, brizzling with unusual terminology, have made the scribes commit all types of imaginable errors except i n 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, etrauc sandhi-s and splitting

XVI

PANCASIDDHANTIKA

of words, omission of vowel signs, verses made to stop short in the middle or to r u n into another, numbering of verses i n 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. T h e said five manuscripts have been designated A l , A 2 and B l , B 2 , B 3 , according to the twc recensions and reladve reliability ofthe manuscripts. A l l the manuscripts are in paper, written in Devanagari script. A , . Ms. N o . 338/1879-80 of the Bhandarkar Oriental Research Institute, Pune, described i n A Catalogue of Collections of Mss. deposited in the Deccan College by S.R. Bhandarkar (Bombay, 143. It has 22 folios with 11 lines per page. It is complete and has been copied at Stambhatirtha (modern Cambay i n Gujarat) i n Sam. 1673,Saka 1538(AD. 1616),bySaAkarasonofGovinda.This manuscript is the 'better of the two manuscripts' used i n the T S . edition o f the PS. T h e manuscript is far from perfect and exhibits numerous scribal errors and some transposidons, but it is definitely better than the B manuscripts. A j . M s . N o . 49, currently preserved i n the National Library, Calcutta, but it originally belonged to the erstwhile Imperial Library, Calcutta. It is i n 24 folios with 9 lines a page. It is incomplete and extends to a pordon of X V I I I . 90 d. T h e writing is very readable but is very much error-ridden. The readings are closely associated to A , . Pingree suspects that it "agrees almost entirely with A (our A , ) of which it is most probably a copy." (see his edition of PS, Introducuon, p. 20). T h i s cannot be a copy of A , 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 is "perhaps the copy utilized by Thibaut and Dvivedin" (Introduction, p.20). T h i s goes against Thibaut's statement that his "edition of PS is founded on two Manuscripts belonging to the Bombay Government" (T's Introduction, p. L X ) . It is also to be noted that while A j is complete, is incomplete. It is again to be noted that minor over-writings and corrections above the lines occur i n A^ at several places obviously having been added by a modern user of the manuscript. These latter, being modern, have not been noted as variants i n the footnotes to the present edidon.

B, . M s . N o . 37/1874-75 of the Bhandarkar O r i . Res. Inst., Pune, described in A Catalogue of Co lections of Mss. deposited in the Deccan College (Bombay, 1888). C o p i e d i n modern "Universal fo paper, with a dde page i n Devanagari reading "number 37-Satra 1872 [A.D.] Pancasiddhandka, patrani 49-15-1930", it is i n 49 pages, with 15 to 17 lines a page. T h i s is the second of the two manuscripts used by T S , from which they have documented only some of the variants, as recorded i n the footnotes of their edition. Pingree states (Intro., p.20), that i n the edition he has documented only those variants recorded by T S i n their footnotes. I n the present edidon, however, the manuscript has been fully collated and all the variants therein recorded. T h i s manuscript carries, through its entire length, corrections, obviously made by Thibaut. B^. Ms. N o . 64 of the National Library, Calcutta. It contains 108 pages numbered 7 to 114, and is incomplete, commencing only from 1.22, the previous verses having been written on the folios 1-6, now lost. T h e manuscript is shapely and the writing readable, but the matter contained is extremely

INTRODUCTION

XVII

corrupt. T h e numbering of the verses is also erratic. Several verses are broken i n their middle and verse numbers are interposed. A t times the last line of a verse is continued with the beginning letters of the next verse, entailing at times, the beginnings and ends being half-words, (see III. 1 and 2). T h e manuscript seems to be the handiwork of a good-handed scribe from a highly corrupt original. Corrections by a modern hand i n 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). B. . Ms. N o . 7165 of the Oriental Institute, Baroda. T h i s manuscript i n 33 folios contains the complete work. A post-colophonic statement says that it was copied i n Sarti,. 1928/saka 1793 ( A . D . 1872) by Uttamarama Durlabharama, a resident of Amadavada (Ahmedabad). T h e wridngis readable but corrupt readings persist. Verse numbers are written for the first chapter, but not for the later chapters. Numbers expressed i n the verses are written also i n digits i n many places. A few more manuscripts of Pafkasiddhdntika are known to exist (or to have existed) but could not be used for the present edition. T h e y are : 1. Ms. N o . 288 of the Bombay University. T h i s is at present missing i n the Library. Pingree has rsed this manuscript. In 32 folios it contains the full text of PS. It was copied i n Saih. 1928, corresDonding to A D . 1871, by Nathurama Parika. 2. Ms. N o . 6288 of the India Office, L o n d o n , (Buhler 268) described i n the A Catalogue of Skt. and °kt. Mss. in the India Office Library, vol. II by A . B . Keith. T h i s is a copy of our Ms. A , , copied i n Sath 1936, Saka 1802 ( A . D . 1879). We have not used it nor has Pingree. About still other manuscripts, Pingree states : "Besides these seven manuscripts, there existed i n 1890 the manuscript belonging to J . B . M o d a k of T h a n a which was copied from B (our B,), and we enow of a manuscript (no. 6674) of the Pancasiddhantika i n the Anandasrama i n Poona. T h e man- . iscripts, recorded as the property of Sjt. Pushpachandra Sarma Daloi o f Helach i n Assam and of he Arsha Library i n Vijayanagara (no. 506), probably contain the Bhdsvati of Satananda, which is lometimes confused with o u r text." (Introduction, p. 21). C. T h e emended text of Thibaut-Sudhakara Dvivedi, as printed i n the right hand columns of heir edition. O n this Thibaut says (Introduction, pp. Ix-lxi): "The present edition o f the Paiicasiddhantika is founded on two manuscripts belonging to the Bombay Government. T h e text of the better one of these two Manuscripts is reproduced in the left hand columns of our edidon, while the foot notes give all the more important different readings from the other Manuscript... the emended one as given i n the right hand columns ofthe edition. "What, in the attempt to reconstruct the text of an astronomical or mathemadcal work, has chiefly to be kept i n view, is of course, to arrive at rules which are capable of being proved mathematically. T h i s consideration has, i n 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." »Jotwithstanding the wild emendations which Thibaut-Sudhakar Dvivedi have made, at times, heir emended readings have been recorded as C i n the footnotes o f the present edition. D. T h e edition, Translation and Notes of TS by O . Neugebauer and D . Pingree, (2 vols., Copenhagen, 1970). Pingree edits and translates the PS, while Neugebauer offers the Notes. A l l

