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Books > Astrology > Original Texts > Pancasiddhantika of Varahamihira
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Pancasiddhantika of Varahamihira
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K.V. Sarma

The Pancasiddhantika of the sixth century astronomer Varahamihira is a major work on mathematical astronomy of early India, and is particularly significant for the fact that it provides a resume, though uneven, of five astronomical schools, viz., Vasistha, Paitamaha, Romaka, Paulisa 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 Pancasiddhantika 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 (Benares, 1889) and by O. Neugebauer and David Pingree (Copenhagen, 1970).

The present Critical edition of the Pancasiddhantika, 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 introductions are prefixed to chapters indicating the contents and the method of approach adopted in those chapters.

 

About the Author

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 Mahabhaskariya of Bhaskara I with two commentaries, and the Vedanga Jyotisa with Translation and detailed notes. Jointly with K.V. Sarma, he edited the Vakyakarana 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).

 

About the Editor

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 Drgganita, Grahacaranibandhana, Tantrasangr’aha, Sphutanirnaya, Rasigolasphutaniti, Goladipika, Candrasphutapti and Jyotirmimimsa. 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.

 

Preface

The Pancasiddhantika of the sixth century astronomer Varahamihira 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 resume, though uneven, of five astronomical schools, to wit, the Vasistha, Paitamaha, Romaka, Paulisa 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 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 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 obstacles which the corrupt and bare text of the Pancasiddhantika 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 previous 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, formerly Professor in the Sanskrit College, Madras. A scholar in Sanskrit, a student of modern mathematics and one fully conversant with Jyotissastra, Prof. Sastry was an ideal combination of Indian and Western schools of astronomy. And, as such, he was best fitted for the task of expounding a difficult text on Indian astronomy like the Pancasiddhantika.

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 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 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 prepared on the basis of the readings adopted by Prof. Sastry. Copies of all manuscripts of Pancasiddhantika 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 0 the critical text was prepared. Varied typography for the half a dozen different items of the edition was also selected to set off the same distinctly in print.

The 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.

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 cooperation 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. 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 Pancasiddhantika.

 

Introduction

The Pancassiddhantika (PS) of Varahamihira (VM), (6th cent. A.D.), occupies an important place the history of early Indian astronomy, for, herein we have been given certain aspects of five systems 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:

purvacaryamatebhyo yad yad srestham laghu sphutam bijam

tat tad ihavikalam aham rahasyam udyato vaktum

Paulisa-Romaka-Vasistha-Saura-Paitamahas tu panca siddhantah

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 siddhanta-s, of which this work is a compendium, are the Paulisa, the Romaka, the Vasistha, the Saura and the Paitamaha.

Following the above statement, VM specifies also how he is intending to deal with the said five astronomical schools:

yat tat param rahasyam bhavati matir yatra tantrakaranam

tad aham apahaya matsaram asmin vaksye graham bhanoh

dik-sthiti-vimarda-karna-pramana-vela grahagrahav indoh

taragrahasamyogam desantarasadhanam ca ‘smin

samamandala-candrodaya-yantra-cchedyani sankavacchaya

upakaranady aksajya- ‘valambaka-’ pakramadyani

I shall tell in this work, avoiding all jealousy, the computation of the solar eclipse which is as a great secret and in which the mind 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, 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 ant 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 preparation of a correct edition of the work a formidable task, affecting, in its turn, a proper understanding, 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:

“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 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 Pancasiddhantika. 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, however imperfect, of our tong continued endeavours to restore and elucidate the text of the Pancasiddhantika. In 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. And, in the second place, we feel convinced that even from that pan of the Pancassiddhantika 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 him and the editorial criteria adopted by him Thibaut says in his Introduction to the edition:

“The present edition of the Pancasiddhantika 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 man’ cases, to be treated with great liberty. Not unfrequently, the emended text is merely meant a an equivalent in sense of what we suppose Varaha Mihira to have aimed at expressing, while we attach no importance to the words actually employed in the emendation.” (p.lx).

The Pancasiddhantika has again been edited recently by O. Naugebauer and D. Pingree, (NP). And 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 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 manuscripts that have become available, all go back to the two manuscripts used in the first edition, t shown by the commonality in them of omissions and corruptions which occur in the newly available manuscripts.

The edition of Pancasiddhantika which is now issued is also based on the manuscripts used for the 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 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 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 Pancasiddhantika, the principle of sthitasya gatis cintaniya, ‘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 t the language and the subject of the text. ‘Real’ emendations have been comparatively small and 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 errors and in square brackets in the case of editorial supplementation. And, whenever there has 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 a en 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 Varahamihira.

