A History of Indian Literature, Volume VI: Scientific and Technical Literature, Part 3, Fasc. 4: Jyotiḥśāra: Astral and Mathematical Literature

154 Pages·1981·3.87 MB·English

by  David Pingree

A HISTORY
OF INDIAN LITERATURE
DAVID PINGREE
JYOTIHSASTRA
ASTRAL AND MATHEMATICAL LITERATURE
OTTO HARRASSOWITZ . WIESBADEN
A HISTORY
OF INDIAN LITERATURE
EDITED BY JAN GONDA
VOLUME VI
Fasc. 4
1981
OTTO HARRASSOWITZ • WIESBADEN
DAVID PINGREE
JYOTIHSASTRA
ASTRAL AND MATHEMATICAL LITERATURE
1981
OTTO HARRASSOWITZ . WIESBADEN
A HISTORY OF INDIAN LITERATURE
Contents of Vol. VI
Vol. VI:
Fasc. 1: E. te Nijenhuis Musicological Literature
Fasc. 2: B. K. Matilal Nyaya-Vaisesika
Fasc. 3: M. Hulin Samkhya Literature
Fasc. 4: D. Pingree Jyotihsastra
A. Kunst Vedanta
T. Gelblum Yoga Philosophy
G. Maximilien Purva-MImamsa
B. Dagens Architecture, Sculpture, Technics
N. N. Other Sciences
CIP-Kurztitelaufnahme der Deutschen Bibliothek
A history of Indian literature / ed. by Jan Gonda. - Wiesbaden : Harrassowitz.
NE: Gonda, Jan [Hrsg.]
Vol. 6. Scientific and technical literature: Pt. 3.
Vol. 6. Fasc. 4. -> Pingree, David : Jyotihsastra
Pingree, David:
Jyotihsastra : astral and mathemat. literature / David Pingree. - Wiesbaden : Harrassowitz, 1981.
(A history of Indian literature : Vol. 6, Fasc. 4)
ISBN 3-447-02165-9
© Otto Harrassowitz, Wiesbaden 1981. Alle Kechte vorbehalten. Photograpliische und photomechanische
Wiedergabe nur mit ausdrucklicher Genehmigung des Verlages. Gesamtherstellung: Allgauer Zeitungsverlag
GmbH, Kempten. Printed in Germany. Siegel: HIL.
TABLE OF CONTENTS
Introduction 1
CHAPTER I Sulbasutras 3
CHAPTER II Astronomy 8
CHAPTER III Mathematics 56
CHAPTER IV Divination 67
CHAPTER V Genethlialogy 81
CHAPTER VI Catarchic Astrology 101
CHAPTER VII Interrogations 110
CHAPTER VIII Encyclopaedias and Dictionaries 115
CHAPTER IX Transmission of Jyotihs'astra 118
Abbreviations 131
Index 134
INTRODUCTION
Traditionally jyotihsdstra is divided into three skandhas: satnhitd (omens),
ganita (astronomy), and hord (astrology) (see BS 1, 9); and, according to the
medieval muhurta treatises, was originally promulgated by the eighteen sages
Brahmacarya, Vasistha, Atri, Manu, Paulastya, RomaSa, Marici, Angiras,
Vyasa, Narada, Saunaka, Bhrgu, Cyavana, Yavana, Garga, Kasyapa, Para-
sara, and Surya. The validity of the first tradition was maintained only by
artificially including new forms of scientific writing—e.g., treatises on math-
ematics, on muhurta, or on pradna—in one or another of the three skandhas,
while there was never any validity to the second. In this volume an attempt
has been made to establish a more accurate classification of the areas of
jyotihsdstra actually made the subject of independent works, and to survey
the literature in each area (but omitting the sectarian Jaina contributions) in
order to establish a correct historical origin (often from outside of India) and
development of each. To have included discussions of the technical aspects of
these sciences, however, would both have duplicated much that has already
been done (though in some areas it desperately needs to be done better) and
have extended the length of this volume far beyond reasonable bounds.