XVIII

PANCASIDDHANTIKA

our manuscripts are used i n this edidon too. H e r e i n 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 Pancasiddhantika 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 Brhatsamhita of Varahamihira. Other authors who quote from the PS are Prthiidakasvamin ( A . D . 854), Makldbhatta (14th cent.), Parame^vara of Kerala (1360-1460), Nilakantha Somayaji, (b. 1443), 9'^ain of Kerala, and Siiryadevayajvan (b. 1191) of T a m i l n a d u , i n South India. These PS quotations are taken as External Testimonia and the variants found i n such readings have been noticed in the footnotes with ' E ' prefixed to the abbreviations o f authors/works which quote the verses. These sources are : E. Jy. Jyotirmimdmsd of Nilakantha Somayaji. E.M. Makkibhatta's C o m . on the Siddhdntasekhara o f Sripati. E.N. Nilakantha Somayaji's Bhasya on the Aryabhatiya. E.Pa. Paramesvara's com. on the Aryabhatiya. E.Pr. Prthudakasvamin's com. on the Brdhmasphutasiddhdnta of Brahmagupta. E.S. Suryadevayajvan's com. on the Aryabhatiya. E.U. Utpala's com. on the Brhatsamhitd of Varahamihira. 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 h i m . O n the provenance of PS, Pingree states that: "So far there is no indisputable evidence that the Paiicasiddhantika 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 drgganita school i n their commentaries o n the Aryabhatiya. T h u s Paramesvara (c. 1380-1460) cites a verse, and Nilakantha (b. 1443) several others. It is noteworthy that all four verses that they quote are also found i n Utpala's commentary on the Brhatsrtihita, which was known in Kerala; it is not proved, then that they had a copy o f the Pancasiddhantika." (Introduction p. 17).

Pingree's assertion as above is not correct for the reason that Kerala and South Indian astronomers quote not only the said four verses occurring i n Utpala's commentary, but five more PS verses which do not occur i n Utpala's commentary, they being PS, 1.3, 4 by Nilakantha in his Jyotirmimdmsd, the verses safikhyd tu tesdm andydny atahprati again by Nilakantha i n his AryabhatiyaI V . 10 and PS X I I I . 3 6 by Siiryadevayajvan i n his Aryabhattyavydkhyd. (See below A p p . II: Index o 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 i n footnotes i n the present edition are restricted to be above-said material listed under A , B , C , D and E . Some o f 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 docitmented by Pingree i n his edition of the PS and so can be referred to therefrom.' 3. Presentotionof theText While the generally accepted conventions of critical editing o f Indie texts are duly followed i n the present edition, attention might be drawn to certain methodologies which are stressed herein, in view of the technical nature o f the text, the defective nature o f the manuscripts and the tentativeness of many of the emendations and textual changes effected i n the two earlier editions. i. O n account o f the inadequacies o f the copyists o f the parent manuscripts a n d also due to deficiencies i n the parent manuscripts themselves, some emendations have to be done i n the edited text. However special care has been taken i n 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 Varaha Mihira's Pancasiddhantika',//. of Asiatic Society of Bengal, 53 (1884) 259-93. ii. S.B. Dikshit, 'The Original Surya-siddhanta', Indian Antiquary, 19 (1890) 45-54. iii. S.B. Dikshit, 'The Romaka Siddhanta', Indian Antiquary, 19 (1890), 133-42. iv. S.B. Dikshit, 'The Paiicasiddhantika', Indian Antiquary, 19 (1890) 439-40. V. J . Burgess, 'The Romaka Siddhanta', Indian Antiquary, 19 (1890) 284-85. vi. J . Burgess, 'The sines and arcs in the Pancasiddhantika', Indian Antiquary, 20 (1891) 228. vii. M.P. Kharegat, 'On the interpretation of certain passages in the Pancha Siddhantika of Varahamihira, an old historical work'//, of the Bombay Branch of the Royal Asiatic Society. 19 (1895-97) 109-41. viii. K.S. Shukla, 'On three stanzas from Pancasiddhantika,' Ganita, 5 (1954) 129-36. T.S. Kuppanna Sastri ix. 'The Vasistha Sun and Moon in Varahamihira's Paiicasiddhantika', Jl. of Or. Research, Madras, 25 (1955-56) 19-41. X. 'Some misinterpretations and omissions in Thibaut and Sudhakara Dvivedi in the PS of V M ' , Vishveshvaranand IndologUal Journal, 11 (1973) 107-18. xi. 'The epoch of the Romaka Siddhanta in the PS and the epoch longitudes of the Sun and Moon the Vasistha Siddhanu', Indian Jl. of Hist, of Science, 13 (1978) 151-58. xii. 'The Vasistha-Paulisa Venus in the PS of V M ' , Collected Papers of T.S. Kuppanna Sastry, Tirupati, 1989, pp. 141-47. xiii. 'The Vasistha-PauliSa Jupiter and Saturn in the PS', Collected Papers, pp. 148-68. xiv. 'The Vasistha-PauliSa Mars in the PS of V M ' , ColUcted Papers, pp. 169-87. XV. 'The epoch-constants ofthe Vasistha-Paulisa star-planets', Collected Papers, pp. 201-5. xvi. 'Saurasiddhanta of PS : Planetary constants and computation', Collected Papers, pp. 206-40. xvii. 'Paiicasiddhantika XVIII. 68-81 : A n interpolation", ColUcted Papers, pp. 241-54.

