Astronomy and Cosmology

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur
Catalog link: https://jainqq.org/explore/001618/1

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國凱凱
EXACT SCIENCES FROM JAINA SOURCES
VOL.-2
Astronomy & Cosmology
凯凯凯凯凯凯員 凯凯凯凯 H E M AT BHARATI SASTHAN
JUT JUTJUT JUI
RAJASTHAN
JAIPUR
SACO
SITARAM BHARTIA INSTITUTE OF SCIENTIFIC RESEARCH
NEW DELHI
319

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PRAKRIT BHARTI PUSHPA-29
EXACT SCIENCES FROM JAINA SOURCES
Vol.-2
ASTRONOMY AND COSMOLOGY
by
Prof. L. C. Jain Principal, Govt. P. G. College, Chhindwara
Foreword
Dr. G. C. Patni Ex-Prof. and Head of Deptt. of Mathematics,
University of Rajasthan. Jaipur
Publishers
RAJASTHAN PRAKRIT BHARTI SANSTHAN, JAIPUR; SITARAM BHARTIA INSTITUTE OF SCIENTIFIC RESEARCH,
NEW DELHI

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Publishers : DEVENDRA RAJ MEHTA Secretary Rajasthan Prakrit Bharti Sansthan Yati Shyamlalji Ka Upashray 3826, Moti Singh Bhomiyon-Ka-Rasta, Jaipur-302003.
O. P. BHARTIA Sitaram Bhartia Institute of Scientific Research 27-Bara Khamba Road, New Delhi-110001
© Rajasthan Prakrit Bharti Sansthan
First edition, 1983
Price : Rs. 15.00
Printed by : Friends Printers and Stationers Johari Bazar, Jaipur.

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Rajasthan Prakrit Bharti Sansthan, Jaipur, has many streams of publications; it brings out books on philosophies, religions their comparative studies, history, art & culture, ancient literary works, Prakrit language and secular scientific subjects etc. On the last one presently we propose to bring out a series of ten books in collaboration with Sitaram Bhartia Institute of Scientific Research, New Delhi, out of which this is the second one.
PUBLISHER'S NOTE
We are indeed grateful to Professor L. C. Jain, an eminent authority on history of mathematics, to have written this book which might be useful in appreciating the contribution of ancient scholars to the development of mathematics.
We are also indebted to Dr. G. C. Patni formerly Professor and Head of Department of Mathematics and Dean, Faculty of Science, University of Rajasthan, Jaipur for contributing the foreword of the book.
Mahopadhyaya Shri Vinay Sagarji Sahab, Joint Secretary of our Society arranged its publication through Friends Printers & Stationers, Jaipur. We are grateful to both of them.
O. P. BHARTIA
Sitaram Bhartia Institute of
Scientific Research NEW DELHI

D. R. MEHTA Secretary,
Rajasthan Prakrit Bharti Sansthan, JAIPUR

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ERRATA (VOLUME-II)
FOR
PAGE
LINE
READ
against Newyork
above New York
c.
DU
speeculating anubhāg
speculating anubhāga
16 (from top)
5 (from bottom) 15 (from top) 2 (from botton) 7 (from top) 14 (from top)
4 (from bottom) 12 (from bottom) 16 (from bottom)
7 (from top) 8 (from top) 10 (from top) 19 (from top) 7 (from bottom) 9 (from bottom) 3 (from bottom) 6 (from top) 5 (from bottom) 18 (from bottom)
EQUINOXE Jyo16tişa fitst NAKSATRAS
naksatres comperative Ārybhaga Chakraverty Ārybhaga Cirumference
EQUINOXES Jyotisa16 first NAKŞATRAS nakşatras comparative Aryabhata Cakravarti Āryabhata Circumference

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CONTENTS
PAGES
TOPICS 0. Foreword
1-12
1. Introduction
a) Science Awakening b) Jaina Cosmos
8-11
2. Technical Terms
a ) Celestial Diagram b) Index of the Diagram
12-15
3. Source Material
a) Vedic Literature b) Vedā iga Jyotişa c) Jaina Tradition d) Literature in Svetāmbara School e) Literature in Digambara School f) Certain Contributors
16-28
4. Cosmological Concepts
a) Evaluation of Rajju b) Volume of Universe c) Another Value of Rajju d) Frame of Descartes e) Cosmic Periods and Cycles f) Yuga Bhagana g) Concepts of Palya and Sāgara h) Concept of Kalpa i) Parāvartana Periods j ) Comparability
5. Astronomical Concepts
a) Precession of Equinoxes b) Date of Adoption of Calendar

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c) Pañcānga d) Graduation of Celestial Sphere e) Note
6. Kinematics of Astral Bodies
a) Nakşatra System Abroad b) Mathematical Astronomy c) Symmetric Setting d) Shadow Planets e) Motion of Astral Bodies f) Relative Motion of Nakştras g) Relative Motion of the Sun h) Relative Motion of the Moon
50-53
50
7. Rationalization of Yojana
a) Chinese Li b) Types of Angulas c) Evolution of Yojana d) Rationalization e) Height as Latitude
51
52
3
54
55-60
57
8. Calendrical Yuga System 9. Astronomical Theory
a) Principle Theories b) Constructive Theories c) What is Jaina Theory ? d) Eclipse Theory e) Evolution of Epicycles
57 58 58
59
A. Bibliography of Source Material
61-62
B. Bibliography of Some Research Material
63-66
67-69
C. Bibliography of Books D. Abbreviations
APPENDIX-A APPENDIX-B

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FOREWORD
Cosmology and Astronomy are some of those topics of 'Exact Sciences' towards the development of which the Jaina School of Parsvanātha and Vardhamana Mahāvira has contributed a lot. This School, noted for its mathematicophilosophic pursuits, flourished in India very much close round about the same period in which the School of Pythagoras flourished in Greece, that is, in sixth century B. C. and later on. The vast available ancient Jaina literature is primarily religion-cum-philosophy oriented, but the use of mathematics is found in abundance, showing that the Jainas at that time had developed mathematics to a great extent. The ancient Jaina literature is divided into four main groups, called prathmānuyoga,' karaṇānūyoga, caraṇānūyoga and dravyānūyoga where looking to the importance of science, most of the literature of the karaṇānuyoga group deals with mathematical, astronomical and cosmological concepts besides the study of cosmos and self and the Karma Theory. As a matter of fact for this study, two worlds, one the macroworld and the other microworld, are to be well manifested to a human intellect and with this object, in view, the Jaina scholars in ancient India have worked on Astronomy, Cosmology and the Karma Theory with mathematical approach.
It is
The original Jaina Agamas discuss, amongst other things, the Karma Theory. In these lie the deep secrets of periodic events of nature. unfortunate that many of these Agamas in which mathematics has been developed either as post-universal (alaukika) study of measures and counting or applied in the form of results through analysis and comparability, e. g., the works of Bhadrabāhu of 3rd-4th century B. C. either have been lost or are not traceable at present.Some of the important available Agamas and other texts, their extracts and commentaries are the Kasaya-pāhuḍa, the Satkhaṇḍāgama, the Sthānāṇga-Sūtra, the Tattvārtha-Sūtra, the Tiloyapanṇatti Kṣapaṇāsāra, Labdhisāra, the Gommaţasāra, the Trilokasāra, the Dhavala, the Jayadhavalā, the Mahādhavala, the Jambudivapaṇṇatti Samgaho, the Gaṇitasara Samgraha, the Suryaprajñapti, the Candraprajñapti, the Lokavibhāga etc. Some of these works are more than 2000 years old and many of them lay hidden and could be brought to light only recently through the

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efforts of some Indian and foreign scholars. The names of M. Raigācārya (c. 1912 A. D.), D. E. Smith, S. K. Das, H. L. Jain, A. N. Upāļhyāya, Kāpadiyā, A. N. Singh, B. B. Datta, N. C. Jain, T. A. Saraswati, L. C. Jain (the present author), R. C. Gupta, Lishk and Sharma, J.C. Sikdar, Voloďarski etc, are worth mentioning as main workers in the field of Jaina Mathematics.
In Sthānānga-Sūtra, the Jain canonical work of about 300 B. C., rāśi forms one of the ten topics for discussion. Here rāśi is synonymical with samūha, ogha, puñja, that is, a set, though the rāśi appears in other Jaina texts in several contexts also; cosmological sets are found in detail in Tiloyapannatti, a work of Yati-Vfşabha of 5th century A, D, Philosophical sets relating souls, their becomings, nature of Karma, the number of particles involved therein, alongwith their intensity of reactions and stay periods, the deep-rooted theory of 'bhāva' becoming operators etc, may be found in great details in the other important Jaina source work, 'Satkhaņdāgama', compiled and composed by Puşpadanta and Bhūtabali during the first two centuries of the Christian era and the commentaries on this work by Virasenācārya given in early part of the 9th century A. D. under the name 'Dhavala' which contains a lot of valuable information about Mathematics. Trilokasāra, summary of the three universes as the name indicates, has been compiled by Nemicandrācārya of ilth century A. D. from earlier Prakrit texts, one of them being the Tiloyapannatti mentioned above; this work and its commentaries by Madhavacandra Traividya (c. 1203 A. D.) and translated into a dhūndhāri work 'Artha Samdjsti' by Todaramala (c. 1720-1768 A. D.) also describe various other mathematical topics and concepts, for example, the fourteen types of sequences for elaborating the number-measure (Samkhyāmāna) and the simile-measure (Upamā-māna).
In the literature of karaṇānuyoga group, detailed description of the universe is given and related to this, the description of the sun, the moon, the nakşatras, the oceans, the islands, etc. using a lot of mathematics has been provided. All these works are very useful in following the development of ancient Indian Mathematics and Astronomy. In Vedic tradition, the subject of Mathematics has been dealt with cursorily in texts like Vedārga Jyotişa. However Aryabhata First of 5th century A. D. was perhaps the first Indian mathematician-astronomer who in his book, "Āryās Bhațiyam), has added a separate independent chapter consisting of 33 verses on Mathematics and Astronomy. He was also the first astronomer who had pointed out that the sun and the stars were fixed and also calculated the circumference of the earth and gave scientific reasoning for the occurrence of the solar and lunar eclipses. Another Indian Mathematician, Brahma

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gupta of 7th century A. D. also added one separate chapter on mathematics in his book, Brahmasphuţa Siddhānta. But it was the Jaina scholar-saint Mahāvirācārya (c. 850 A, D.) who for the first time had written a separate book, 'Gazitşāra Samgraha', entirely on mathematics. Even the Bakhşāli manuscript found in Bakhşālı village near Peshawar in 1881 is said to belong to 12th century A. D., though according to some scholars, it may belong to 3rd or 4th century A. D. also. However, much long before Aryabhata I, mathematics, astronomy and cosmology along with other subjects of science, arts, humanities and social sciences, had been developed in India-a fact which has been acknowledged now even by western scholars. Various astronomical phenomena whether they be related to the sun, the moon, the other heavenly bodies, the constellations, the eclipses, the conjuction of planets, tripraśna (direction, position and time), the measurements of small or extensive dimensions of lengths and heights of small or big bodies like the paramāņās, the cities, the oceans, the islands, the mountains, interspace distances between the different worlds-universe and sub-universes the hellish universe, the human universe, the sub-human universe, the gods' universe (heavens) and also subjects like the configuration of living beings, the lengths of their lives, their progress, their staying together, that is, in other words whatever there is in all the three worlds (triloka) which consist of moving and non-moving beings (the six fluents) and which cannot exist apart from gazita, have been described in the ancient Jaina Prakrit texts.
As mentioned in the book, "Science Awakening' by B. L. Vander Waerden, the use of the sexagesimal system in Astronomy is 5000 years old. The Babylonians needed knowledge of calendar in connection with agricultural problems and for this they had taken the beginning of their year, with effect from the vernal equinox. These Babylonians had adopted this system from Sumerians and from the Babylonians. The Greek scholar-astronomer Ptolemy (c. 150 A, D.) had adopted it in Greece. Further Neugebauer has opined in The exact Sciences in Antiquity' that the decimal place value notation is a modification of the sexagesimal system with which the Hindus became familiar through Hellenistic astronomy. Whether it is correct, is doubtful since the period of 300 B. C. to 300 A, D. is the Hellenism Yuga; during this period Greek science and astrology was developed in Alexandria (Greece) while arithmetic and astronomy remained static. For the period before 300 B. C., even Herodotus, the pioneer of ancient Greek history, is generally silent.
As mentioned in Encyclopedia Americana, the two Greek Scholars Thales (640 B. C.) and Pythagoras (6th century B. C.) both travelled to Egypt in Saitic period (663–525 B. C.) and Pythagoras is believed to have