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 Pancasiddhantika, of which five have been collated for preparing 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 expect 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 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 Al, A2 and B 1, 82, 83, 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 Stambhatirtha (modern Cambay in Gujarat) in Sam. 1673, Saka 1538 (AD. 1616), by Sankara 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, l0a, 12a and a number of other contexts.

Pingree doubts also that A2 is “perhaps the copy utilized by Thibaut and Dvivedin” (Introduction, p.20). This goes against Thibaut’s statement that his “edition of PS is founded on two Manuscripts 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 corrections above the lines occur in A2 at several places obviously having been added by a modem 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 Collections 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.] Pancasiddhantika, patrani 49-15-1930”, it is in 49 pages, with 15 to 17 lines a page. This is the second of the two manuscripts 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, cornet dons, 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 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 letters 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 original. Corrections by a modern hand in lighter ink is seen at places.

 

Contents

 

Preface V
Contexts IX
Introduction Introductory - Source Material - Presentation of the Text - Translation - Notes - Division of Pancasiddhantika - Ch. XVIII of Pancasiddhantika - The Five Siddhantas in PS: Their distribution - Content analysis of the Pancasiddhantika - Depiction of the Siddhantas in the PS - Comparative study of the Siddhantas - Varahamihira: His life and works. XIII
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: Paulisa (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 Hora etc. (20-25) 20
Names of the 30 days of the Parsi months 24
Ch.II. Vasistha-Siddhanta: Planetary Computations etc.  
Introductory 25
True Sun (1) 25
True Moon (2-4) 27
Naksatra and Tithi (7) 33
Day-time (8) 34
Gnomonic Shadow (9-10) 35
Lagna from shadow and vice versa (11-13) 37
Ch.III. Paulisa- Siddhanta: 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
Desantara (13-14) 51
Local Sunset time (15) 53
Naksatra computation (16) 54
Sun’s daily motion (17) 56
Karanas (18-19) 57
Vyatipata and Vaidhrta (20-22) 58
Sadasiti-punyakala (23-24) 64
Solstices (25) 65
Sankranti-kala (26) 65
Tridinasprg-yoga (27) 66
Rahu (Node) (28-29) 67
Moon’s latitude (30-31) 69
Defect in Bhadravisnu (32) 71
Defect in Padaditya (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-sanku) and its shadow (35) 110
Astronomer’s qualifications (36-37) 112
Gnomonic shadow and the prime vertical (38) 113
Agra Sine amplitude (39) 113
Latitude from Agra (40) 114
Shadow at desired time (41-44) 115
Time after sunrise (45-47) 118
Time for Sunset (48) 121
Shadow from time (49) 122
Moon’s shadow (50-51) 123
Directions from shadow (52-54) 126
Sun from shadow (55-56) 132
Ch.V. Paulisa-Siddhanta: Moon’s Cusps  
Introductory 137
Time of Moon’s visibility (1-3) 137
Diagram of the Moon’s cusps (4-7) 143
Daily rising and setting of the Moon (8-10) 147
Ch.VI. (Vasistha-) Paulisa-Siddhanta: Solar Eclipse  
Introductory 152
Sun and Moon of equal longitude (1) 152
Probability of an eclipse (2) 154
Duration of the eclipse (3-4) 156
Total obscuration (5) 160
Direction of the eclipse (6-8) 162
Moment of the eclipse and its colour(8-10) 165
Diagrammatic representation (11-13) 168
Lunar and Solar eclipses-Differences (14) 171
Ch.VII (Paulisa-Siddhanta): Solar Eclipse  
Introductory 172
Parallax of longitude (1) 172
Parallax in latitude (2-4) 176
Eclipse computation (5-6) 178
Ch.VIII. Romaka-Siddhanta: Solar Eclipse  
Introductory 181
True Sun (1-3) 181
True Moon (4-6) 183
Daily motion of the Sun and the Moon (7) 185
Rahu (8) 186
Parallax in longitude (9) 187
Declination of the Nonagesimal (10-12) 187
Parallax correction and orbital diameter (13-14) 189
True diameter of the orbs (15) 191
Moment of the eclipse (16) 192
Eclipse diagram (17-18) 192
Ch.IX. Saura-Siddhanta: Solar Eclipse  
Introductory 197
Mean Sun (1) 197
Mean Moon (2-4) 198
Rahu: Maximum latitude (5-6) 201
True Sun and Moon (7-9) 203
Epicyclic theory 206
Bhujantara correction 209
Udayantara correction 209
Desantara correction (10) 209
Mean motion of the Sun and the Moon (11) 210
Motion of Moon’s anomaly (12) 211
True motion of Sun and Moon (13-14) 211
Kaksa of the Sun and the Moon (15) 214
Measure of the orbs (16) 215
Sin Zenith Distance of Meridian point(17-18) 216
Drksepa of the Sun (19-20) 219
Gnomon (21) 220
Parallax-corrected New Moon (22-23) 221
Parallax in latitude (24-25) 223
Duration of the eclipse (26-27) 225
Ch.X. Saura-Siddhanta: Lunar Eclipse  
Introduction 228
Diameter of the Shadow (l-2a) 228
Duration of the Eclipse (2b-4) 230
Obscuration at any desired moment (5-6) 232
Time of total obscuration (7) 235
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. Paitamaha Siddhanta  
Introduction 241
Days from Epoch (1-2) 241
Tithi, Naksatra etc. (3) 243
Vyatipata (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 Lanka and Ujjayini (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 yasti (12) 269
Moon’s longitude (13) 269
Cardinal directions by means of a gnomon (14-16) 270
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 Nadi or Ghati (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 Siddhanta: Mean Planets  
Introductory 292
Mean positions of the Star-planets (1-19) 293
VM’s Bija corrections (10-11) 298
Ch.XVII. Saura - Siddhanta: True Planets  
Epicycles of the planets (1-3) 300
True planets (4-9) 301
Special work for Mercury and Venus (10-11 a) 307
Retrograde motion (11b) 309
Heliacal rising (12) 309
Latitudes of planets (13-14) 310
Ch.XVIII. Vas-Pau. Siddh.: Rising and Setting of Planets  
Venus (1-5) 312
Jupiter (6-13) 316
Saturn (14-20) 322
Mars(21-35) 339
Mercury (35-36) 341
Hints (57-60) 351
General (61-63) 353
Spurious Supplement: True Plants  
Introduction (64-66) 355
True Mars (67-69) 357
True Mercury (70-72) 359
True Jupiter (73-75) 361
True Venus (76-78) 362
True Saturn (79-81) 363
Appendices
(I.) Verse Index 367
(II.) Index of PS verses quoted by later astronomers 371
(III.) Bhutasankhya used in the PS 372
(IV.) Index of Places, Persons and Texts quoted in the PS 373
(V.) Bibliography 374
(VI.) Subject Index 377