XX

PANCASIDDHANTIKA

ii. Thibaut and Dvivedi who print their emended text i n the right hand column of their edition do not specifically indicate their emendations and one has to identify the emendations oneself Pingree indicates his emendations in many places by angular brackets but i n many other places prints the emended text without any indication. In the present edition, all their emendations are idendfied and nodced i n the footnotes denoting them by the sigla C and D . W h e n these emendations are accepted i n the present edition also, they are not separately marked as above. This procedure is expected to enable the comparison between the emendations of T S and N P 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 T S and N P , especially of the latter, are often far-fetched, ungrammadcal, offending the metre or failing to give a cogent sense. See, for example, the T S / N P emendations in 1.23; I X . 5 ; X I . 2 , 4, 5; XII.5a, 5d; X I I I . 3 8 d , 4 I d : X V I I . I , 12; X V I I I . 2 d , 3, 19, 24, 25. iii. In order that a discernmg student ofthe text shall have before him, i n full, what occurs in the several manuscripts, an attempt has been made to record all variants, right or wrong. T h i s has been done for three reasons : (a) Correct forms of corrupt passages can be visualized only i f all the readings, as found i n the manuscripts, are before one's eyes; (b) T h e n alone would it be possible for an editor to vindicate the emendations suggested by h i m ; (c) T h e corrupt and apparently meaningless readings i n the manuscripts which the editor could not correct or has wrongly emended can be corrected or better emendations suggested by other scholars i f all the variants are given. However, obvious errors of a purely scribal nature, like separate words written jointly, using anusvdra for anundsika 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 corrected silently and not noticed i n the footnotes. 4. Translation T h e translation provided i n the edition is as literal as possible without sacrificing readability and not going against the English idiom. Elucidatory expressions and words which are understood i n 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 T h e 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. T h e emendations made by T S and N P are also examined and observations offered. A n 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 chapters, towards setting out the significance ofthe contents ofthe respective chapters. 6. Division of Pancasiddhantika T h e colophons ofthe several Sections of P S , as found i n 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 adhydya-s (chapters) and also indicate the numbers thereof. T h e several colophons read :

INIRODUCTION

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

XXI

Karanavatarah Naksatradicchedah Iti Paulisasiddhantah Id Karanadhyayas caturthah Id Sasidarsanam Candragrahane sasthodhyayah Paulisasiddhante ravigrahanam Id Romakasiddhante 'rkagrahanam astamo 'dhyayah Id Suryasiddhante 'rkagrahanam navamo 'dhyayah Candragrahanam dasamo'dhyayah A(nu)varnanam ekadaso 'dhyayah Id Paitamahasiddhante dvadaso 'dhyayah Trailokyadarsanam nama trayodaso 'dhyayah Iti Chedyakayantrani caturdaso 'dhyayah Jyotisopanisat paiicadaso 'dhyayah Siiryasiddhante madhyagatih Taragrahasphutikaranam sodaso (? saptadaso) 'dhyayah Paulisasiddhante taragrahah

However, whether there be full chapter headings and chapter numbers or there be only the mention of the topics in the colophons, the commencement of a new subject helps to ascertain the beginnings of the chapters. T h e omission of the specification of the chapter headings and numbers has to be ascribed to the imperfections i n the original archetype.

This helps us to correct Pingree's edition where Chs. X V I and X V I I are taken as a single chapter, which he numbers as X V I . N o w , after eleven verses, here, there occurs the colophon 'Suryasiddhante madhyagatih', which is the subject of those eleven verses. After still another fourteen verses occurs i n the colophon 'Tdrdgrahasphutikaranam sodaso 'dhyayah', and an entirely different subject is treated in those fourteen verses. Ignoring the radical difference i n 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 ofthe second set of verses, Pingree combines the two sets of verses, 11 plus 14 = 25, to constitute ch. X V I and takes ch. X V I I I of TS and ofthe present edition as ch. X V I I . 7. Chapter XVIII of Pancasiddhantika T h e theme of C h . X V I I I is the heliacal rising and setting o f the star-planets according to the Vasistha and Paulisa 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, Varahamihira, 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. H a v i n g thus completed his treatise, couched entirely i n the Arya metre, following a convention, adopted by Sanskrit writers, of concluding works by a closing colophonic verse couched i n a different metre, V M breaks into a different metre, the Vasantatilaka, for the purpose : dvantyahah samdsdc chisyahitdrtham sphutdnkasamam cakre Vardhamihiras tdrdgrahakdrikdtantram || 61 | Pradyumna-bhumitanaye jive saure 'tha Vijayanandikrte \ budhe ca bhagnotsahah sphutam idam karanam bhajatdm 11 62 11