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travelled to Babylon and other countries as far as India also. The astronomy in Egypt however could not develop in comparison with the Babylonian and Greek astronomy but it is now an admitted fact that the Hindus had developed their mathematics and astronomy many centuries before Christ and as mentioned above, the ancient Jaina School of Mahāvira flourished very much in India round about the same period in which the Pythagorian School flourished in Greece.
According to vander Waerden in his book, "Science Awakening', “Herodotus has reported that Thales had predicted the event of solar eclipse of 585 B. C. It is believed that Thales was the first Greek astronomer to predict a solar eclipse. Such a feat required the experience of more than forty years, no matter how one proceeds. It is not possible for one man alone to gather this experience. But Thales had no Greek predecessors. The conclusion is inescapable that he must have drawn upon the experience of Oriental astronomers." These Oriental astronomers might be Babylonians and Hindus only. It is possible that Pythagoras might have been influenced by thc Jaina thinking of his time which is evident from the fact that he took the number 59 as the basis of his lunar calculations. In Prakrit Jaina texts, the number 59 has been taken as the basis of all lunar calculations since the days and nights in every one of the moon's months total to 59; it is because of the fact that in relation to the sun, the moon lags behind 62 celestial parts in one muhurta and therefore takes 591 days to cover 109800 celestial parts. It is important to note here that the ayan system of the Hindus is different from that of the Jainas and does not consider 59 days as above.
Taking into account the various factors, we can say that one of the important links, in the sequential history of the Science Awakening in the field of mathematics-philosophic pursuits that occurred in the world during the Pythogorean period, is the ancient Jaina School of Vardhamana Mahavira,
In Chapter I of this book, the author quotes Lincoln as saying, "The dogmas of the quiet past are inadequate to the stormy present" and states that the science awakening round about the period of Vardhamāna Mahāvira and Gautam Buddha, was a simple rise above the inadequacy of the scientific knowledge which became indispensable according to the needs of the times throughout the world.” This science awakening covered many fields including Astronomy and Cosmology by framing the concepts of the universe to which the Jaina School contributed a lot after the era of the Vedānga Jyotişa and prior to

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the
the Siddhantic period of Indian astronomical atmosphere and continued through Ptolemy (c. 150 A. D.), Aryabhaţa First (c. 498 A. D.), Copernicus (c. 1500 A. D.), Galileo (c. 1600 A. D.), Newton (c. 1680 A. D.), Einstein (c. 1925 A. D.), Eddington (c. 1925 A. D.) and many other Indian and foreign scholars and scientists. Sometimes the scientists had to pay very dearly for telling the truth. Regarding the solar system, Copernicus was the first western scientist who declared in very clear terms his assertion, "We therefore assert that the centre of the earth, carrying the moon's path, passes in a great orbit among the other planets in an annual revolution round the sun; that near the sun is the centre of the universe and that whereas the sun is at rest, any apparent motion of the sun can be better explained by motion of earth.' Galileo, practical had to scientist accepted the Copernican theory and pay dearly through his trial, insult and imprisonment. Einstein theory of gravitation resulted in two types of universes; Einstein's closed spherical universe containing matter but no motion and the other the de Sitter universe But as containing motion but no matter. we know, the actual visible universe contains both matter and motion, According to Eddington, the universe is expanding till one comes to a de Sitter's universe (motion but no matter) while according to Hoyle, the concept of universe involves a continuous creation of matter, otherwise due to the condensation of the background material into galaxies, a dead state of universe may occur in future. Thus even during the modern advanced scientific age, the scientists are not unanimous in their theories about the nature of the Universe.
According to the Jaina School, it has been made undoubtedly clear that there are six eternal fluents (dravyas), viz, bios (souls), puḍgala (puḍgala paramāņus or ultimate particles of matter), time particles (kālāņus), aether (dharma), anti-aether (adharma) and space (ākāśa); further the space has been divided into two types, viz, finite non-empty space), containing all the remaining five fluents) called Lokākāśa (universespace) and the infinite 'all-empty space' (containing nothing except the space itself,) called Alokākāśa (non-universe space). The Lokākāśa has a volume of 343 cubic rajjus (a measure developed and defined specially by the Jainas) and as mentioned above, accommodates all the remaining five fluents, viz, souls (jiva-bios), pudgala (matter), dharma (of cooperator motion), adharma (of cooperator rest) and kāla. It is situated in the very central portion of the endlessly endless (unfinite) space surrounded on all sides by the infinite Alokākāśa. Thus the Jainas have propounded the theory of two types of universe, viz., Lokākāśa containing both matter and motion and Alokākāśa containing none of them. Further the Jaina literature describes various

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sub-universes, for example, general universe, hellish universe, human universe, sub-human universe. god's universe and astral-uinverse, the three major division of the Lokākāśa being the upper, the intermediate and the lower universes. Further according to the Jaina Philosophy, the specific relation between the bios and matter is a Karmic one and the dynamical laws are derivable only from the Kārmic relations.
Chapter II describes some of the terms related to the celestial sphere and celestial diagram as envisaged at present; this has been given in order to facilitate a comparison of the modern technical terms with those used in the ancient Jaina literature where the frame of reference of celestial coordinates is different.
In Chapter III, the author, while giving a very short description of the historical evolution of the astronomy of the Vedic era, the Vedānga era and the Astro-theoretical era, and of the Jaina School, based on the book,
Indian Astronomy' by Shankar Balkrishna Dixit, mentions that the Vedic literature which is regarded as the oldest literature giving us information about the efforts of the ancient Indians, in compiling the contemporary knowledge, may be deemed to belong to the period from 2000 or 2500 B. C. to 500 B. C. or so (while Vedārga-Jyotişa belongs to later period and is not a work on Astronomy as it is essentially a five-year perpetual calendar meant for prediction of times for religious purposes). While considering the Jaina School, the author describes the source material, still available at present in the Jaina literature in spite of the fact that a major part of the ancient literature has been destroyed and is not available. The main authentic works available at present and relevant to Mathematics, Astronomy and Cosmology are Jyotişa-karaņdaka-prakirņaka (c.-3rd century), Tiloyapannatti of Yati Vrşabha (5th century A.D.), Gasitasāra-Samgraha and Jyotiga Patala of Mahāvīrācārya (c. 850 A. D.), Triloksāra (18th century A. D.),
Şatkhaņdāgama (c. 2nd century A. D.) and its commentaries, Lokavibhāga, Sūrya-prajñapti, Candra-prajñapti, Jambūdvipa prajñapti etc. A number of later writers and scholars, for exampie, Hemahamasagani, Rājāditya (c.+1120), Mahendra Sūri (c.+1370), Malayendu Sūri, Mahimodaya (c. 1665), Labdhicandra gani (c. + 1693), Bāghaji muni (c.+ 1720), Sumati harşa (c. + 1626), Bhāvaprabha Sūri (c. + 1711) and many more have written books and discussed therein various aspects of Astronomy and Cosmology.
In Chapter IV, the author has discussed and described many cosmological concepts. In Jaina literature, the space-measure, rajju, occupies an important place and has been defined in a number of ways.
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Some definitions are very complicated to be deciphered or to be computed. Based on these and by comparing the volume of the finite universe of Einstein Theory of Relativity with the volume of the universe as given in Jaina literature, G. R. Jain has come to the conclusion that one rajju=1.45 x 1021 miles based on Digambara School and equal to 1.63 x 1021 miles based on Svetāmbara School.
According to one definition of C. T. Colebrook, Jain also finds one rajju= 1.15 x 2021 miles roughly, but as pointed out by Muni Mahendra Kumar II and many other scholars, these values of one rajju can't be taken as accepted. Taking the same definition of Colebrook and interpreting it in two different other ways, Muniji finds that
one rajju=7,44 x 10 {1.47 x 10196+20} miles
or =4.00 x 10 {1.8 X 10245 + 3} miles The author also remarks that the Tiloyapaņņatti gives a very vivid description of the shape and the volume of the universe (the Lokākāśa) and also about the volumes of the three types of layers of air and water vapour all round the universe, showing that there is no outer surface of the universe without these layers. The author further mentions that in the Jaina School, the concept of eight central space-points of the loka, as well as the movement of matter and souls along the world-lines subject to instantaneous conditions defines a coordinate frame of the universe, full of space-points or time points and there is no corner of the universe which is not reachable before four instants, thus speaking of the principle of least time or the principle of quickest approach and the principle of least path, thus conforming to the theory that amongst all movements, the nature selects only those which reaches the desired location with expenditure of least action (energy x time).
Regarding the Yuga system in India, the author quotes Roger Billard and from his book, 'L' astronomie indienne investigation des textes Sanskrits et des données numèriques, Paris' and states that for astronomical studies what was being done in Greece during the period 8th Century B. C. to 2nd Century A, D., was being done in India also and the Jaina School was further studying the maximum and minimum periods of life-time of human, sub-human, gods and hellish beings in terms of muhūrtas, palyas and sāgaras etc. In this very context, he gives the meaning of palya, sāgara and briefly discusses the concepts of kalpa and parāvartana periods and comparability so important in the Jaina School. In the end, the author summarises, "The Jaina universe (Lokākāśa) is finite, lying in the very central portion of all space, with non-material media of motion and rest which have specific functional character. Space is a fluent and time-particles
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are also fluents. Motion of ultimate particles in an indivisible instant could be minimum (one space-point) and maximum (14 rajjus). For bonds of particles, snigdha and ruksa could be associated with positive and negative charges. For Karmic bonds, yoga and kaşaya bind a bios with nişekas, measured through particle number, configuration, life-time and energy-level of impartation (pradeśa, praksti, sthiti, and anubhāga).”
In Chapter V, certain astronomical concepts, for example, precession of equinoxes general calendar as well as Indian Calendar (pañcāiga) etc. have been discussed. The author also mentions, as it is well known, that the calendar adopted in Vedānga Jyotişa has something to do with that adopted in the ancient Prakrit texts and that there is a great similarity in the treatment of the heavenly bodies and their motion in practically all ancient Prakrit iexts of the Jaina karapānüyoga
oup. In Hindu Calendar, 27 nakşatras while in the Jaina Calendar 28 nakşatras have been reckoned, the Jainas having added one more nakşatra 'Abhijit'. The author also points out that considering certain aspects of the astronomical incidences, Lishk and Sharma have concluded that the probable period of the Jaina canon may be about 6th Century B. C.
In Chapter VI, kinematics of the astral bodies have been discussed as available in ancient texts of India, China, Greece, Egypt, Babylonia etc. As stated by Needham and Ling, "In these texts there is never any mention of any Zodiac or of constellation lying along the ecliptic; the earliest documentary evidence of this conception occurs just after. On the other hand, seleucid cuneiform texts of the 3rd and 2nd centuries B. C., give great prominence to the Zodiac and use ecliptic coordinates extensively." But the
uthor (Jain) points out that the above authors do not appear to have gone into details of the nakşatra system of the Jaina School. The Zodiac of the Jaina School was so predominant that every nakşatra of the Zodiac had its sign and Yogatāräs. However, there is some difference of sign of in the two Jaina texts, the Candraprajñapti and the Tiloyapaņņatti, the reason may be that the, Candraprajñapti was based on observations taken in the north while Tiloyapaņņatti belonged to the observations taken in the south of India,
The commentaries of Candraprajñapti by Malayagiri and Amolak Rși give greater details of a Jaina Calendar based on calculation of motion of various heavenly bodies, specially that of the sun, the moon and the nakşatras while Tiloypaņņatti, Trilokasāra, Lokavibhāga and Jambūdvipa prajñapti give concise knowledge of the same. According to Neugebauer, only since the Assyrian period, a turn towards mathematical description became visible and texts based on a consistent mathematical theory of lunar
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and planetary motion came into existence only during the last three centuries B. C. In this connection it has been pointed out that the Jaina School had already developed a mathematical theory of the motion of heavenly bodies by the early centuries B, C., though as Yati Vrşabha mentions in his Tiloyapaņņatti that by his time, the description of the motion of the planets had become extinct but whatever remained in Candraprajñapti, Suryaprajñapti, or Tiloyapangatti, clearly proves that the Jaina School was in possession of a complete calendar based on a highly developed ingenious and original mathematical theory. This is clear even from the example that the total number of astral images was given by the Jaina School as the quotient set obtained by dividing the square of the Jagašreni (set of points) by the product of the set of the squared finger width and the square of 256. The Jaina School also believed that the distribution of the astral objects was symmetrical and based on five kinds of astral-groups, viz., the moon, the sun, the planets, the constellations and scattered stars (prakirņaka tārās) and that the moon was the head of the family of eighty-eight planets, twenty-eight nakşatrās and 66975 (10)14 stars.
As mentioned in this very Chapter, the Jaina School also believed that the phenamena of the heavenly events in all the islands was also symmetrical and could be represented by those, occurring in the Jambūdvipa island only except that in far off islands, the astral bodies were assumed at rest. From this it is clear that such a symmetry denotes the manipulation of the causality theory through an abstract mathematical model, principle theoretic in nature and consistent. It is also remarkable to find that like other world traditions, the Jaina tradition also believed in shadow invisible planets as found in the texts Jinendramālā and Jñānapradipikā. In the end of the Chapter, topics, like motion of astral bodies, relative motion of the nakşatras, the relative motion of the sun and the relative motion of the moon have been described.
In Chapter VII, the author gives a vivid description of the various meanings and measures of a 'Yojana' as stated by a number of different schools and scholars, for example, the Chinese School, the Jaina School, Needham and Ling, Lishk and Sharma, Muni Mahendra Kumar II, Megasthenes (3rd – 4th centuries B. C.) etc. In the Jaina School and in some other systems, the Yojana has been taken as primarily depending upon angula and equal to 768000 arigulas. But only in Jaina School, there are 3 types of yojana depending upon 3 types of aigūlas-mātmāigula, utsedhārgula, and pramāņā ngula which are used for measuring different types of objects as indicated in all concerned literature. The ātmāigula is used to measure the lengths of ornamental objects, gardens, cities, and residences
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etc. belonging to human beings while utsedhārgula is used to measure the heights of sub-human and hellish objects and the cities and residences of four types of gods. In Svetāmbara School, 1000 utsedhārgulas while in Digambara tradition, 500 utsedhāngulas are taken equal to one pramāņāigula. Thus according to the Svetāmbara tradition, the pramāņa yojana is equal to modern 8000 miles while the Digambara pramāņa yojana comes out to be equal to 4000 miles and is used to measure the regions, the islands, the oceans, the high mountains, rivers etc., described in the Jaina cosmology. The Buddhist School takes its own angūli-parva equal to two argūlas of the Jainās. The Chinese generally take one yojana equal to 30 li or equal to 6.12 miles, they also take a yojana equal to 40 li or even equal to 16 li only. The concept of yojana occurs in Süryasiddhānta also and according to Vācaspati and Sabdārņava košas, a yojana may be taken equal to 5 miles as pointed out by Dixit. Fleet and Cunningham have estimated one yojana equal to 9.4 miles and 6.7 miles respectively, the former value being accepted by L. C. Jain, the author of the present text while the latter value being accepted by Lishk and Sharma. Thus we find that a yojana is taken equal to different measures, by different texts and scholars, generally also depending upon its use.
Based on the concepts of the Jaina School, Lishk and Sharma have calculated the obliquity of the eclipitic as 23° 5' (in structure of the mathematical model of Meru) very close to the modern value. They have also calculated the maximum north polar distance of the moon from the sun or eclipitic as 7.7° which may however approximate to the modern value 5° 8' 40" if a yojana is taken equal to 5 miles.
In Chapter VIII, the author mentions about the calendrical yuga system. As stated by him, the various Indian Schools including the Jaina School accepted the quinquennial yuga or cycle but as pointed out by the author, this yuga (or cycle) began with the nakşatra, Abhijit, a concept found in the Jaina School. This cycle was found to be of 780 solar years or 285480 days (one solar year=366 days).
In the last Chapter on Astronomical Theory, the author discusses many important modern concepts in the light of the concepts given in the Jaina literature. He quotes Albert Einstein as distinguishing between the various types of theories in Physics, specially the Principle Theories and the Constructive Theories. The Principle Theories, which are based on analytic methods, are logically perfect and have a secured foundation while the Constructive Theories follow the synthetic methods and could be made complete, clear and adaptable. However, if a singie principle fails or if a
14

