PAÑCASIDDHĀNTIKĀ
OF VARĀHAMIHIRA
WITH TRANSLATION AND NOTES
BY
T.S. KUPPANNA SASTRY
CRITICALLY EDITED
WITH INTRODUCTION AND APPENDICES
BY
K.V. SARMA
P.P.S.T. FOUNDATION
ADYAR, MADARS
1993

THE BOOK
The Pañcasiddhāntikā of the sixth century
astronomer Varāhamihira is a major work on
mathematical astronomy of early India, and
is particularly significant for the fact that it
provides a résumé, though uneven, of five
astronomical schools, viz., Vāsiṣṭha,
Paitāmaha, Romaka, Pauliśa and Saura, which
flourished in India during the early centuries
of the Christian era. The full texts of all these
systems are now lost, which makes the Pañ-
casiddhāntikā all the more significant. All the
available manuscripts of the work go back to
a defective original. This makes the full and
correct understanding of the work difficult
and indefinitive, there being also occasional
lacunae and obscure passages. These have, in
many places, affected adversely the text and
the translations of this work as issued earlier,
by G. Thibaut and Sudhakara Dvivedi (Be-
nares, 1889) and by O. Neugebauer and David
Pingree (Copenhagen, 1970).
The present Critical edition of the
Pañcasiddhāntikā, which makes use of all the
available manuscripts of the text as also
external testimony, attempts to present a
much more perfect text and translation of the
work. To the edition has been added an
authentic translation of the work with
explanatory notes in terms inclusive of
modern mathematics, adumbrated by tables
and diagrams. Wherever computations are
involved, illustrative examples are worked
out. Besides an informative and analytical
General Introduction, explanatory introduc-
tions are prefixed to chapters indicating the
contents and the method of approach
adopted in those chapters.
THE EDITORS
Professor T.S. Kuppanna Sastry (1900-1982),
M.A., L.T., was a polymath. A Sanskritist by
profession, he was also a keen student of the
sciences, both eastern and western. His forte
was early Indian astronomy, which he studied
in comparison with modern astronomy. The
combination had given him the insight and
analytical skill to understand and appreciate
early Indian astronomy in terms of
modern astronomy. His publications include
critical editions of the Mahābhāskarīya of
Bhāskara I with two commentaries, and the
Vedāṅga Jyotiṣa with Translation and detailed
notes. Jointly with K.V. Sarma, he edited the
Vākyakaraṇā of Vararuci with commentary. A
number of papers which he wrote on Indian
astronomy have been collected together and
issued under the title Collected Papers on
Jyotisha (Kendriya Sanskrit Vidyapeetha,
Tirupati, 1989).
Professor K.V. Sarma, (b.1919), B.Sc., M.A.
(Skt.), D.Litt. (History of Astronomy), formerly
Director of the wellknown V.V. Institute of
Sanskrit and Indological Studies, Hoshiarpur
(Punjab), and presently Hon. Professor of
Sanskrit, Adyar Library and Research Centre,
Madras, has been a student of Indian astronomy
for nearly forty years. He has edited and
translated a large number of astronomical
texts, mainly produced in Kerala. These include
Dṛggaṇita, Grahacāranibandhana, Tantrasaṅgraha,
Sphuṭanirṇaya, Rāśigolasphuṭānīti, Goladīpikā,
Candrasphuṭāpti and Jyotirmīmāṁsā. He is the
author, jointly, of Indian Astronomy: A Source
Book (Bombay, 1985). His writings include
also about 250 research papers on different
subjects including Indian astronomy.
Price: Rs. 350/-

P.P.S.T. SCIENCE SERIES NO. 1
PAÑCASIDDHĀNTIKĀ OF VARĀHAMIHIRA
EDITED AND TRANSLATED
Appendix 7 added at end by A.K Upadhyay

P.P.S.T. SCIENCE SERIES NO. 1
PAÑCASIDDHĀNTIKĀ
OF VARĀHAMIHIRA
WITH TRANSLATION AND NOTES
BY
T.S. KUPPANNA SASTRY
Appendix 7 added at end by A.K Upadhyay
CRITICALLY EDITED
WITH INTRODUCTION AND APPENDICES
BY
K.V. SARMA
Adyar Library and Research Centre, Madras
P.P.S.T. FOUNDATION
ADYAR, MADRAS
1993