PANCASIDDHANTIKA

XXII

drstam Vardhamihirena sukhaprabodham \ • II 63 II T h e manuscripts are defective here, omitting the next three lines of the concluding verse, some exhibidng also a gap. In continuation of the above, the manuscripts commence another short work with a mahgalasloka ('verse of salutation') and then a second verse expressing a pratijnd ('resolve') to compose a 'better work' by 'Varahamihira himself.' prastdve 'pi na dosan jdnann api vakti yah paroksasya \ prathayati gundrhs ca tasmai sujandya namah parahitdya \ astddasabhir baddhdny d tdrdgraham etad drydbhih \ varam iti Vardhamihiro daddti nirmatsarah karanam \ \ These verses end abruptly without any closing colophonic verse, as might be expected.

Not taking into consideration the fact that V M had closed the PS most formally with all attendant paraphernalia, with verse 63, both T S and N P treat this short work, as the concluding part of Pancasiddhantika and as a work of Varahamihira himself, and translate it and explain it as such. It is no noticed by T S and N P 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 i n the computation of Venus and Mercury, which one cannot expect to be committed by VM.

T h e prose colophon 'Paulisasiddhante taragrahah evam' ('Thus the star-planets of the Paulisasiddhanta') does not have any reality behind it since the computations therefrom do not accord with those o f the Paulisasiddhanta elucidated earlier. These points have been discussed in detail in the Notes, below, to these verses. Obviously, these verses are apocryphal and are the handiwork o f a n inferior astronomer who has ascribed them to V M . F o r this reason, in the present edition, Pancasiddhdntikd is formally closed with verse 63 and the verses following given as'-a praksepa (interpoladon) 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 Siddhantas in PS : Their Distribution It had been mentioned earlier that V M ' s treatment of the five siddhantas in the PS are uneven. It is not that each Siddhanta is taken u p one by one and a resume of the same given fully or systematically. Select topics are taken up, apparently arbitrarily, and are dealt with individually or jointly when the enunciations o f two schools are similar. Alongside, chapters are devoted also to general astronomical topics which are applicable to all the schools. T h e assortment of the treatment of the subjects i n the several chapters are as indicated below.

9. Content Analysis of the Pancasiddhantika C h . I . 1-7 8-10 11-13 14-16

General Romaka Paulisa Saura-Romaka

Introducuon Days from epoch (Ahargana) Days from epoch (Ahargana) Yuga o f S u n and Moon, Lords ofthe year, month, and hora.

XXIII

INTRODUCTION

C h . I . 17-25

Romaka

Ch.II

1-13 1 2-6 7 7 8 9-10 11-13

Vasistha

Ch.III 1-37 1-3 4 5 6-9 10 11-12 13-14 15 16 17 18-19 20-22 23-24 25 26 27 28-29 30-31 32 33 34-35 36-37

Paulisa

General

C h . I V 1-58

General

1-15 16-18 19-22 23-25 26-28

//

n It If II 11 ti

11 11 II It It It 11 II II If 11 11 11 11 II II II II 11 II 11

11 11 11

II

11

Lords of the days of the month

T r u e Sun (Ravi-sphuta) T r u e M o o n (Candra-sphuta) Naksatra computation T i t h i computation Day-time (Aharmana) Gnomonic shadow (Saiikucchaya) Lagna

T r u e Sun (Ravi-sphuta) T r u e motion of M o o n (Candragati) Equation of the centre (Mandaphala) Sense obscure Cara Day-time (Aharmana) Desantara Local time (Istadesakala) Naksatra computation Sun's daily modon (Ravi-gati) Karana-s Vyatipata and V a i d h r t i Sadasiti-kala Solsdces (Ayana) Saiikrand-kala Tridinasprk-yoga Rahu (Node) Moon's latitude (Candra-viksepa) Bhadravisnu, defect i n Padaditya, defect i n Romaka, defect i n Astronomy, importance of Problems of Time, Space and DirecUon (Triprasna) Table of R sines (Jyah) Declination of Sun and M o o n (Krand) Gnomonic shadow and derivatives (saAkucchaya) Sine colatitude and Day-diameter (Lambajya and Dinamana) Cara and derivatives

PANCASIDDHANTl K A

XXIV C h . I V . 29-30

"

31-34 35-36 37-38 39-40 41-49

" " " " "

50-51 52-54 55-58

" " "

Rt. ascensional difference (Lartkodaya-rasimana) Rising of signs (Rasyudaya) Gnomonic shadow (Sartkucchaya) Astronomer's qualifications Sine amplitude (Agra) Gnomonic shadow at required time (Istacchaya) Moon's shadow (Candracchaya) Directions from shadow (Diksadhana) Sun from gnomonic shadow (chayatah ravih)

Paulisa

Moon's horns (Candrasrngonnati)

Ch.VIl-14

Vasistha and Paulisa

L u n a r eclipse (Candragrahanam)