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Pancasiddhantika of Varahamihira

Item Code:
NAC921
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Paperback
Edition:
1993
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Language:
Sanskrit Text with English Translation and Explanation
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412
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Weight of the Book: 704 gms
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About the Book

K.V. Sarma

The Pancasiddhantika of the sixth century astronomer Varahamihira is a major work on mathematical astronomy of early India, and is particularly significant for the fact that it provides a resume, though uneven, of five astronomical schools, viz., Vasistha, Paitamaha, Romaka, Paulisa 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 Pancasiddhantika 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 (Benares, 1889) and by O. Neugebauer and David Pingree (Copenhagen, 1970).

The present Critical edition of the Pancasiddhantika, 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 introductions are prefixed to chapters indicating the contents and the method of approach adopted in those chapters.

 

About the Author

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 Mahabhaskariya of Bhaskara I with two commentaries, and the Vedanga Jyotisa with Translation and detailed notes. Jointly with K.V. Sarma, he edited the Vakyakarana 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).

 

About the Editor

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 Drgganita, Grahacaranibandhana, Tantrasangr’aha, Sphutanirnaya, Rasigolasphutaniti, Goladipika, Candrasphutapti and Jyotirmimimsa. 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.

 

Preface

The Pancasiddhantika of the sixth century astronomer Varahamihira 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 resume, though uneven, of five astronomical schools, to wit, the Vasistha, Paitamaha, Romaka, Paulisa 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 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 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 obstacles which the corrupt and bare text of the Pancasiddhantika 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 previous 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, formerly Professor in the Sanskrit College, Madras. A scholar in Sanskrit, a student of modern mathematics and one fully conversant with Jyotissastra, Prof. Sastry was an ideal combination of Indian and Western schools of astronomy. And, as such, he was best fitted for the task of expounding a difficult text on Indian astronomy like the Pancasiddhantika.

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 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 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 prepared on the basis of the readings adopted by Prof. Sastry. Copies of all manuscripts of Pancasiddhantika 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 0 the critical text was prepared. Varied typography for the half a dozen different items of the edition was also selected to set off the same distinctly in print.

The 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.

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 cooperation 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. 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 Pancasiddhantika.