Nor has any attempt been made to deal with the literary qualities of the
works discussed. The primary texts are certainly all in metrical form, but are
generally written in a very crabbed and obscure style designed to stimulate
the student's memory of the procedures to be followed, but frequently not
even pretending to provide the full algorithm for solving a particular problem;
that was to be found, if not in the repetitiousness of the science, in the guru's
oral tradition or in the prose commentary. Thus, while cleverness and impre-
cision both abound in this poetry, the normal canons of alankdra are simply
not applicable; only rarely, as in the rtuvarnana in Bhaskara's S&B, is any
poetic feeling made manifest.
Two of the difficulties generated by the use of a poetic form were the neces-
sity of expressing numbers metrically, and the difficulty of maintaining a
fixed technical vocabulary. The latter impediment led to the invention of
many synonyms, and the use of single terms in several different, if related,
senses; this, of course, increased the ambiguity and imprecision inherent in a
system where the texts' purpose is to jog the memory rather than to teach the
complete course. The former problem was solved in two ways: by using com-
mon objects that appear or are understood to appear in the world in fixed
quantities as synonyms for those quantities (e.g., "eyes" are "two," "fires"
are "three," "Vedas" are "four"), and by using aksaras to refer to numbers.
The former system, called the bhutasankhyd, already appears in the third
century in Sphujidhvaja's Yavanajataka. Sphujidhvaja also seems to be the
2 Introduction
first to use a symbol for zero (bindu) in the decimal place-value system (YJ
79, 6 and 7), though, of course, a dot or a circle had been, used previously by
both Babylonians and Greeks in the sexagesimal place-value system to rep-
resent a place with no other number in it. Aryabhata invented a different
way of expressing numerals, in which the consonants of the Sanskrit alphabet
are used to indicate the numbers and the vowels their places (up to eighteen);
unfortunately, the "words" formed thus were often unpronounceable and in
any case had no meaning other than the numerical one. A different system
was invented in South India that obviated this difficulty. The Jcatapayddi
system (in which k, t, p, and y equal 1 regardless of the vowel they are followed
by) uses the consonants as equivalents of the numbers 1 to 9 and 0; four
varieties of this system are known. A clever jyotisl, then, can construct verses
that are superficially on one subject while each sequence of consonants can be
read as a significant number; a good example of this is Paramesvara's Hari-
carita.
The following pages will show that our knowledge of Indian jyotihsdstra is
rather spotty. This is due both to the accidents that cause the preservation
(and availability) of one text rather than another, and to the lack of reliable
and accurate descriptions of the many unpublished manuscripts. The second
disability is being slowly alleviated as CESS progresses; I have generally
referred the reader to it, when available, for information about an author, his
works, and what modern scholars may have said about them, though I have
attempted in all cases to give reasonably complete listings of published
editions as they are a useful guide to modern interests. Those modern interests
lie overwhelmingly in jdtaka, tdjika, muhurta, prasna, and various forms of
divination; classical astronomy and mathematics had virtually ceased to be
studied or taught by the end of the nineteenth century. A new group of Indian
and foreign scholars has, however, begun to work in these areas since World
War II; and, while much is still unfortunately published that is of little or no
value, some progress toward an understanding of the origins and developments
of these sciences has been made. I hope that this volume will stimulate more
serious interest in this field.
CHAPTER I
SULBAStfTRAS
In the performance of Vedic srauta rituals an essential prerequisite is the
piling up of the fire altar (agnicayana). These altars (citis) take the form of
various objects; the forms mentioned in Taittirryasamhita 5, 4, 11 (after
the chandasciti1 or "meter altar") and the sacrificers who should erect them
are:
1. 4yenaciti or "hawk altar"2 by one desiring heaven (suvarga);
2. kankaciti or "heron altar" by one desiring a head in the other world;
3. alajaciti or "alaja-hird altar" with four furrows by one desiring support;
4. praiigaciti or "triangle altar" by one desiring to repel his foes;
5. ubhayatah praiigaciti or "triangle on both sides altar" by one desiring to
repel both present and future foes;
6. rathacakraciti or "chariot-wheel altar" by one wishing to defeat his foes;
7. dronaciti or "trough altar" by one desiring food;
8. samuhyaciti3 or "things to be gathered together altar" by one desiring
cattle;
9. paricdyyaciti* or "circle altar" by one desiring a village;
10. dniasdnaciti* or "cemetery altar" by one desiring the world of the fathers
(pitrloka).