C h . V I I 1-6

Paulisa

Solar eclipse (Ravi-grahana)

C h . V I I I 1-18

Romaka

Solar Eclipse (Ravi-grahana)

C h . I X 1-27

Saura

Solar eclipse (Ravi-grahana)

C h . X 1-7

Saura

L u n a r eclipse (Candra-grahana)

C h . V 1-10

C h . X I 1-6

General

C h . X I I 1-6 1-2 3-4 4 5

Paitamaha "

"

Eclipse diagram (Grahanaparilekha)

Days from epoch (Ahargana) T i t h i , Naksatra etc. Vyatipata Day-time (Aharmana)

C h . X I I I 1-42

General

Situadon of ther worlds (Trailokyasathsthanam)

C h . X I V 1-41

General

Astronomical instruments (Chedyaka-yantrani)

C h . X V 1-29

General

Jyotisopanisat

Ch.XVII-II 1-9 10-11

Saura " "

Mean planets Mean planets (Graha-madhya) Bija correction by V M

XXV

INTRODUCTION

C h . X V I I . 1-14 1 -11 a lib 12 13- 14

Saura " " " "

True planets True planets (Graha-sphuta) Retrograde motion (Vakragati) Heliacal rising (Grahastodaya) Planetary latitudes (Graha-viksepa)

C h . X V I I I 1-60

Vasistha-Paulisa

Heliacal rising and setting of planets (Grahastodaya) Venus (Sukra) Jupiter (Guru) Samm(Sani) Mars(Kuja) Mercury (Budha) Hints Conclusion of PS

1-5 6-13 14- 20 21-35 36-56 57-60 61-63 64-81 64-66 67-69 70-72 73-75 76-78 79-81

" " " " " " General Spurious Supplement " " " " " "

True planets Introduction True Mars True Mercury Truejupiter True Venus True Saturn

10. Depiction of the Siddhantas in PS The above Content Analysis of the PS would enable the identification ofthe extent of selective depicuon of the different siddhantas by V M in the work, as shown below.

PAULISA-SIDDHANTA

Ahargana Naksatra Mandaphala Ravigati Raviphuta Candra-sphuta Ayana SaAkranti Tridinasprkyoga Desantara Cara Aharmana Istadesakala Karana Vyatipata Vaidhrti

I.1I-13 H I . 16 III.5 III.17 III.1-3 III.4 III.25 III.26 III.27 in.I3-14 III. 10 III.I1-12 HI.15 III.18-19 III.20-22 III.20-22

Sadasltikala Candra-viksepa Rahu Candra-grahana Ravi-grahana CandrasrAgonnati Grahastodaya

III.23-24 III.30-3I III.28-29 V I . 1-I4 V I I . 1-6 V.1-10 X V I I I . 1-60

ROMAKA-SIDDHANTA Ahargana Yuga Lordoftheyear L o r d ofthe month L o r d ofthe H o r a L o r d ofthe Days Ravi-grahana

1.8-10 1.14-16 1.17-18,21 1.19,21 1.20,21 1.23-25 V I I I . 1-18

XXVI

PANCASIDDHANTIKA

SAURA-SIDDHANTA Yuga L o r d of the year L o r d of the month L o r d of the H o r a Graha-madhya Graha-sphuta Graha-viksepa Candra-grahana Ravi-grahana Grahastodaya

1.14-16 1.17-18,21 1.19,21 1.20,21 X V I . 1-11 XVII.1-11 XVn.l3-I4 X.I-7 I X . 1-27 X V I I . I 1-12

VASI§THA-SIDDHANTA Ravi-sphuta

II. I

II.2-6 II.7 II.7 II.8 II.9-10 ILIl-13 VI.I-I4 X V I I I . 1-60

XII.I-2 XII.3 XII.3 XII.4 XII.5

With regard to the Chapters and verses not included i n the above table, some, like chapters X I to X V , and several verses, are o f a general nature, applicable to all the siddhantas and i n the case of the others it is difficult to identify positively the siddhantas to which they pertain. 11. Comparative Study of the Siddhantas It can be seen from the above Table that several of the topics selected by V M from the different siddhantas for depiction in the PS are common. T h i s should enable a comparative study of the common topics, the more important o f which are noticed i n the Table below.

In this connection it is necessary to point out, an erroneous view current, to the effect, that the Paulisa siddhdnta is accurate, the Romaka is equally accurate, the Saura is still more accurate and tha the Vasistha and Paitdmaha highly inaccurate. T h i s view has been brought into vogue through two unwarranted emendations introduced by T S and N P into the text of the following verse i n the PS: Paulisatithis sphuto 'sau tasydsannas tu Romaka-proktah \ spastatarah sdvitrah parisesau duravibhrastau \ \ PS. 1.4 'The tithi resulting from Paulisa is tolerably accurate and that o f the Romaka approximate to that. T h e tithi of the Saura is very accurate. B u t that of the remaining two (viz., die Vasistha and the Paitamaha) have slipped far away (from the real).' H e r e V M speaks only about the tithi, (lunar day), as computed d u r i n g his time according to the different siddhantas; H e is not making a relative estimate ofthe siddhantas as such or i n respect of the various other computations. As elucidated i n the Note to this verse i n the body of this book (p.5):