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single inconsistency arises, the whole structure has to be re-modelled, because of almost impossibility then to retain its originality while the constructive theories can be subjected to re-modelling without shattering the complete structure.
The author further discusses to which type of the above two categories, the ancient Jaina Astronomical Theory belong On one hand the abstraction method leads us to such small entity as the Samaya (44) and Pradeśa (sau) which are both regarded as indivisible just like the ultimate particle Paramāņu, while on the other hand there are such big quantities as the Rajju and Sāgara or Jagaśrěni and the periods like Pudgala or Bhāva Parāvartana, infinities in space and time. Most of the Jaina Astronomical principles have been found to be true but in some cases, for example, in the prediction of the time of eclipses, when the Jaina Principle Theory was found inadequate to explain and get consistent results of the processes and phenomena, it was replaced by the Constructive theories evolved all the world over. Lastly the author discusses the evolution of epicycles depicting the unified motion of the moon or the sun as described in Prakrit texts and comprising the two motions, (i) the rotation of the earth, which in turn relatively gives a kinetic view of them, and (ii) their motion along the fixed stars,
Due to the continuity of the motion in circles, for each day, with a radius varying from day to day, the geometrical figure of the path comes out to be a spiro-elliptic one, winding and unwinding represented by the equation
f+go * htk cos 8.
en The dynamical laws of Newton, Einstein etc. have been found from this equation,
In the end the author has given very useful and brief bibliographies of the source material, research articles and related books. Thus we see that the author has tried and tried very successfully, to give as much information and exposition as possible about the ancient Jaina Astronomical and Cosmological systems and other allied world systems, which is very praiseworthy and creditable.
Prof. L.C. Jain has got a keen interest not only in the study of the ancient Indian Mathematical and Astronomical works in general and the Jaina works in particular but also in the study of modern mathematics. He has got a vast experience of about three decades in this field and has himself brought out a large number of expository, survey and research articles on ancient Jaina mathematics, quite a good number of them dealing with the modern aspects inherent in the ancient Jaina principles.
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It is hoped that this work of Prof. Jain would prove to be a very useful source of reference for any future work in this field.
G. C. PATNI Ex. Prof. and Head of Deptt. of Mathematics and Dean, Faculty of Science and Faculty of Social Sciences, University of Rajasthan, Jaipur
Jaipur, 20th Dec., 1983
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THE JAINA SCHOOL OF EXACT SCIENCES
PART II COSMOLOGY AND ASTRONOMY
CHAPTER I INTRODUCTION
“Give me to learn each secret cause;
Let Number's, Figure's, Motion's laws Reveal'd before me stand;
These to great Nature's scenes apply, And round the globe, and through the sky, Disclose her working hand.”
-Akenside, M. According to Lincoln, “The dogmas of the quiet past are inadequate to the stormy present." The Science awakening, round about the period of Vardhamana Mahāvīra and Gautama Buddha, was a simple rise against the inadequacy of the scientific knowledge which became indispensable according to the needs of the times, throughout the world.
One has to see with supreme clarity and certainty, whether during the hatching of a Science awakening, there has been a desperate attempt towards development of a scientific methodology. The methodology, usually, involves founding of general postulates or principles from which conclusions
ld be deduced. The principles are wormed out of nature by perceiving in comprehensive complexes of empirical facts and events ce features (say, cycles of births and deaths, regeneration and degeneration, evolution as well as devolution) which permit of precise formulation. Then may follow inference after inference revealing unforeseen relations, extending beyond the province of the reality from which one started the method out of pre-scientific thought.
Thus there has been awakening in framing the changes in concepts of the universe, the astral-universe being only an observable part of it. The