 

Introduction

The Pancassiddhantika (PS) of Varahamihira (VM), (6th cent. A.D.), occupies an important place the history of early Indian astronomy, for, herein we have been given certain aspects of five systems 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:

purvacaryamatebhyo yad yad srestham laghu sphutam bijam

tat tad ihavikalam aham rahasyam udyato vaktum

Paulisa-Romaka-Vasistha-Saura-Paitamahas tu panca siddhantah

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 siddhanta-s, of which this work is a compendium, are the Paulisa, the Romaka, the Vasistha, the Saura and the Paitamaha.

Following the above statement, VM specifies also how he is intending to deal with the said five astronomical schools:

yat tat param rahasyam bhavati matir yatra tantrakaranam

tad aham apahaya matsaram asmin vaksye graham bhanoh

dik-sthiti-vimarda-karna-pramana-vela grahagrahav indoh

taragrahasamyogam desantarasadhanam ca ‘smin

samamandala-candrodaya-yantra-cchedyani sankavacchaya

upakaranady aksajya- ‘valambaka-’ pakramadyani

I shall tell in this work, avoiding all jealousy, the computation of the solar eclipse which is as a great secret and in which the mind 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, 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 ant 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 preparation of a correct edition of the work a formidable task, affecting, in its turn, a proper understanding, 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:

“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 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 Pancasiddhantika. 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, however imperfect, of our tong continued endeavours to restore and elucidate the text of the Pancasiddhantika. In 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. And, in the second place, we feel convinced that even from that pan of the Pancassiddhantika 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 him and the editorial criteria adopted by him Thibaut says in his Introduction to the edition:

“The present edition of the Pancasiddhantika 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 man’ cases, to be treated with great liberty. Not unfrequently, the emended text is merely meant a an equivalent in sense of what we suppose Varaha Mihira to have aimed at expressing, while we attach no importance to the words actually employed in the emendation.” (p.lx).

The Pancasiddhantika has again been edited recently by O. Naugebauer and D. Pingree, (NP). And 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 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 manuscripts that have become available, all go back to the two manuscripts used in the first edition, t shown by the commonality in them of omissions and corruptions which occur in the newly available manuscripts.

The edition of Pancasiddhantika which is now issued is also based on the manuscripts used for the 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 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 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 Pancasiddhantika, the principle of sthitasya gatis cintaniya, ‘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 t the language and the subject of the text. ‘Real’ emendations have been comparatively small and 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 errors and in square brackets in the case of editorial supplementation. And, whenever there has 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 a en 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 Varahamihira.

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 Pancasiddhantika, of which five have been collated for preparing 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 expect 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 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 Al, A2 and B 1, 82, 83, 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 Stambhatirtha (modern Cambay in Gujarat) in Sam. 1673, Saka 1538 (AD. 1616), by Sankara 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, l0a, 12a and a number of other contexts.

Pingree doubts also that A2 is “perhaps the copy utilized by Thibaut and Dvivedin” (Introduction, p.20). This goes against Thibaut’s statement that his “edition of PS is founded on two Manuscripts 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 corrections above the lines occur in A2 at several places obviously having been added by a modem 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 Collections 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.] Pancasiddhantika, patrani 49-15-1930”, it is in 49 pages, with 15 to 17 lines a page. This is the second of the two manuscripts 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, cornet dons, 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 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 letters 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 original. Corrections by a modern hand in lighter ink is seen at places.

 

Contents

 