"The five Siddhantas are compared here with reference to their tithi alone because that is the chief of the five afigas, viz., tithi, vara, naksatra, yoga and harana; that is most useful not only religous purposes but also for civil purposes; that is independent of the origin o f reference in the ecliptic and can be examined for correctness by observation of eclipses and heliacal rising; and that is used i n finding the days from Epoch, ihesine qua non of all astronomical computation. "This being the case, the change o f tithi into krta by the late D r . 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. D o i n g this, they have condemned the Vdsistha Siddhdnta 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 ( N P for short). See below. Explanatory Notes, for die real reason for this 'slipping away fr®m the real'." O n this subject might be advanUgeiously referred to the section 'The place of the Vasistha i n the history of H i n d u astronomy' i n T . S . K . Sastry's paper T h e Vasistha Sun and M o o n ' i n the/Z. of Or. Research, Madras, 25 (1955-56) 19-41, reprinted i n his Collected Papers on Jyotisa (Tirupati, 1989, pp.I-28)

Table of Common topics Ahargana Paulisa Romaka Paitamaha

I.I1-13 1.8-10 XII.1-2

III.16 II.7

Paulisa Vasistha

ni.1-3 n.i

Candra-sphuta Paulisa Vasistha

III.4 II.2-6

Aharmana Paulina

III.11-12

III.20-22 X1I.4

Candra-grahana Vasistha-Paulisa Saura

Ravi-sphuta

n.8 xn.5

Vyatipata-Vaidhfti Paulisa Paitamaha

Naksatra-Tithi Paulisa Vasistha

Vasistha Paitamaha

VI.1-14 X.I-7

Ravi-grahana Paulisa Romaka Saura

V I I . 1-6 vni.1-18 I X . 1-27

Grahastodaya Vasistha-Paulisa Saura

xvni.i-60 X V I I . I 1-12

12. Varahamihira: His l i f e and Works One ofthe foremost early Indian astronomer and astrologer, Varahamihira belongs to the sixth century A . D . I n the PancasiddhdntUtd (1.8) he takes the cut-off date or epoch for computations using the Paulisa Siddhdnta as Saka 427, which corresponds to A . D . 505. Since the practice i n Indian astronomical manuals (Karatia-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 P S was composed some time after A . D . 505. Regarding his demise there is a statement by Amaraja i n his commentary on Brahmagupta's Brdhmasphutasiddhdnta, which reads : navddhika-pancasarhkJiydsake Vardhamihirdcdryo divamgatah."In saka 509 Varahamihira attained to the heavens.' This would mean that V M passed away i n A . D . 587. T h i s date is corroborated by V M ' s mention i n P S X V . 10, of Aryabhata who composed his Aryabhatiya i n A . D . 499, which work should have become well known by the time that V M composed his P S .

XXVIII

PANCASIDDHANTIKA

Personal details about V M are forthcoming from his own writings as also from those of others. Towards the close of his Brhajjdtaka, V M says: Adityaddsa-tanayas tadavdptabodhah Kdpittakah savitrlabdhavaraprasddah | Avantiko munimatdny avahkya samyag Hordm Vardhamihiro ruciram cakdra \ \ (Br.J. 26.1 (Edn. Triv. Skt. Ser., No.91) T h u s V M was the son of Adityadasa; he learnt the sastra from his own father; his native place was Kapitthaka; he was blessed by L o r d Sun (at Kapitthaka). H e (later) resided at A v a n d (Ujjain) where he composed his v/ork Hord (Brhajjdtaka). O n Kapitthaka V M ' s commentator Utpala says : Kdpitthdkhye grdmeyo 'sau bhagavdn savitd suryah, tasmdt labdhah prdpto varah prasddo yena lage of Kapittha where he received the blessing of G o d Sun'). Kapitthaka, the nadve village of V M , has been idenufied by Ajay M i t r a Shastri (vide his India as seen by Varahamihira, ( M L B D , Delhi, 1969, p. 19) o n the basis ofthe mention thereof by 7th century Chinese traveller Y u a n Chwang with Kapittha populary known as "Sartkasya (modern Sankisa) i n the Farrukhabad district o f Uttar Pradesh...."

Utpala states in his commentary on V M ' s Brhatsarhhitd (1.1) that V M was a 'Magadhadvija' : tad ayam apy Avantyakdcdryo MagadhMvija-Vardhamihiraharkahbdhavaraprasddojyotissdstrasungra (Ed. Sarasvati Bhavana Granthamala, Varanasi, 1968, p.2). Utpala makes such a statement also in his commentary on V M ' s Yogaydtrd. T h i s and the surname 'Mihira' which is borne by many Sakadvipa brahmanas, who are worshippers ofthe Sun, would indicate that V M belonged to this clan of Brahmanas whose forefathers migrated to India from the Maga country in Persia and settled in the village of Kapitthaka whence V M came to the city of Ujjain where he wrote his works. By all accounts, Varahamihira had the Sun as his tutelary deity. T o quote A . M . Shastri (op. cit., pp. 20-21): 'That Varahamihira was a devotee of the Sun admits of no doubt. H i s father's name was Adityadasa, his own name-ending ' M i h i r a ' , derived from 'Mithra', the Iranian Sun-god, his obtaining a boon from the Sun, his obeisance to the Sun i n all his works except the Vivdhapatala, (which, appropriately enough, opens with an invocation to Kama, the Indian god o f love), and his devoting a comparatively larger number o f verses to the description of Surya icons, all indicate that the sun was his family deity. H i s son Prthuyasas also invokes the Sun i n the opening verse o f his SatpancdJikd. A s we have seen, Varahamihira was regarded as an incarnation of the Sun.' T h e fame of V M has given rise to several legends about his birth and incidents i n his life, including his being a courtier o f K i n g V i k r a m a and one of the nine gems (nava-ratnas) i n his court. A l l these have to be considered as more fable and eological, not based on facts. Varahamihira was an astute astronomer and astrologer and wrote extensively on all the three branches of the science, viz., Tantra or mathematical astronomy, Hord (Jdtaka) or horoscopy, and Sarhhitd or mundane or natural astrology. It is interesting that for all his major works. V M has prepared abridged versions also for the benefit o f those who desist from works which are too lengthy, who, as Utpala says, are vistaragrantha-bhiru-s.