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stories of such awakening cover the role played by Lucretiusi (-98 to--55), Ptolemy2 (c+-150), Copernicus3 (+1473 to +1543), Galileo4 (+ 1564 to
+ 1642), Newton5 ( + 1642 to + 1727), Einstein ( + 1879 to + 1955 ), Eddington? (+ 1882 to + 1944) and Hoyle8 (+ 1915 to-...), All have left indelible marks in the history of astronomy and cosmology, and even before them all, one could discover out the Jaina system which also championed the science awakening for the cause of research on truth and non-violence, prior to the Siddhāntic period of Indian astronomical fervour, after the era of the Vedārga Jyotişa
SCIENCE AWAKENING
Titus Lucretius Carus was a great poet of science, unparalleled in Rome, fighting fear of gods, of sin and death. He belonged to the class among whom was stated, “Then, my noble friend, geometry will draw the soul towards truth and create the spirit of philosophy, and raise up that which is now, unhappily, allowed to fall down."9 Lucretius argued 10 “Bear this well in mind, and you will immediately perceive that nature is free and uncontrolled by proud masters and runs the universe by herself without the aid of gods. For who- by the sacred hearts of the gods who pass their unruffled lives, their placid aeon, in calm and peace !- who can rule the sum total of the measureless ? Who can hold in coercive hand the strong reins of the unfathomable ? Who can spin all the firmaments alike.
1. Vid. Nature of the Universe', trans, R. E. Latham, Penguin Books
Ltd., 1951. 2. Vid. "The Almagest', trans. R. C. Taliaferro, 'Great Books of the
Western World', series, vol. 16, Book I-Chicago, 1952. 3. Vid. “De Revolutionibus Orbium Coelestium ( 1543 )', published by
Royal Astronomical Society. 4. Vid. "Diologue concerning the two chief world systems- Ptolemic and
Copernican', trans. Stillman Drake, Univ. of California Press, 1933. 5. Vid. Philosophiac Naturalis Principia Mathematica', Drake, A, M.,
trans. rev. by F. Cajori, Univ. of California Press, 1946. (Cf. also
Mein Weltbild, Amsterdam, 1934). 6. Vid. "The World As I See It', Newyork. 7. Vid. “The Expanding Universe,' Cambridge, 1933. 8. Vid. “The Nature of the Universe', New York, 1960. 9. Cf. Coolidge, J. L., A History of Geometrical Methods, Oxford, 1940. 10. Cf. ‘Nature of the Universe', op. cit.
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and foment with the fires of ether all the fruitful earths? Who can be in all places at all times, ready to darken the clear sky with clouds and rock it with a thunderclap- to launch bolts that may often wreck his own temples, or retire and spend his fury letting fly at deserts with that missile which often passes by the guilty and slays the innocent and blameless ?"
Claudius Ptolemy of Alexandria, an astronomer of first rate, argued in the Almagest, the spherical movement of the heavens as follows, "If for example, one should assume the movement of the stars in a straight line to infinity, as some have opined, how could it be explained that each star will be observed daily moving from the same starting point? For how could the stars turn back while rushing on to infinity? Or how could they turn back without appearing to do so? Or how is it they do not disappear with their size gradually diminishing, but on the contrary seem larger when they are about to disappear, being covered little by little as if cut off by the earth's surface ?" His scheme served as a new edition of Hipparchus (c-2nd century), his universe being a geometrical pattern of epicycles, eccentrics and deferents. It neither opposed Aristotle nor the Bible and reigned supreme for 14 centuries till the advent of sun-centred scheme of Nicholas Copernicus. The work of Copernicus was declared false and altogether opposed to the Holy scripture by the Pope in +1616, (earlier in 1600, Giordano Bruno had been burnt for supporting the views). His assertion was, "We therefore assert that the centre of the Earth, carrying the Moon's path, passes in a great orbit among the other planets in an annual revolution round the Sun; that near the Sun is the centre of the Universe; and that whereas the Sun is at rest, any apparent motion of the Sun can be better explained by motion of the Earth." 11
Galileo Galilei, a practical scientist par excellence, had to pay dearly for accepting Copernicanism, because his experiment with falling bodies went against Aristotle and his telescope opposed the Pope and Ptolemy. An excerpt from his book on Dialogue, which led to his trial, insult and imprisonment, is as follows," Simplicio: The first and greatest difficulty is the repugnance and incompatibility between being at the centre and being distant from it. For if the terrestrial globe must move in a year around the circumference of a circle- that is, around the Zodiac- it is impossible for it at the same time to be in the center of the Zodiac. But the earth is at that center, as is proved in many ways by Aristotle, Ptolemy, and others. Salviati: Very well argued. There can be no doubt that any one who wants to have the earth move along the circumference of a circle must
11.
Cf. De Revolutionibus, op. cit.

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first prove that it is not at the center of the circle. The next thing is for us to see whether the earth is or is not at the center around which I say it turns, and in which you say it is situated. And prior to this, it is necessary that we declare ourselves as to whether or not you and I have the same concept of this center. Therefore, tell me what and where this center is that
""12
you mean.
It was left for the genius of Isaac Newton to formulate the laws of celestial mechanics in the Principia on the basis of the works of Galileo, Kepler, and Tycho Brahe, consistent with the Copernican system. Discussing about the absolute and relative, true and apparent, mathematical and common, Newton writes, "Absolute time, in astrnomy, is distinguished from relative by the equation or correction of the apparent time. For the natural days are truly, unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality that they may measure the celestial motions by a more accurate time. It may be that there is no such thing as an equable motion whereby time may be accurately measured. All motions may be accelerated and retarded, but the flowing of absolute time is not liable to any change." 13
Albert Einstein contributed to relativistic mechanics replacing Newtonian space-time by a super-edifice of four-dimensional continuum on the basis of Riemannian geometry and tensor calculus of Levi Civita. Writing on the fundaments of theoretical physics, he explains, "The general theory of relativity owes its origin to the attempt to explain a fact known since Galileo's and Newton's time but hitherto eluding all theoretical interpretations the inertia and the weight of a body, in themselves two entirely distinct things, are measured by one and the same constant, the mass. From this correspondence follows that it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether its motion is straight and uniform and the observed effects are due to a gravitational field (this is the equivalence principle of general relativity theory). It shatters the concepts of the inertial system, as soon as gravitation enters in, It may be remarked here that the inertial system is a weak point of the Galilean-Newtonian mechanics. For there is presupposed a mysterious property of physical space, conditioning the kind of coordinate-systems for which the law of inertia and the Newtonian law of motion hold good." 14
Einstein's theory of gravitation on introduction of a cosmological term results in two types of universes; Einstein's closed spherical universe
12.
op. cit.
13. Cf. Principia Mathematica, op. cit.
14. Einstein, Ideas and opinions, London, 1956, p. 330.

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and the de Sitter universe. Einstein's universe contains matter but no motion, whereas the de Sitter's universe contains motion but no matter, The actual universe, however, contains both matter and motion. Eddington's study has given rise to an expanding universe, till one finishes up in a de Sitter's universe. Hoyle's theory, in addition, postulates a continuous creation of matter in order to compensate for the condensation of the background material into galaxies, otherwise a dead state of the universe in future is the consequence. JAINA COSMOS
The Jaina school has clearly distinguished between all empty space and non-empty space, the former being alokākā’sa (non-universe-space) and the latter being lokākāśa (universe-space).15 Alokākāśa extends to infinity all around beyond the finite lokākāśa which has a volume of 343 cubic rajjus (ropes).16 The lokākāśa accommodates the five eternal fuents (dravyas), viz., souls, ultimate particles of matter (pudgala paramāņus), time particles17 (kālāņus), aether (dharma) and anti-aether (adharma); space (ākāśa) being the sixth eternal fluent. The lokākāsa is situated in the very central portion of the endlessly endless empty-space. Souls are infinite, and endless times this infinity is the cardinal number of the set of time-particles, situa at every space-point (pradeśa). Space-point is the space occupied by an
ate particle at rest, which by virtue of its motion may occupy more than one space-point in an indivisible instant (avibhāgi samaya). Thus pradeśa and samaya are the ultimate units of space and time18, the samaya 15. Vid. T. P., I, vv. 1.91 et seq. Cf. also G. A., pp. 1, et seq. Vid. also
Cosmology, old and new by Jain, G. R., Indore, 1942. See appendix A and appendix B for the shape of the universe in Digambara School.
In the other it contains steps all around. 16. Cf. T. P., I, vv. 1.133 et seq. According to Svetāmbaras, 239 c. r. 17. Siddhasenagani regards time as a modification of bios & matter. In
Svetāmbara work Jivā jīvā bhigama, the same view is expressed, but in Bhagavati and other works, time has been regarded as a separate fluent. “Kālaścetyeke”, in Svetāmbara and Kālaśca” in Digambara.
Cf. Kirfel, Die Kosmographie der Inder, Bonn, 1920. 18. Time (Kāla ) has been defined to be of two types : niscaya and
vyavahāra. Niscaya ( absolute) time is a fluent, whereas vyavahāra (relative) time is a measure. Similarly niscaya (absolute) space is a fluent, where as vyavahāra (relative) space is a measure, “Anoraşvantara vyatikrama kālaḥ samayaḥ. Coddasa rajjuāgāsa padesa kamaņa metta Kāleņa jo Coddlasā rajju kamaņakkhamo paramāņu tassa ega paramāņuakkameņa kālo samao nāma." Cf. Dhavalā, book 4; 1, 5, 1, p. 318, Satkhaņdāgana.
.
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being the interval in which an ultimate particle crosses another ultimate particle or else is able to cross all space-points situated in a stretch of fourteen rajjus.
Rajju is a familiar historical word from Egyptian rope-stretchers. Through it are measured the distances between the ends of the immense universe (loka), the cardinal number of space-points of which is innumerate, as also of those of a fully stretched soul, of the aether and of the anti-aether as well as of the time-particles.
Out of all these fluents, only the matter (pudgala ) has been endowed with five types of taste, five types of adour, five types of colours, and eight types of touch. The ultimate particle, has however, only one taste, one odour, one colour, two types of touch (either cold or hot, and either smooth or rough). Smoothness or roughness has been associated with levels from zero to infinity, corresponding well with positive and negative types of charges in so far as their story of bonds is concerned in Jaina literature. One may call the touch to be of affine and anti-affine types, again corresponding with love and malice of a bios, or affinity and anti-affinity, causing karmic (action) bonds between a bios and ultimateparticles. 19 Thus pudgala is material, other fluents being abstract. Motion is defined for the bios and matter alone, the other fluents being stationary, ākāśa being an accommodator, kāla being a modifier, dharma being motioncooperator, and adharma being rest-cooperator. Consciousness is accorded to the bios alone.20
Common properties or controls of all the fluents are interesting :
i) Astitva (existence): signifying it as eternal and indestructible ii) Vastutva (objectivity): signifying it as having some norm of
action. iii) Dravyatva (fluence) : signifying it as being, flowing through
its own controls and events, Prameyatva (measurability ) : signifying that it could be the subject of knowledge.
19.
Cf. P. A., vv. 127-134. A fluent (dravya) is that which flows through its own controls (gunas) and events (paryāyas). Each is endowed with regeneration, degeneration and immutability (utpāda, vyaya evam dhrauvya). These describe the special properties or controls (guņas) of the six fluents.
20.

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v) Agurulaghutva (non-gravity-levity ) : signifying the power by
virtue of it, the fluent does not lose its own controls and remains always what it is.
vi) Pradeśatva (pointedness ): signifying that every fluent has
some or other form (shape, size, etc.)
Further, space (ākāśa) forms a continuum absolutely, but relatively it consists of or is composed of infinite space-points (pradeśas) whose cardinality is greater than that of the instants (samayas) in the past, the present and the future. Similarly the cardinality of the infinity of the time-instants is greater than the cardinality of the set of all ultimate particles (paramāņus).21 Matter, souls, aether, anti-aether and space are each called astikāya because each of them is many-pointed. Soul may contractor expand, forming a continuum. Aether and anti-aether also form a continuum. Time-particles do not form astikāya in so far as each is single pointed and discrete, 22
In the works on karaṇānuyoga, description of various subuniverses is available. For example in the Tiloyapaņņatti, chapters have been devoted to the general universe, hellish universe, human universe, sub-human universe, astral universe, and gods universe. 23 Loka is also of four types : fluent (dravya), quarter (kşetra), time (kāla) and phase (bhāva) universes.
Thus under various controls of their own, the fluents modify themselves through various types of events. The specific relation between the bios and matter being karmic one. The astral universe relates the astronomy in terms of celestial parts (gagana khandas), project-measure (yojana), and forty-eight-minute set (muhūrta),24 The dynamical laws are derivable only from the Karmic (action) relations, as it appears, which may be subject to deeper probe, later. Yojana may be compared with Chinese 'li'
21. Cf. D., book 3, p. 30, 31. 22. All the six types of fluents (in various number) enter each other,
continually mixing with each other, accommodating each other
mutually, yet do not lose their own nature (special property). 23. Cf. T.P., I & II. The three major divisions are the upper, interme
diate and lower universes. Cf. also G. A., p 9. 24. Cf. ibid. Cf. also S. P., C. P., T. S., and L. V.