Published by :
PPST Foundation,
POB 2080,
Adyar,
Madras 600 020
(India)

©

ALL RIGHTS RESERVED
First Edition 1993

Printed in India

By Vipin Sachdev, Printers Plates,
231, Royapettah High Road, Madras 600 014

PREFACE

The Pañcasiddhāntikā of the sixth century astronomer Varāhamihira is a major work on
mathematical astronomy of early India. The work is particularly significant for the fact that,
besides providing an insight into the level of contemporary development in the discipline, it forms
also a resumé, though uneven, of five astronomical schools, to wit, the Vāsiṣṭha, Paitāmaha, Romaka,
Pauliśa and Saura, that were in vogue in India during the early centuries of the Christian 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 editions 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. The main difficulty in gaining a proper
understanding, let alone producing a correct edition, of the Pañcasiddhāntikā 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 in the words of G. Thibaut in the Preface (p.v.)
to his edition of that work. He says :
“Imperfect and fragmentary as (the) text and (the) translation are, we may
assert, at any rate, that in our endeavours to overcome the quite unusual obs-
tacles which the corrupt and bare text of the Pañcasiddhāntikā opposes to the
interpreter, we have spared no trouble. The time and thought devoted to the
present volume would, I may say without exaggeration, have amply sufficed
for the editing and explaining of twenty times the amount of text presenting
only normal difficulties.”
Hence the need for a further attempt for a better edition and interpretation of this important text
on early Indian astronomy.
The present edition which is based on all the available manuscripts of the text and also external
testimonia and which takes into consideration the work of interpretation attempted in the two pre-
vious editions, presents as critical and readable a text as is possible on the basis of the above-said
material. To this is added a literal translation with explanatory words added as necessary. This is
followed by detailed explanatory notes in terms inclusive of modern mathematics, and adumbrated
with tables and diagrams. Whenever computations are involved, illustrative examples are given
and worked out. There again, most of the chapters are provided with explanatory introductions
indicating the general contents and method of approach of the matter contained in the chapters.
The above work has been a labour of love pursued by the late Prof. T.S. Kuppanna Sastry, for-
merly Professor in the Sanskrit College, Madras. A scholar in Sanskrit, a student of modern
mathematics and one fully conversant with Jyotiśśāstra, Prof. Sastry was an ideal combination of
Indian and Western schools of astronomy. And, as such, he was best fitted for the task of expoun-
ding a difficult text on Indian astronomy like the Pañcasiddhāntikā.

VI PREFACE
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 XIV had
been left untouched and so also were verses 35 to 55 of chapter XVIII. The later chapters, portions
of which had been issued in the form of articles, were in their rough draft form.
The 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 chal-
lenge and set to work on it without delay. In this matter I had the cooperation of two eminent scho-
lars in astronomy, Prof. K.S. Shukla of Lucknow and Shri. S. Hariharan of Bangalore.
Work on Prof. Sastry's manuscript was twofold. The 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 Ch. XIV with notes and diagrams and Shri. Hariharan supplied the
Translation and Notes for the verses left out in Ch. XVIII. While the above was done at Lucknow
and Bangalore, respectively, in Madras, the end chapters were put in proper form. Alongside, the
entire manuscript, running to about 500 pages, was duly perfected. This 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.
The second task related to the critical editing of the textual verses. A draft press copy was pre-
pared on the basis of the readings adopted by Prof. Sastry. Copies of all manuscripts of Pañca-
siddhāntikā available at different repositories were procured and collated with the draft press copy.
The text in the two printed editions and in the external testimonia, which had also been assembled,
was collated similarly and the variants recorded. And, on the basis of the above, the final press copy
of the critical text was prepared. Varied typography for the half a dozen different items of the edi-
tion was also selected to set off the same distinctly in print.
The resultant edition, provided with an Introduction and necessary Appendices including a Sub-
ject Index, is now placed before scholars. It is to be hoped that this edition of Pañcasiddhāntikā will
contribute, in some measure, to the furtherance of the study and appraisal of early Indian
mathematics and astronomy.
The publication of this volume had been made possible by the generous contribution of friends
and patrons of academic studies. The Birlas made a gracious donation of Rs. 20,000/- and Dr.
T.K. Balasubramanian, of Rs. 5,000/-. The 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. The 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 coöperation

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 :