INTRODUCTION

XXIX

O n Tantra the major work o f V M is the Pancasiddhdntikd i n eighteen chapters. It would seem from a statement of Utpala towards the beginning of his commentary on VM's Laghujdtaka that V M had prepared on abridgement also o f that work Cf. Vardhamihira jyotissdstrasangraham krtvd tadeva vistara-granthn-bhtrunarh krte' 'sanksiptam ganitasdstram' krtvd hordsdstram vaktukdmah e O n horoscopy V M has produced two works, the Brhajjdtaka, called also Hordsdstra i n 26 chapters, and its abridged version, the Laghujdtaka, called also Svalpa-jdtaka and Sdksmajdtaka, i n thirteen chapters.

O n natural or mundane astrology also V M has two works, the Brhatsamhitd called also Vdrdhisarhhitd in 106 chapters and Samdsasamhitd, known also as Laghu-samhitd and Svalpa-sarhhitd known through quotations. These are works of an encyclopaedic nature, dealing with astrological and many other subjects of human interest, such as architecture and iconography, water divining, omens, cosmetics, horticulture, characteristics of animals, gemmology, weapons, species of men and women and their qualities and the like. A wide range of information on the geography of India and its people is also to be round in the Brhatsamhitd. Vatakanikd, which exists only i n the form of quotations, is a work of V M on omens.

O n military astrology, three works of V M are available; (i) Mahdydtrd, known also as Brhadydtrd, Brhadyogaydtrd, Yaksyesvamedhikdh-yatrd (based i n the commencing expression yaksye 'svamedhe vijitya i n the second verse of the work), (ii) Svalpaydtrd or Tikanikdydtrd, and (iii) Yogaydtrd. O n marital horoscopy, V M has written a work endtled Vivdhapatala, a n d according to Utpala, there is also a Svalpavivdhapatala (vide, his com. on Brhajjdtaka X X . 10). M o r e than 30 more texts are mentioned, i n manuscripts and elsewhere, to have been composed by V M (Cf. A . M . Shastri, op. cit., pp. 29-31) but these lack authenticity i n their ascription. Alongside his wide range of scholarship, V M ' s writings are also characterised by chaste language, brevity and linguistic elegance. H e is a master not only of expression but also of metre. In illustration of his poetic talents one might refer to the figures of speech expressed through verses X I X . 13-15 of the Brhatsarhhitd describing Agastyodaya, the rising of the star Agastya. In the same work, Brhatsamhitd, he utilises the entire chapter 104, containing 64 verses, the Gocarddhydya ('Transits of planets'), to illustrate the metres, including the dandaka-s, alongside depicting the subject proper. It is also instructive that the names ofthe several metres are also deftly incorporated i n the verses by means of slesa or double entandre. Utpala is not, perhaps off the mark when he says, towards the commencement of his commentary on Brhatsamhitd, extolling V M as an incarnation ofthe S u n : Yac cdstram savitd cakdra vipulam skandhatrayair jyautisam tasyocchittibhaydt punah kaliyuge sarhsrjyayo bhdtalam \ bhuyah svalpataram Vardhamihira-vydjena sarvam vyadhdd ittham yam pravadanti moksakusalds tasmai namo bhdsvate 'The science of Jyautisa i n its triple aspects (oi Tantra, Jdtaka, and Sarhhitd) was propounded at length by G o d Sun. Fearing that it would be lost i n the K a l i age, G o d Sun incarnated i n the world in the form of Varahamihira and expounded all (the said three aspects) again i n shorter form. So say about the Sun those who are knowledgeable about salvation. Obeisance to that Sun.' Madras January 4,1993

K.V. SARMA

PANCASIDDHANTIKA

Chapter One INTRODUCTION OF THE WORK

cb sin lat, then sin colat > day-diameter. Therefore sin rt. asc. > 120', for which there is no arc, which means that at no aldtude, or at no time does the Sun cross the prime verdcal. T h i s is what was referred to earlier and here shown mathematically.

34. Multiply sine declination by 240 and again by sin co-latitude and divide by the

product of the

sine of latitude and day-diameter. F i n d its arc in

degrees and divide by six. (The time in nadis, taken by the Sun to move from

110

PANC;ASIDDHA.\TIkA

IV. 35

the unmandala to the p r i m e v e r t i c a l is got.) A d d to it the t i m e o f half-cara. T h i s is the t i m e f r o m sunrise for the S u n to r e a c h the p r i m e v e r t i c a l . T h e following is the work: (i) Sin (arc corresponding to time from unmandala to prime vertical) = 240 ' X sin dec X colat (sin lat X day-diameter) (ii) T h e arc in degrees of (i) is to be got. Dividing by 6, the time in nddis is got. (iii) T h e time got by (ii) -I- the half-cara is the time after sunrise, for the Sun to cross the prime vertical. Note that the formula here given is what we arrived at earlier, as what the author's formula reduces to in verses 32-33. T h e n , why is this repetition? In the previous two verses, the work was not given clearly and fully. Here it is clear and full.