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2. TECHNICAL TERMS
For an interesting reading, it is desirable to acquaint the readers with certain terms used in astronomy at present, so that the ancient material could be brought under relevance.
Z
CELESTIAL DIAGRAM
The above is a celestial diagram used in spherical trigonometry and astronomy. An observer is set at O inside a hollow sphere, serving as two hemispherical domes, with Z as the Zenith and Z' as the nadir. This is presumed to be his range of vision in which all the heavenly bodies appear in different positions, measured through various types of celestial coordinates. S N is his horizon, with East (E), West (W), North (N), South (S) as its
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cardinal directions. Above N in the northern direction is the Pole star (roughly) or the celestial pole at P, the south celestial pole being at P'. All are great circles with O as centre and O Nas radius, except the Co-D which is a small circle, with P as its Pole.
ZEZ' is the prime-vertical East, and Z WZ' is the prime-vertical West. The perpendicular to the polar axis and Pro'P is the celestial equator QER W. The secondary to this is the Pro' P'. Here is any star whose declination is o'r, the declination circle being Co-D.
The celestial equator cuts the ecliptic F-GV (path of the sun) at - and p, called the first point of Libra and the first point of Aries, or the equinoctial points. The position of the sun at these points make days and nights equal all over the earth. The pole of the ecliptic is denoted by K, near P.
The circle Pro’P may be called the hour circle as it measures the hour angle of the star's movement from the celestial meridian PZSP', always westwards, from Oh to 24h or 00 to 3600. Thus the declination o'and hour angle Z Po as substracted from 360° gives a system of celestial coordinates measured with the help of celestial equator and its secondary.
A second system of coordinates is set up from the ecliptic F-GP and its secondary through K H. Here Ho is called the celestial latitude of the star o, and the angle at K, measured eastwards from op between the secondaries K p and KoH to the ecliptic is celestial longitude of the star. plo' measures the right ascension of - 25.
The angle between the ecliptic and the equator is 234 degrees and is the same as the arc PK. The distance N P gives the altitude of the pole star or latitude of the observer. This is also equal to ZQ. Now F and G are solstitial points, when the sun is nearest or farthest from the earth,
When the star is at C, it is said to culminate or at upper meridian transit, at D it is at lower transit. o-B is the altitude of the star o, and Zo is its zenith distance.
25. Right ascension
coordinates
and declination forms another system of celestial

Page #29

INDEX OF THE DIAGRAM
O
SENW
Observer horizon, with south, east, north, west as cardinal points at S, E, N, W. Zenith
nadir
ZEZ' PZQP
NÊ NAAM Ô d m
prime vertical east celestial meridian north celestial pole south celestial pole celestial equator
QERW
Gop PN
(celestial ) ecliptic (path of the sun along zodiac)
G
altitude of pole star or latitude of the place. pole of the ecliptic first point of Libra
Equinoctial points first point of Aries ) solstitial points star, with its path Co-D, declination circle. Secondary to celestial equator or hour circle. Secondary to ecliptic altitude of star o zenith distance of star o declination of star o
Poo'p
& Eb Ab NON
Ꮋ
to 9
9
.
ZP
360° minus the hour angle of star o Flor FaQ obliquity of ecliptic (2310) Ho
celestial latitude of star o p FH celestial longitude of staro op Qo' right ascension of star o
point of culmination of star o
point of intersection of hour circle with horizon.
10.