A few other altar-shapes are described in other Brahmanas, where also are
prescribed the rituals to be performed at these altars. The Srautasutras be-
longing to the Yajurveda often include as appendices treatises that give rules
concerning the geometry involved in the construction of these altars. These
treatises are known as the Sulbasutras.5
1 An imaginary altar constructed in the sacrificer's mind, but with the recitation
of the appropriate mantras.
2 Called swparnaciti in &B. 6, 7, 2, 8. This is the principle altar shape of which
the others were regarded as derivatives.
3 Called the samuhyapurisaciti in i§B.
4 Omitted by SB.
5 See B. DATTA, The Science of the Sulba, Calcutta 1932; A. MICHAELS, Beweis-
verfahren in der vedischen Sakralgeometrie, Wiesbaden 1978; and T. A. SARASVATI
AMMA, Geometry in Ancient and Medieval India, Delhi—Varanasi—Patna 1979,
pp. 14—60. Still informative is G. THIBATJT, "On the Sulvasutras," JASB, NS 44
(1875), 227-275.
4 David Pingree • Jyotihsastra
The Srautasutras containing Sulbasutras are those of Baudhayana,6 in which
the &ulbasutra is prasna 30 ;7 of Apastamba,8 in which the Sulbasutra is also
prasna 30 ;9 of Vadhula,10 whose Sulbasutra is said to survive in a manuscript
at Madras;11 of Manava,12 in which the Sulbasutra is adhyaya 1013 (a recension
of this is entitled the Maitrayaniyasulbasutra14); of Varaha,15 whose &ulbasutra
survives in a manuscript at Mysore;16 and of Katyayana,17 in which the &ul-
basutra is parisista 7.18 The last of these belongs to the Suklayajurveda (the
Vajasaneyisamhita), the first five to the Krsnayajurveda (Baudhayana,
Apastamba, and Vadhula to the Taittirlyasamhita, and Manava and Varaha
to the Maitrayanlyasamhita).
Precise dating of any of these texts is impossible. The earliest, that of
Baudhayana, was perhaps written before 500 B.C., and the remainder presum-
ably antedate the Christian era. It was, indeed, during this period also, prob-
ably in the second century B.C., that the most striking syenaciti of which
remains survive was built in Kausambi.19 The Apastamba appears to be the
second oldest of the major Sulbasutras, and the Katyayana, which consists of
6 J. GONDA, The Ritual Sutras, Wiesbaden 1977, pp. 514—518.
7 Edited with the commentary, f^ulbadipika, of Dvarakanatha Yajvan by G. F.
THIBATJT, "The Sulvasutra of Baudhayana with the Commentary of Dvarakana-
thayajvan," The Pandit 9-10 andNS 1 (1874/75-1876/77); by W. CALAND, BI 163,
vol. 3, Calcutta 1913, pp. 389ff.; and by S. PRAKASH and R. S. SHARMAN, New
Delhi 1968.
8 GONDA, pp. 520—521.
9 CESS Al, 50a. Edited with a German translation and a commentary by A.
BURK, "Das Apastamba-Sulba-Sutra," ZDMG 55 (1901), 543—591, and 56 (1902),
327—391; and, with the commentaries of Kapardisvamin, Karavinda, and Sundara-
raja, by D. SRINIVASACHAR and S. NARASIMHACAR, MSS 73, Mysore 1931, and by
S. PRAKASH and R. S. SHARMA, New Delhi 1968.
10 GONDA, pp. 522—524. The Apastamba is closely related to a section (prasna
25) of the Satyasadhasrautasutra; see MICHAELS, pp. 173—180.