Now for the reading: F r o m the words khajinaghni krdntijyd lambaghni, it is clear that the produc of two sines must be the divisor. Therefore, we have corrected dhruvaguna dyudairghyahrtd into dhnivaguna-dyudairghya-hatd, which is otherwise also a better reading. Other small corrections have been made according to the idea intended to be expressed, and according'to syntax. T h u s it is clearly seen that in the work sin colat appears as part of the numerator, and sin lat. as part of the denominator, from which it can be seen clearly that the formula is concerned with finding the dme of the Sun's rise from unmandala to the prime vertical, and not the half-cara. T h e mention of the half-cara here is just to say that it should be added to find the whole dme. However, both T S and N P have been misled by the mention of the expression 'half-cara' into thinking that the formula itself is to find the half-cara, with the result that they take the numerator as the denominator, and the denominator as the numerator, not realising that by their interpretation the rule for half-cara would be a repedtion, because in I V . 26 also the same has been given, and in the same form, which N P , too, have, noticed and observe: "This in fact, is only a repetition of I V . 26. It is here out of place." (pt.II, p.43). But it may be asked whether the work according to our interpretation is not a repetition of the work of the previous two verses. We say the work as given here is clear, succinct and full. B u t when what is the use of the two previous verses? T h e work there given is easy to explain on the basis of the rule for the Rt. ascension o f the ecliptic point, gone before. O r , that method perhaps is that of the Paulisa, the author giving the same in a better form here. T h e example on this has already been worked out i n Example 12.

34a. A l . ^ % r a t ; A 2 . ^ i ^

d. C . D . ^ ? 1 ^

b. C D . (HM^dl ^'^''W. A.ffcng^

A.f^^l^^HI^:; C f ^ ^ ^ ^ ^ ^ K ^ : ;

c. A.d^lMi^l

D.f^[fsr]^^^:

I V . 35

IV. IHRF.K I'ROBI.K.MS

111

Great gnomon (Sama-saftku) and its shadow 3 5 . W h e n the S u n is i n the n o r t h e r n h e m i s p h e r e , (i.e. i n the six signs, A r i e s etc.), m u l t i p l y the sine o f the l o n g i t u d e o f the S u n by the sine o f the m a x i m u m d e c l i n a t i o n , (i.e. by 4 8 ' 48"), a n d d i v i d e by the sine o f l a t i t u d e . T h e m i n u t e s so o b t a i n e d are c a l l e d the m i n u t e s o f the ' G r e a t g n o m o n ' o r $anku, (i.e. sine o f a l d t u d e ) , ( a n d i n this case, the sine o f P r i m e v e r d c a l altitude). F r o m this the s h a d o w o f the S u n o n the p r i m e v e r t i c a l m u s t be c a l c u l a t e d . (i) Sin prime vertical altitude = sin Sun's long x 48' 48"-^ sin latitude. T h i s is the Great gnomon, and the radius is the Great hypotenuse. T h e square root of the square of the hypotenuse lessened by the square o f the gnomon is the shadow. Therefore the Great shadow = Vradius' — sin ' prime vertical alt. Therefore, by the similarity between the Great shadow and the shadow triangles, we have the proportion. Great gnomon: Great shadow :: Twelve unit gnomon: shadow. F r o m this, the required, (ii) Shadow = 12 x V 120' - s i n ' prime vertical alt.

sin prime vertical aldtude.

Example 13. The longitude of the Sun is rdsi 1-0. The latitude is 30°. Find the Great gnomon of the Sun at prime vertical, and thereby the gnomonic shadow at that time. (i) T h e Great gnomon = sin prime vertical altitude = Sin Sun's longitude X 48' 48" sin ladtude = 60' X 48' 48" 4- 60' = 48' 48". (ii) Shadow = 12 X V120' - 48' 48"' ^ 48' 48" = 12 X 109' 38" H - 4 8 ' 4 8 " = 12 X 109 19/30 4- (61/L50) = 1644 - 30 ^ 61 = 26 units and 58 parts, angulas and vyangulas T h e equation (i) can be written as. Sin prime vertical alt. = sin Sun's l o n g . X sin max. dec. sin lat. = sin Sun's long. X sin max. dec x radius ^ (sin lat x radius) = (sin Sun's long. X sin max. dec -H radius) x (radius X sin lat) Here, it can be shown that sin Sun's long x sin max. dec

radius =

' *^ Kig. IV. Vi

d e c , thus:

Sin Sun's l o n g . X sin max. dec radius = sin Sun's l o n g . X 48' 48" ^ 120' = sin Sun's long^x 61/150 = sindc. (by I V . 16). O r , from Fig. 13, thus: In the triangle right-angled at R, rS is the Sun's long, and SR is the declination o f the Sun. SrR is the m a x i m u m declination. B y fundamental formula II, sin rS x sin SrR 4- radius = sin SR. .-.sin Sun's long x sin max. dec ^ radius = sin dec. 35. Quotedby Utpala o n B S 2, p.42 35b. A.+ISlTli'Juil

d. A.*liy