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It is now important to note how various positions of the heavenly bodies were depicted in the Jaina school, Concepts were the same, but the frame of reference of celestial coordinates was different. The researches of Lishk and Sharma 26 are attracting attention of scholars in so far as their interpretations are bringing the secrets of the school to light in terms of modern usage.
26. Cf. bibliography of research papers,
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3. SOURCE MATERIAL
Shankar Balkrishna Dixit, in his Indian Astronomy 27 has given the historical evolution of the astronomy into three stages : Vedic era, Vedānga era, and Astro-theoretical era,
VEDIC LITERATURE
As is well known, the Vedic literature28 is regarded as the oldest literature as well as the outstanding effort of the ancient Indians towards collection of the contemporary knowledge, leaving apart the still unknown treasures of the civilization of the Indus valley, or of the pre-Harappan cultures. The three distinct classes of this literature are the Samhilās (the Rgveda, the Sāmaveda, the Yajurveda and the Atharvaveda ), the Brāhmaṇas (Aitareya, Kauşitaki, Pancavimśa, Jaiminiya, Katha-fragment, Taittiriya, Satapatha, and Gopatha), as well as the Aranyakas-Upanişads (forest texts and secret doctrines; including Chāndogya, Kena, Mahānārāyaņa, Svetas'vatare, Maitrāyaṇi, Bșhadāraṇyaka, İşā, Mundaka and Praśna).
According to Winternitz, the view on Vedic chronology generally followed is, “we shall probably have to date the beginning of this development about 2000 or 2500 B. C. and the end of it between 750 and 500 B. C.”29. During this period, the times of occurence of the parvas ( "Knots of time"), viz., full moon, new moon, equinoxes, solstices etc. were investigated for religious performances. Dixit have tried to find out relevant astronomical details in various parts of the literature. 27. Cf. Bhāratiya Jyotişa, Hindi trans. by S. N. Jharkhandi,
Lucknow, 1975. 28. Cf. Bose, D.M., Sen, S, N., Subbarayappa, B. V, A concise History of
Science in India, New Delhi 1971. 29. Max Müller holds the view that the oldest of the Vedas could not have
been composed earlier than 1200 B. C. Hermann Jacobi and B. G. Tilak, on the basis of precession, etc. opine this date to be in the third millennium B. C. Cf. ibid. pp. 22-23.
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VEDĀNGA JYOTISA
The next group of literature comes under the Vedārgas comprising of Sikşā, kalpa, vyā karana, nirukta, chandah and jyotişa. The joytişa is found in recensions of the Rga and the Yajurvedas : Arc-jyotişa and Yajuşa-jyotişa, The Atharva-Jyotişa, astrological in character belongs to a later date, These works take the winter solstice at the time of Sun and Moon's conjunction as the first point of the Dhanişthā (a point of the ecliptic lying 193° 20' east of the star Zeta Piscium). The epoch might be 1400 B, C. From the lengths of the day and night at summer solstice, viz. 36 and 34 ghatis, it may be inferred that the author belonged to a place in latitude 35° north (near north of Kashmir, in India). 30 According to Shukla, the Vedānga-Jyotişa is not a work on astronomy, but it is essentially a five-year perpetual celendar meant for prediction of the times for religious purposes, and that the Vedānga calendar had two main defects. Actually there are 1826-2819 civil days in a 5 solar year period (yuga), and not 1830 days (as supposed in the Vedānga Jyotişa), therefore, after every new cycle, the winter solstice fell about 4 days earlier.
Moreover, as there are 1830.8964 days in a period of 62 lunar months and not 1830 as supposed in the text, a deficit of one tithi approximately in a period of 5 solar years resulted, 31
JAINA TRADITION
The Jain school is said to have tradition of twenty-four tirthařkaras, Mahāvīra was the last. The name of the first tirtharkara, Rşabhadeva, appears in Vedic literature, Bhagavat purā ņa and even in Shiva mahāpurāņa. Dr. H. L. Jain presumes that there was a parallel Sramaņa tradition to the Vedic tradition. The ascetics of the former were called Munis and those of the later as Rşis, and that there could have an exchange of knowledge between both the traditions. 32 The historicity of Pārsvanātha
30. Cf. Shukla, K. S., Astronomy in India before Aryabhaţa-I, paper read
at B. G. P., Lucknow. Cf. also Renoy, L., and Filliozat, J.-L'Inde classique, École Française d'Extrême-orient, Hanoi, 1953; they find the text to be of c. 400 B. C., but the astronomical elements belong to the
period of the Samhitās. Cf. also, Dixit, op. cit., p. 126. et seq. 31. The Vedāniga calendar consisted of 61 civil, 62 lunar, and 67 sidereal
months. A solar day, reckoned from sun rise to another, the year consisted of 366 civil days. This calendar commenced on the first
tithi of the white half of the month Māgha. 32. Cf. Bhāratiya Saņskrti men Jaina Dharma kā Yogadāna, Bhopal,
1962, pp. 11 et seq.
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tirthařkara has also been established, the nirvāņa of Mahāvīra being accepted as -527. The bifurcation of Jaina tradition of literatue into that of Svetāmbara and of Digambara appears to be round about + 73.33 LITERATURE IN 'SVETAMBARA SCHOOL
A question may be posed whether these was any literature of the Jaina School prior to Mahāvira ? Two types of scriptures, dravya and bhāva, in Jaina tradition, has been described according it is worded or else thought, or normed. The later may be brought under the caption of the pūrvas (the earlier). Fourteen such pūrvas of knowledge of the tradition are described as utpada pūrva, agrāyaņiya, viryānuvāda, astināstipravāda, jñana pravāda, satya-pravāda, ātma pravāda, karma pravāda, pratyakhyāna, vidyānuvāda, kalyāņavāda (or abandhya, according to Svetāmbara), prāņāvāya, kriyā viśāla and lokabindusāra. Mention has been made from place to place in available Jaina literature about these pūrvas, still they are said to have become extinct about 162 years after Mahāvira. By this very time, the Svetāmbara tradition is said to have held a conference of Jaina Sramaņas in Patliputra at the instance of Sthūlabhadra and compiled the eleven argas of āgama : āyārārga, thaņāňga, samavāyanga, viyāhapaņņatti, nāyādhammakahão, uvā sagadesão, antagadadasão, aņuttarovaiya dasāo, panhavāgarana and vivāga suyam. The twelfth anga was digthivāda (having five divisions-parikarma, sūtra, pūrvagata, anuyoga and cūlikā), excepting perhaps a part of pūrvagata of which, rest material is not available.
Apart from the above, the council of Valabhi, at the instance of Devarddhi Gani (c. +454) compiled twelve upāngas, six cheda sūtras, four mula sūtras, ten prakirņakas and two cūlikā formulas. Upāngas : aupapātika, rāyapaseộiyam, jīvājivābhigama, prajñapanā,
sūryaprajñapti, jambūdvipa prajñapti, candraprajñapti,
kalpikā, kalpāvateņsikā, puşpikā & vịşņidaşā, Chedasūtras : niśitha, mahāniśītha, vyogahāra, ācāradaśā, kalpasūtra and
pañcakalpa, Mūlasūtras : uttarādyayana, āvaśyaka, deśavaikālika, and piņdaniryukti. Prakirņkas : catuḥ śaraņa, atura-pratyakhyāna, mahāpratyākhyāna,
bhaktaparijña, tandula vaicārika, samstāraka, gacchācāra,
garividyā, devendra stava, & maraṇasamādhi, Cūlikā sūtras : nandi sūtra and anuyogadvāra.
33
Cf. Jain. I. P., “The Jaina Sources of the History of Ancient India, (100 B. C. to A. D. 900)", Delhi (1964).
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LITERATURE IN DIGAMBARA SCHOOL
The Digambara tradition, however, regards a part of agrāyaṇi. pūrva, Şatkhanļāgama (c. + 2nd century), as well as a part of jñānapravāda, Kasāyapāhuļa sutta (c. + 1st century), to be authentic compilation. Other works appear to be those of Kundakunda (c. + 5th century). The Karaņānuyoga group of Digambara literature is known to be in Lokavibhāga (present edition of + 11th century), Tiloyapauņatti (c. +51h century), Trilokasāra (c.+11 century) and Jambūdvípaprajñapti (c. earlier to +1461). CERTAIN CONTRIBUTORS
The Karaņānuyoga group of Svetāmbar literature may also found to be in kşetra samāsa, saņgraheni of Jinabhadragani. These have been modified and extended as Bșharkshetra samāsa and Brahat sa mgrahaņi (compiled by Candrasūri of+ 12th century). Then there are Laghukşetra samāsa of Ratnasekhara (c. + 14th century), Bșhatkşetra samāsa of Somatilaka (c. 14th century), vicārasāra prakaraņa of Devasūri (c.13th century), and Jyotişa karandaka-prakirņaka (c.-3rd century ?)
Nemicandra Shastri, in his Bhäratiya Jyotişa, mentions some astronomical texts of astro-theoretical era, compiled by Jaina astronomers. He mentions Mahāvīrācārya to have compiled Jyotisapatala which is available in part, relating motion, state and number etc. of planets, constellations and stars.34 He regards Sridhara, the compiler of Jyotirjñanavidhi, to have become Jaina in later years. Udayaprabhadeva sūri (c.+-1220) is said to have compiled ārambhasiddhi (vyarahāra caryā); whose commentator Hemahamsagani appears to have some prakrit texion planetary mathematics with him. A kannada astronomer; Rājāditya (c. +1120) appears to have compiled mathematical texts applicable to astronomy. Mahendrasūri (c. +1370) completed a work on Yantra rāja, on various celestial diagrams, commented by his disciple, Malayendusūri 35
Contributions to astronomy inay also be mentioned of Mahimodaya's pañcāngānayana vidhi (c. +1665), Labdhicandragani's janmapatri paddhati (c.+1693), and Bāghajímuni's tithisāriņi (c.+1726). Karņakutūhala vștti of Sumatiharşa (c. + 1626), Mahādevi Sāraại vịtti of Dhanarāja (c. +1635), Grahalāghava vstti of Yaśasvatasāgara (c. + 1703), Jyotirvidā bharaṇa vștti of Bhāvaprabha Sūri (c.+1711), Candrārki vștti of kịpāvijayā, may also be mentioned.36
The contribution to astrology has been excluded in the above.
34. op. cit. p. 91. 35. Published at Bombay, 1936, 36.
Cf. Nahata, A.C., Jaina Jyotişa aura Vaidyaka Grantha, Sri Jaina Siddhānta Bhāskara, vol. 4, no. 2, 1937, pp. 110-118. Cf. also, Jain, A., Some Unknown Jaina Mathematical works (Hindi), Ganita Bhārati, 4:1-2 ( 1982), 61–71.
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4. COSMOLOGICAL CONCEPTS
Certain fundamental ideas have already been related in the introduction. The first curiosity is now as to what is a rajju through which the enormous distances of the ends of the loka (universe) are measured. EVALUATION OF RAJJU
In some Jaina works, a rajju is defined as the diameter of the Svayambhūramaña ocean 37. In Ratnasañcaya prakarana, a rajju is defined as follows : "A god can go 100,000 yojanas in the winking of an eye. The distance travelled by him, thus in 6 months is a rajju.”38
Rajju has also been defined as follows :
“If a powerful god were to throw down forcibly an iron ball heated and weighing one thousand bhāras, the distance which it could travel in six months, six days, six praharas, and six ghaţikas is equal to a rajju,”39
G. R. Jain, however, opines that the above definition can not be subject to computation, for the law of the falling of bodies is not known. He goes further to correlate the radius of finite universe of Einstein's theory of relativity, with the rajju as follows : 40 37. Cf. L. P.. (I, v. 65). 38. Joaņa lakkha pamāṇam,
Vimesa mitteņa jāi jo devo. Chammāseņa ya gamaṇam,
Eyam rajjū pamāņeņam. 11 483 11. (Cf, R.S.V.,P. 483, p. 189) 39. Milhal suhumāi koi suro,
A golo a ayamao ḥittho, Bhāra sahassamayam so, Chammāse chahim dişehim pi. 111911 Cha pahare cha ghadiya, Jāvakammal jaivi evaiyā. Rajjū tatth pamāņo,
Divasamuddā havai eya. 1/2011 Cf. R. S. P., vv. 19,20. 40. Cf. Cosmology, old & new, op. cit. pp. 105-117.
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Radius of the universe =(1068 million) (light years)
=( 1068 x 106) (5.88 x 1012 miles) Volume of the spherical universe ( by formula 1713)
= $(1068 x 106 x 5.88 x 1012) 3 cu. miles
= 1037 x 1063 cu. miles -(A) The volume of the loka = 343 cu, rajjus --(B) Equating (A) and (B), one gets
One rajju = 1,45 x 1021 miles -(E) From Svetāmbara measure, the volume=239 cu, rajjus - (C) Equating (A) and (C), one finds
One rajju = 1.63 x 1021 miles - (F) Now, Jain further takes the definition of a rajju according to Colebrook, as the distance which a deva (god) flies in six months at the rate of 2,057,152 yojanas in one kşaņa (instant).41 He takes a big yojana to be 4000 miles, hence the distance travelled in six months, or one rajju,
= 2057152 x 4000 X (6 months) miles. = 2057152 X 4000 x 6 x 30 x 24 x 60 x 54000 miles 42 = 1.15 x 1021 miles roughly. --(G)
The comparison between (F), (G) and (H) gives the evaluation of a rajju, subject to controversial points. The value of a yojana is to be discussed later in detail, as it carries a great historical importance. VOLUME OF UNIVERSE
Regarding the volume of universe, Muni Mahendra Kumar II agrees with the Digambara tradition, as the squared loka measure does not signify the cubic loka measure and hence the volume as 343 cubie rajjus is confirmed to be same in both traditions,43 Regarding the evaluation of the 41. Quoted by Von Glassnapp in “Der Jainismus" Berlin, 1925, 42, Taking an instant to be a prativipalā msa,, Jain finds 60 prativipalāmśas = 1 prati vipala,
60 prati vipalas = I vipala 60 vipalas
= 1 pala 60 palas
- 1 ghati = 24 minutes :: 1 minute = 54000 prativipalāmśa and so on, 43. Cf. Viśva Prahelikā, Bombay, (Hindi), 1969, pp. 93-101.
Cf. also Loka Prakāśa, ch. 12, vv. 110 to 115, by Vinaya Vijayagani, and also vv. 116 to 137, Pts I. II, Surat, 1932, Pt. IIT, Bhavnagar, 1933.
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rajju, Muni Mahendra Kumar 11, goes still further and first finds the value of Širşa prahelikā :44 Māthuri vācanā, 7.58 x 10 193 Vālabhya vācanā, 1.87 X 10249 Using the Māthuri vācanā value, he finds the least yoked innumerate (jaghanya yukta asamkhyāta to be (7.58 x 10193) (700x 10"), ie, the value raised to its own power, or multiplied as many times as it is. This gives the number of instants in an avalikā.
Now I muhūtra = 48 minutes = 1,67,77,216 avalikās and 6 months = 5400 muhūrtas. This, ultimately leads to the value of a rajju, as per definition of Colebrooke to be 1 rajju = 1.86 x 10 { ( 1.47 x 10186) + 17} yojanas. When a yojana is taken to be 4000 miles, then 1 rajju = 7:44 x 10 { ( 1.47 x 10196) + 20 } miles
= 1.45x10{ ( 1:45 x 10 196 ) + 8 } light years. ANOTHER VALUE OF RAJJU 45
There is one more basis on which the value of rajju could be calculated. If the number of the continuous stretch of the islands and oceans upto the Svayambhūramaņa ocean, in the intermediate universe
aken to be n, then the following equation gives the value of a rajju : log2 ( rajju ) = n + (1 or Samkhyāta) + log2 (diameter of
Jambūdvipa ), where n could be related as
ورک _
rajjal
=
...... (I)
n - 5
log
- 240 pramānāngula 1 - Samkhyāta, Now the total number of astral bodies are given to be 7 rajjus
21 256 pramāņāigula 1655361
....... (II) which may be calculated to be approximately as ( 669 x 1018 )564 176 {2 (3-6)} – 2(0-5) – 57 ...... (III) the value of a rajju could be calculated by equating I and III. 44. Cf. V, P., pp. 116 - 119. 45. Cf. T. P. G., pp. 99-102.
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Muni Mahendra kumar II, has approximately calculated this value to be 1 rajju = 4.00 x 10 {( ?:8 x 10245 ) + 3} miles by taking the same values of Sirşaprahelikā and yojana as mentioned carlier. 46
He has concluded that the volume of the universe, thus, could not be less than
296
(10) 10
cubic miles.
The figures of the universe, given ahead, speak for themselves, the shape and the volume of the universe (loka). For details of the volumes of the three types of layers of air and water-vapour, all around the universe, the Tiloyapanpatti gives very vivid description, showing that there is no outer surface of the universe without these layers. 47
FRAME OF DESCARTES
Descartes (+ 1596 to + 1650), a soldier and mathematician desired only tranquillity and repose. He emphasized order and measure in mathematics and discovered coordinate geometry, from which algebraic equations could be framed for a curvilinear path of a moving point.