11 N. K. MAJTJMDAR, "On the Different Sulba Sutras," PAIOC 2 (1923), pp. 561
to 564.
12 GONDA, pp. 525—526.
13 Edited and translated by J. M. VAN GELDER, The Manava ^rautasutra, 2 vols.,
New Delhi 1961—1963. See also N. K. MAZUMDAR, "Manava &ulba Sutram,"
JDL/U Calcutta 8 (1922), 327—342.
14 DATTA, p. 6.
15 GONDA, p. 527.
16 DATTA, pp. 6 and 230.
17 GONDA, p. 528—529.
18 An incomplete edition with the Sulbasutravrtti of Rama was published by
G. F. THIBATJT, "Katyayana Sulbaparisishta, with the commentary of Rama, son
of Suryadasa," The Pandit, NS 4 (1882); edited with the commentaries of Karka
and of Mahldhara by G. S. NENE and A. S. DOGRE, KSS 120, Benares 1936; and
by S. D. Khadilkar, Poona 1974.
19 G. R. SHARMA, The Excavations at Kausambi (1957—59), Allahabad 1960,
pp. 87—126; on the interpretation of this monument see D. SCHLINGLOFF, "Men-
schenopfer in Kausambi?," IIJ 11 (1969), 175—189.
Sulbasutras 5
a sutra section (to a large extent repeating sutras of the Apastamba verbatim),
followed by a verse section, is among the latest; the Manava has apparently
copied some verses from the Katyayana.
Each of the basic altars must be constructed with five layers of bricks, and
there must be a fixed number of bricks in each layer; moreover, the bricks in
the second and fourth layers must not be directly above or below those in the
first, third, and fifth layers. And the surface covered by the altar, regardless
of its shape, must cover an area of seven and one half square purusas or, for
certain purposes, that area increased by specified numbers of square purusas,
or it must be multiplied by a given factor. Finally, the altar must be correctly
oriented with respect to the cardinal directions. The task faced by the authors
of the Sulbasutras was to prescribe rules for laying out these altars with only
a rope (rajju or sulba) of determined length and posts or gnomons (sanku).20
The geometrical problems that were solved by these altar-builders are indeed
impressive, but it would be a mistake to see in their works the unique origin of
geometry;21 others in India and elsewhere, whether in response to practical or
theoretical problems, may well have advanced as far without their solutions
having been committed to memory or eventually transcribed in manuscripts.
The solutions utilized by the sutrakaras involve the knowledge of a number
of specific right-angled triangles (e.g., 3, 4, 5; 5, 12, 13; 7, 24, 25; 8, 15, 17;
12, 35, 37; and 15, 36, 39) as well as the general rule that the square on the
diagonal of a rectangle (square or oblong) is equal to the sum of the squares
on two sides; of the approximation
1 1 1
V2*> 1 -fir '
3 x4 3 x 4 x 3 4'
and the radius, r, of a circle whose area is approximately equal to a square
of side x:
They also give particular solutions to certain indeterminate equations, though
without any hint at the method by which they arrived at them.22
The Baudhayanasulbasutra in the edition by Prakash and Sharman contains
ten adhydyas divided into 21 Jchandas (4, 3, 2, and 6 Jchandas in the first four
20 A. K. BAG, "The knowledge of Geometrical Figures, Instruments, and Units
in the Sulbasutras," EW 21 (1971), 111—119.
21 A. SEIDENBEKG, "The Origin of Mathematics," AHES 18 (1978), 301—342.
22 For specific aspects of the geometry of the Sulbasutras one should consult, in
addition to the books and articles previously cited, those listed in the article on
Apastamba in CESS Al, 50a, as well as R. C. GUPTA, "Baudhayana's Value of
f2," ME 6 (1972), B 77—79, and R. P. KULKABNI, "The Value of TU Known to
Sulbasutrakaras," IJHS 13 (1978), 32—41.