Preface V
Contexts IX
Introduction Introductory - Source Material - Presentation of the Text - Translation - Notes - Division of Pancasiddhantika - Ch. XVIII of Pancasiddhantika - The Five Siddhantas in PS: Their distribution - Content analysis of the Pancasiddhantika - Depiction of the Siddhantas in the PS - Comparative study of the Siddhantas - Varahamihira: His life and works. XIII
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: Paulisa (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 Hora etc. (20-25) 20
Names of the 30 days of the Parsi months 24
Ch.II. Vasistha-Siddhanta: Planetary Computations etc.  
Introductory 25
True Sun (1) 25
True Moon (2-4) 27
Naksatra and Tithi (7) 33
Day-time (8) 34
Gnomonic Shadow (9-10) 35
Lagna from shadow and vice versa (11-13) 37
Ch.III. Paulisa- Siddhanta: 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
Desantara (13-14) 51
Local Sunset time (15) 53
Naksatra computation (16) 54
Sun’s daily motion (17) 56
Karanas (18-19) 57
Vyatipata and Vaidhrta (20-22) 58
Sadasiti-punyakala (23-24) 64
Solstices (25) 65
Sankranti-kala (26) 65
Tridinasprg-yoga (27) 66
Rahu (Node) (28-29) 67
Moon’s latitude (30-31) 69
Defect in Bhadravisnu (32) 71
Defect in Padaditya (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-sanku) and its shadow (35) 110
Astronomer’s qualifications (36-37) 112
Gnomonic shadow and the prime vertical (38) 113
Agra Sine amplitude (39) 113
Latitude from Agra (40) 114
Shadow at desired time (41-44) 115
Time after sunrise (45-47) 118
Time for Sunset (48) 121
Shadow from time (49) 122
Moon’s shadow (50-51) 123
Directions from shadow (52-54) 126
Sun from shadow (55-56) 132
Ch.V. Paulisa-Siddhanta: Moon’s Cusps  
Introductory 137
Time of Moon’s visibility (1-3) 137
Diagram of the Moon’s cusps (4-7) 143
Daily rising and setting of the Moon (8-10) 147
Ch.VI. (Vasistha-) Paulisa-Siddhanta: Solar Eclipse  
Introductory 152
Sun and Moon of equal longitude (1) 152
Probability of an eclipse (2) 154
Duration of the eclipse (3-4) 156
Total obscuration (5) 160
Direction of the eclipse (6-8) 162
Moment of the eclipse and its colour(8-10) 165
Diagrammatic representation (11-13) 168
Lunar and Solar eclipses-Differences (14) 171
Ch.VII (Paulisa-Siddhanta): Solar Eclipse  
Introductory 172
Parallax of longitude (1) 172
Parallax in latitude (2-4) 176
Eclipse computation (5-6) 178
Ch.VIII. Romaka-Siddhanta: Solar Eclipse  
Introductory 181
True Sun (1-3) 181
True Moon (4-6) 183
Daily motion of the Sun and the Moon (7) 185
Rahu (8) 186
Parallax in longitude (9) 187
Declination of the Nonagesimal (10-12) 187
Parallax correction and orbital diameter (13-14) 189
True diameter of the orbs (15) 191
Moment of the eclipse (16) 192
Eclipse diagram (17-18) 192
Ch.IX. Saura-Siddhanta: Solar Eclipse  
Introductory 197
Mean Sun (1) 197
Mean Moon (2-4) 198
Rahu: Maximum latitude (5-6) 201
True Sun and Moon (7-9) 203
Epicyclic theory 206
Bhujantara correction 209
Udayantara correction 209
Desantara correction (10) 209
Mean motion of the Sun and the Moon (11) 210
Motion of Moon’s anomaly (12) 211
True motion of Sun and Moon (13-14) 211
Kaksa of the Sun and the Moon (15) 214
Measure of the orbs (16) 215
Sin Zenith Distance of Meridian point(17-18) 216
Drksepa of the Sun (19-20) 219
Gnomon (21) 220
Parallax-corrected New Moon (22-23) 221
Parallax in latitude (24-25) 223
Duration of the eclipse (26-27) 225
Ch.X. Saura-Siddhanta: Lunar Eclipse  
Introduction 228
Diameter of the Shadow (l-2a) 228
Duration of the Eclipse (2b-4) 230
Obscuration at any desired moment (5-6) 232
Time of total obscuration (7) 235
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. Paitamaha Siddhanta  
Introduction 241
Days from Epoch (1-2) 241
Tithi, Naksatra etc. (3) 243
Vyatipata (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 Lanka and Ujjayini (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 yasti (12) 269
Moon’s longitude (13) 269
Cardinal directions by means of a gnomon (14-16) 270
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 Nadi or Ghati (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 Siddhanta: Mean Planets  
Introductory 292
Mean positions of the Star-planets (1-19) 293
VM’s Bija corrections (10-11) 298
Ch.XVII. Saura - Siddhanta: True Planets  
Epicycles of the planets (1-3) 300
True planets (4-9) 301
Special work for Mercury and Venus (10-11 a) 307
Retrograde motion (11b) 309
Heliacal rising (12) 309
Latitudes of planets (13-14) 310
Ch.XVIII. Vas-Pau. Siddh.: Rising and Setting of Planets  
Venus (1-5) 312
Jupiter (6-13) 316
Saturn (14-20) 322
Mars(21-35) 339
Mercury (35-36) 341
Hints (57-60) 351
General (61-63) 353
Spurious Supplement: True Plants  
Introduction (64-66) 355
True Mars (67-69) 357
True Mercury (70-72) 359
True Jupiter (73-75) 361
True Venus (76-78) 362
True Saturn (79-81) 363
Appendices
(I.) Verse Index 367
(II.) Index of PS verses quoted by later astronomers 371
(III.) Bhutasankhya used in the PS 372
(IV.) Index of Places, Persons and Texts quoted in the PS 373
(V.) Bibliography 374
(VI.) Subject Index 377

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