C
a
...
46. Cf. V. P., pp. 119-123. 47. Cf. T. P. G., pp. 36-39.
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Praiy)
.
K
OK X->
The point P moves in a circle of radius r, and its path equation is given by x2 + y2 = r2.
According to Hankel, H., "The analytical geometry, as Descartes' method was called, soon led to an abundance of new theorems and principles, which far transcended everything that ever could have been reached upon the path pursued by the ancients.":48
In the Jaina school, the concept of eight central space-points of the loka, as well as the movement of matter and souls along world-lines subject to instantaneous conditions define a coordinate frame of the universe, full of space-points or time-points as already described. The deciding verses are : 49
2.25, In transit from one body to another, (there is) vibration of the karmic
body only. 2.26. Transit (takes place) in rows (straight lines) in space. 2:27. The movement of a (liberated) soul is without a bend. 48. Moritz, R. E., On Mathematics and Mathematicians, Dover, 1942,
New York, p. 152, 49. 2:25 Vigrahagatau karmayogāḥ
2:26 Anuśreņi gatiḥ 2.27 Avigrahā jivasya 2.28 Vigrahavati ca samsāriņah prākcaturbhyah 2.29 Ekasamayā avigrahā 2:30 Eka m dvau trinvā anāhārakah
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2.28
The movement of the transmigrating souls is with bend also prior to the fourth instant.
2.29 Movement without a bend (takes) one instant. 2:30 For one, two, or three instants ( the soul remains ) non-assimilative.
The above shows how a transmigrating soul or the matter associated with it moves from a loka-point to another loka-point, in any case, before four instants. In general, the three coordinates are needed for such a depiction :
The movement of the body from 0 to O' involves three paths OA, A B, B O’, each being traversed in an instant, thus three instants in all are involved in such a movement.
o (20%)
Thus there is no corner of the universe which is not reachable before four instants, the eight central points and the rows & columons of spacepoints making worldlines, or paths in the
specific circumstances. This speaks of the principle of least time, or the principle of quickest approach, from which could also be derived the principle of least path. It was believed that amongst all movements, the nature selects only those which reaches the desired location with expenditure of least action (energy X time).49 COSMIC PERIODS AND CYCLES
The Jaina literature, while depicting norms and measures of quantities pertaining to observable events (say, those of astronomy), stand 49. With these theories were connected the contributors Maupertuis
(+1698 to + 1759), Fermat (+ 1601 to + 1665), Hamilton (+ 1805 to * 1865), Jacobi (+ 1804 to 1851) and so on.
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equally competent to express all these regarding non-observable events (pertaining to karmic phenomena), as well. The question is what was the source of inspiration of Yuga system in India. For what purpose their study was started from the time of Aryabhata I (c. +5th century) and continued over for several centuries ?
YUGA BHAGANA
Roger Billard 50 has tried to answer the above problem, and he opines as follows:
"For it is a mathematical method that has allowed us to go far beyond the best results of the scholarly studies in the field. Thanks to such an astronomical investigation of the Sanskrit texts and numerical data, our knowledge of Indian astronomy has just improved greatly. We do know now what was exactly the astronomical science in India and the hows and whens of its history. In particular we can see now how and why Aryabhata is the leading figure in a strange and wonderful history of astronomy.
There is no need to recall here what are the yuga or the yugabhagana, nor how the yuga prevailed on Indian astronomy. To tell the truth, with such common multiples of revolutions, of course devoid of physical meaning, and so huge periods and numbers, the Indian astronomy did look like a pure speculation, a wordy literature displaying astronomical elements of pure fancy.
Now the technical investigation of the yugabhagana has revealed that they are not entirely devoid of reality. The very yuga proceed indeed from a speculation, but I can state that every set of speculative elements or, as we shall say henceforth, every yuga canon is always based directly or indirectly upon a set of astronomical observations, and obviously, on account of the yuga, solely upon one set of astronomical observations. This being so, by a wonderful paradox, it is the very fitting of a speculation upon reality that enables us to detect now the existence, the epoch and the quality of those observations, discover now the key of Indian astronomy, find the fin mot of the question. Thanks to the instrument with which probability theory provides us, many yuga canons afford at present a never-seen means of 50. Cf. L'astronomie indienne, investigation des textes Sanskrits et des
données numeriques, Paris, 1971. Cf. also, “Āryabhata and Indian Astronomy,” I. J. H. S., Vol. 12, no. 2, Nov. 1977, pp. 207-224. Cf, also, Jaina, L, C., Aryabhaţa-I and Yativrşabha a study in Kalpa and Meru, ibid., pp. 137-146.
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mathematical investigation that brings the very numerical data to tell a chronology and a history of Indian astronomy for the most part unexpected till to-day."
The above statement is one of the various aspects of reality, so seriously felt by Billard. According to him such observations are v scattered from 721 B. C. to 141 A. D., in Greece. What was done in India during this dark period ? The Jaina school was speeulating the maxim and mininum periods of life-time of human, sub-human, gods, and hellish beings in terms of palyas, muhūrtas, sāgaras, and so on.
CONCEPT OF PALYA AND SĀGARA
Let us just see the description of a palya,51 "Palya is of three kinds, vyavahāra palya, uddhāra palya and addhāpalya. These are significant terms, The first is called vyavahāra palya as it is the basis for the usage of the other two palyas, There is nothing which is measured by this. The second is uddhāra palya, as the continents and oceans are numbered by the bits of wool drawn out. The third is addhāpalya. Addhā means duration of time.
Now the first palya is described. Three pits of the extent one yojana (consisting of 2,000 krośas) long, one yojana broad and one yojana deep, based on the measure of pramāņārgula, are dug out. These are packed with the smallest ends of the wool of rams from one to seven days old, the bits incapable of being further cut by scissors. This is called vyavahāra palya. Then the small bits of wool are taken out one by one once in every one hundred years. The time taken for emptying the pits in this manner is called vyavahāra palyopama. Each bit is again cut into so many pieces as there are instants in innumerable crores of years. And
nagine that) with such bits the pits are filled up. This is called uddhāra
lya. Then these bits are taken out one by one every instant. The time taken for emptying the pits in this manner is called uddhāra palyopama. Ten crores multiplied by one crore uddhārapalyas make up one uddhāra sāgaropama. The continents and oceans are as numerous as the bits in two and a half uddhāra sāgaropamas. The pits are filled with bits got from cutting each bit of uddhārapalya into the number of instants in one hundred years. This is addhāpalya. Then these bits are taken out one by one every instant. The time taken to empty the pits in this manner is called addhāpalyopama. Ten crores multiplied by one crore addhāpalyas make one
51.
Cf. Jain, S, A., Reality- Eng. Trans. of Shri Pujyapāda's Sarvārtha Siddhi, Calcutta, 1960, pp. 105-106.
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addhā sāgaropama. One descending cycle of time consists of ten crores multiplied by one crore addhā sāgaropamas. The ascending cycle is of the same extent. The duration of karmas, the duration of particular forms, the lifetime and the duration of the bodies of the beings in the four states must be measured by addhā palya, This has been said briefly in the verse:
Vyavahāra, Uddhāra and addhā must be understood as three palyas, Vyavahāra palya is the basis of numeration. The enumeration of continents and oceans is by the second. The duration of karmas is reckoned by the third addhāpalya."52
Further, 1014 vyavahāra palyopama = | vyavahāra sāgaropama
1014 uddhāra palyopama = l uddhāra sāgaropama 1014 addhā palyopama = I addhā sāgaropama.53
It is further important to note how the time-instants and spacepoints cardinals of these big units are correlated as follows54 :
Set of points in finger width
= [ Set of instants in Palya
[ log2 (set of instants in Palya )]
Set of points in stretch of world line (Jaga Sreņi)
log2 (set of instants in Palya )
innumerate
r Set of points in cube of finger
width
CONCEPT OF KALPA
There are two regions, Bharata
and Airāvata where there is
52. Numerically, vyavahāra palyopama = 4.13 x 1046 years, Uddhāra palyopama = (4.13 x 1046 ) x ( innumerate crore years of
instants ) Samayas. Addhā palyopama = (Set of instants in uddhāra palyopama)
X (Set of instants in innumerate crore years). 53. Cf. T. P. G., p. 22. Cf. also V. P., for variations in Svetāmbara
tradition, pp. 245-248. 54. Cf. T. P. G., p. 22.
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regeneration and degeneration 55 in the knowledge, longevity, stature etc. during six periods of the two acons of regeneration and degeneration, known as utsarpiņi (hyperserpentine) and avasarpiņi (hyposerpentine). The full cycle takes 2014 addhā sāgaropoma of time.56 The present period is speculated to be Duşşamā, consisting of 21000 years of avasarpiņi, leading to gradual degeneration, ending in + 18497 of the Christian era.
PARĀVARTANA PERIODS
Then the periods of cycles of wandering or transmigration of a bios based on transmutation, transfer, and other changes attract attention at the speculation of the Jaina school. The transmigration is of five kinds : (1) cycle of material change (2) cycle of spatial change (3) cycle of temporal change (4) cycle of incarnation change and (5) cycle of becoming (phase) change.57
The description of the cycle of phase (bhāva ) is interesting and hence it may be lucidly related here. The period of time taken in the completion of such a cycle is really strange to imagine. Let some bios be endowed with the five senses and the mind and actuated by mythic faith acquires knowledge-obscuring karmas, below (107)2 sāgaras duration, which is the utmost minimum and suited to it. The minimum degree of passion suited to that duration, governed by the six stations58 and of the extent of innumerate times the innumerate space-points of loka, occurs to him. And,
to this minimum degree of affection (Kaşāya), the minimum degree of intensity (impartation) of karmas of the extent of innumerate times the spatial units of the universe occurs to him. In this manner, the utmost mininum degree of vibratory (volition) activity occurs to this bios with the minimum duration, the minimum of affection, and the minimum of impar
55. Cf Reality, op. cit. p. 97. Cf. also Cosmology, old & new, op. cit. p.
231. G. R. Jain, here, finds the value of the mahā kalpa of the two aeons avasarpini & utsarpiņi, each of which consists of 4.13 x 1076 solar years. The Brahma kalpa also consists of 77 digits but digits do not
agree. 56. Cf. V.P., pp. 129–134, for details. 57. These are called dravya, Kşetra, kāla, bhava and bhāva parāvartana.
Cf. Reality, pp. 56–60. 8. CF. Cosmology, Old & New, op. cit., pp. 100-103. The increase and
decrease is in infinitesimal, innumerate part, numerate part, numerate times, innumerate times and infinite times of intensity as an impulse.
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tation. The second degree of vibration activity, which occurs to the bios with the same duration, degree of affection and degree of impartation intensity, is accompanied by an increase of innumerate part. Similarly the third, fourth, etc. degrees of vibratory activity must be understood. All these degrees of vibratory (Yoga) are governed by the four stations59 and are accompanied every time by an increase of innumerate part of Jaga śreņi.
Thus the second degree of impartation occurs to the bios having the same duration and the same degree of affection. Its degrees of Yoga60 must be understood as before, The three things are constant. But the degrees of Yoga are accompanied by an increase of innumerate part of the height of loka (14 rajjus). Similarly for the third, fourth, etc., degrees of impartation upto the limit of innumerate times the space-points of loka. The purport here is that the duration and degree of Kaşāya are at minimum. But the degrees of impartation (anubhāg) gradually increase upto the extent of innumerate times the space-points of loka.
For the increase of each degree of impartation there is an increase of Yoga to the extent of innumerate part of the height of universe. Similarly, the second degree of Kaşāya occurs to the bios having the same duration. For this also, the degrees of impartation and the degrees of Yoga must be understood as before. For the increase of each degree of Kaşāya, there occurs an increase in the impartation to the extent of innumerate part of loka. For the increase of each degree of impartation, there is an increase of Yoga of the extent of innumerate part of height of loka. Thus, gradually from the third degree of kaşāya upto the limit of innumerate times the space--units of loka is to be understood. Similary for the increase of one instant to minimum duration is ascertained. Then for every duration, with the increase of one instant at a time, upto maximum limit of thirty sāgaropama koțā koţi is reached, the degrees of kaşāya etc. is ascertained. Increase & decrease in six stations & four stations ( which exclude infiniterimal part and infinite times). This is to be ascertained for all types and subtypes of karmas. All these combined constitute the cycle of phase61 (bhāva ).
59. As described above. 60. Yoga is the vibratory activity of mind, larynx, and body limbs. Kaşāya
is the activity of affection, Yoga is kinetic or tends to be kinetic, where as kaşāya (Moha disposition) is potential or tends to be potential.
Moha is divided into vision (delusion) and disposition. 61. For details of other cycles of particular remaining changes, of. Reality;
op. cit., pp. 56–60.
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COMPARABILITY
Comparability of the above Periods. 62 It may be noted that (1) In the past, the cycles of phase (bhāva) changes are minimum. (2) The cycles of incarnation changes are infinite times the cycles of
phase changes.
The cycles of temporal changes are infinite times the cycles of incarnation changes.
(4)
The cycles of spatial changes are infinite tiines the cycles of temporal changes.
(5)
The cycles of material changes are infinite times the cycles of spatial changes.
Now the comparability is as follows for the cycles :
(i) (ii)
The period of material change is minimum. The period of spatial change is infinite times the period of material change.
(iii)
The period of temporal change is infinite times the period of spatial change.
(iv)
The period of incarnation change is infinite times the period of temporal change.
(v)
The period of phase (bhāva) change is infinite times the period of incarnation change.
It may further be mentioned that regeneration, degeneration and immutability (permanence) of a fluent every instant prevails. These ensure ts existence or being which is the characteristic of a fluent (dravya).63
Thus we find that the Jaina universe is finite, lying in the very central portion of all space, with non-material media of motion and rest
62. Cf. D., book 4, p. 334. for details of ardha pudgala parivartana, cf.
ibid., 324-332. For further details, cf. G. J. K., v. 560, commentary. 63. Utpāda vyaya dhrauvya yuktam sat. 5.30. Sad dravya lakşaņam. 5.31.
Cf. Reality, op. cit., ch. 5, vv, 30–31.
27

Page #47

which have specific functional character. Space is a fluent, and timeparticles are also fluents. Motion of ultimate parcles, in an indivisible instant could be minimum (1 point ) and maximum ( 14 rajjus ). For bonds of particles, snigdha and rukşa could be associated with positive and negative charges. For karmic bonds, yoga and kaşaya bind a bios with nişekas, measured through particle number, configuration, life-time and energy-level of impartation (pradeśa, praksti, sthiti and anubhāga )
28

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5. ASTRONOMICAL CONCEPTS
There is a strange similarity in treatment of the heavenly bodies and their motion, practically, in all the available ancient Prakrit texts of the karaṇānuyoga group, related earlier. From the following tables, it appears as if the calendar adopted in the Vedānga Jyotişa has something to do with that adopted in Prakrit texts :
PRECESSION OF EQUINOXE
Calendar of the Vedānga Jy046tişa
Year
Sun's
northerly
course
Sun's
southerly
course
Month &
Tithi
Sun's Nakşatra
Moon's Nakşatra
Month & Tithi
Moon's Nakşatra
Sun's Nakşatra Āśleşārdha
Magha Dhaniwhite I sthā
Dhanişthā
Citrā
Srāvana white 7
II
Māgha white 13
Ārdrā
Srāvana dark 4
Pūrvā Bhādrapad
III
Māgha dark 10
»
»
Anuradha
Srāvana white 1
Aslesa
V
Māgha white 7
Ašvini
Sravana white 13
Purva Asādha
V
Māgha dark 4
Uttara Phālguni
Sravana dark 10
Rohiņi
64.
Cf. Dixit, op. cit., p. 101,
29

Page #49

Year
I
II
III
IV
V
Calendar of the Jaina School 65
northerly
65.
Sun's
66.
Month &
Tithi
Magha dark 7
Magha
white 4
Māgha dark 1
Māgha dark 13
Māgha white 10
Sun's
Nakşatra
Abhijit
12
39

ور
39
""
""
""
ور
course
Moon's
Nakşatra
Hasta
Śatbhiṣā
Puşya
Mula
Kṛttikā
Sun's
Month & Sun's
Tithi
Srāvana
dark 1
30.
Śrāvaṇa
dark 13
Sravaṇa
white 10
Śrāvana
dark 7
Śravaga white 4
southerly course
Moon's Nakşatra
Abhijita
Nakşatra
Puşya
""

"3
33
39
""
""
"
33
From the above two tables, it is quite clear that the Sun, which was touching the southern most point in the Dhanistha has shifted to some point in the (added twenty eighth) constellation Abhijit. This is the phenomenon of precession of equinoxes, when seasons begin to change, and is of 3600 in 26000 years.
Mrgśira
That is the first point of Aries itself moves at this rate which is approximately 72 years 2 months for every degree of its precession66 towards
Viśākhā
Revati
Pūrvā Phalguni
Cf. C. P. Sūtra 12.5, pp. 536-556. Cf. also. T. P., II, ch. 7, vv. 526-536, pp. 748-749. Precession is said to have been discovered by astronomer Hipparchus (fl. 146-127 B. C.). This is about 50".26 in celestial longitude per year. K. S. Shukla points out the first point of Dhanistha to be 1930 20' east of star zeta-Piscium, when the sun, Moon's conjunction at winter solstice occurred about -1400. He further finds the first point of Abhijit to be 1750 55'10" east of star zeta-Piscium, when the Sun, Moon's conjunction at winter solstice occurred about -146. However, by a process of counting how many times the same themes have been repeated in the various Jaina canonical texts, Jacobi and Schubring concluded that the most ancient portions of the canon were composed during 3rd & 4th centuries [Cf. Renou, L, etal, L' Inde Classique (1953, pp. 616–617. ]

Page #50

wesi along the ecliptic. Now the shift from Dhanişthā (B Delphini ) of the sun's winter solstice to Abhijit (c-Lyrae) is about 1703', according to Prof. Thibaut. This means that the observations of the above calendrical phenomena were made after a difference of about 1231 years.
Various dates have been suggested about the Vedānga Jyotişa; Colebrooke H. T. : (C.-1108), Max Müller : (-3rd century), Weber, A. : (C.+5th century).
DATE OF ADOPTION OF CALENDAR
Lishk and Sharma 67 have pointed out an important fact about the fitst point of Aries, “It may also be noted that no reference has as yet been found to point out that the order of rāśis (signs) began from a sign other than Meşa (sidereal Aries) or the Meşa sign began from a nakşatra (asterism) other then Asvini (B Arietis). There is no doubt that these terms denoting elliptic signs were not current in Vedārga Jyotişa period. Probably these terms came into vogue when Vernal equinox occurred in Asvini (B Arietis) nakşatra (asterism) and M+şa sign (sidereal Aries) at that time. The tropical longitude of the star B arietis, the identifying star of Aśvini, was 310 53' and that of Arietis, 350 34' in 1850 A. D. Hence the years when the tropical longitudes of these stars were zero, can be worked out, taking 72 years for 10 precession as follows :
310 53' X 72 ( = 2296 ) – 1850 = 446 B. C. 350 34' x 72 ( = 2561 ) --- 1850 = 711 B. C.
and
The mean of these dates is 579 B. C.
Since the winter solstice in Abhijit (Lyrae) corresponds to Vernal equinox in Asvini (B Arietis ), probably it was the period when reckoning of first point of the zodiacal circumference was shifted from winter solstice to Vernal equinox. Thus in the light of this discussion, the probable period of Jaina Canon may be assigned to about 6th century B. C." 68
67. Lishk, S, S., & Sharma, S. D., Sources of Jaina Astronomy, Jaina
Canonical Literature, Jaina Antiquary, 29.2, 19-32, 1976. 68. The eighth equinox occurs, on the white 15 of Vaišākha at the conjun
ction of Aśvini nakgatra, after lapse of 93 parvas from the beginning of Yuga. (T. P., pt. II, v. 7.544, p. 750), Trilokasāra (v. 426) mentions the white 15 of Vaišākha as dark 1 of Vaisakha.
31

Page #51

ZODIAC
East
Past
part denim
-
Celent West
I shifting
horror
Present Cele
ECLIPTIC
qualor
Right
Ascension
The above diagram shows how the Vernal equinox goes on shifting (from V to W), along the ecliptic ( the path of the Sun ), and how it makes change in right ascension and declination of a star.
PANCANGA Certain technical terms used in calendar :
Pancānga is the name given to Indian calendar as it comprises of five types of information which is either collected or calculated on the basis of observations of heavenly bodies and certain theories or formulas developed in due course of time for mechanical manipulation of the data.
Before one goes into details of motion of heavenly bodies, usually kinematical in ancient texts, one has to be familiar with the terms frequently used in advanced theories of astronomy gradually evolved & developed by the ancient people for practical purposes of growing crops, regularizing duties, economizing time and then optimizing their own operations. This might have led them to speculative sports and games of adventurous nature for which statistics and probability in form of astrology, numerology, and so on might have evolved although they could not become the exact sciences, even till today, for their involvement into endless calculations needed in their quasi-theories.
Pañcānga means five parts :
Tithi : The longitudes of the sun and the moon are measured from r (first point of Aries ) towards east along the ecliptic, and the difference of these longitudes determine the tithi, First tithi (pratipadā) lasts till the difference lies between 00 and 12°, the second tithi lasts till the difference lies between 120 and 240, and so on. In a lunar month, there are thirty tithis.
32

Page #52

A tithi is measured in ghați and pala. A muhūrta equals 48 minutes, or 2 ghatis, or 120 palas. A day of 24 hours equals 30 muhurtas. Thus a ghaţi is of 24 minutes. The origin of time is regarded from the instant of sun-rise on a particular day. In the pañcānga, if the time shown for the tithi is 5 ghatis 12 palas, it will signify that the tithi will end at 5 ghatis 12 palas, after the sunrise for the day. The tithis are of unequal duration, due to non-uniform motion of the sun and the moon. The Kṛşna paksa and śukla pakşa, each consists of 15 tithis.
Vara: Any day of the week is called vāra, and it begins with the rise of the sun and ends after 24 hours.
Nakşatra: In Jaina calendar the ecliptic is divided into 28 unequal parts, and each is called a nakṣatra. The sidereal period of the moon is about 27 days, a nakşatra is described in about a day by the moon, Apart from the 27 nakṣatras of the Hindu astronomy, the Jainas added Abhijit nakşatra. When the moon is in Abhijit, it means that duration itself lasts as the Abhijit nakşatra name. The time of birth goes with the moon's position in a nakşatra. where as the time of a season goes with the sun's position in a nakṣatra. The instants, when the moon crosses or transits from one nakşatra to another are shown in the Pancanga.
GRADUATION OF CELESTIAL SPHERE
The Jaina calendar divides the whole stretch of the heaven into 54900 celestial parts (gagana khanḍas) which may be kept equivalent to 3600 of the modern celestial or armillary sphere. A measure of a sign of Zodiac is 300, and that will be equivalent to 4575 celestial parts (abbr. c. p.) The correspondence between stretches of the nakṣatra and Zodiacal constellations in terms of celestial parts and the duration for which they remain with the moon and the sun work out as follows,69
69.
Cf. T. P,. II, ch. 7, specially, vv. 478-488. Cf. also S. P., op. cit.

33

Page #53

34
No.
1
2
3
4
5
6
7
8
9
10
Name of constellation
Aśvini
Bharani
Krttikā
Rohini
Mrgśirsā
Ārdrā
Punarvasu
Puşya
Āśleṣā
Maghā
Stretch in
celestial
parts
2010
1005
2010
3015
2010
1005
3015
2010
1005
2010
Stretch of Zodiac in
c. p. from and upto
Aries from 0 on wards
Aries continued
Aries upto 4575 and
Taurus 0 upto 450
Taurus continued
Taurus upto 4575 and
Gemini 0 upto 900
Gemini continued
Gemini upto 4575 and
cancer 0 upto 345
Cancer continued
Cancer continued
Cancer upto 4575 and Leo 0 upto 795
Duration for which Moon is with constellation
Muhurta 67 Part
30
15
30
45
30
15
45
30
15
30
0
0
0
0
0
0
0
0
0
0
Duration for which Sun is with constellation
Day
13
6
13
20
13
6
20
13
6
13
Muhurta
12
21
12
3
12
21
3
12
21
122
Linear Velocity in Yojanas of constellation in a Muhurta
5265
5265
5285
5288
5319
5319
5273
5319
5319
5273
18263
21960
18263
21960
37
594
20377
21960
15998
21960
15998
21960
11403
21960
15998
21960
15998
21960
11403
21960

Page #54

11
2010
Leo continued

18263 21960
Pūrvā Phālguni Uttarā Phālguni Hasta
3015
18263
Leo upto 4575 and Virgo 0 upto 1245
5265 21960
13
2010
Virgo continued
15998
5319 21960
Citrā
2010
20377
Virgo upto 4575 and Libra 0 upto 690 Libra continued
5288 21960
Svāti
1005
18263
5265 21960
16
Višākhā
3015
Libra upto 4575 and Scorpio 0 to 135 Scorpio continued
16947 21960

35
Anuradha
2010
10454 21960
0
Jyeşthā
1005
Scorpio continued
7024
5304 21960
19 | Mūla
2010
Scorpio upto 4575 and Sagittarius 0 to 585 Sagittarius continued
15998 21960
Pūrvāsādha
2010
15998
5319 21960
Uttarāşādhā
3015
Sagittarius upto 4575 & Capricorn 0 to 1035 Capricorn continued
15998 21960

Abhijit
630
18263
9
5265 21960

Page #55

Name of constellation
No.
Stretch in celestial parts
Duration for which Moon is with constellation
Stretch of Zodiac in | c. p. from and upto
Duration for which Sun is with cons.
tellation
Linear Velocity in Yojanas of conste
llation in a Muhurta
Muhūrta | 67 Part
Day
Muhūrta
23
Srāvaņà
2010
Capricorn continued
30
18263
5265 21960
24
Dhanişthā
2010
30
18263
Capricorn upto 4575 & Aquarius O upto 1110 Aquarius continued
5265 21960
Satbhişā
1005
18263 21960
2015
Aquarius continued
18263
5265 21960
36

Pūrvābhādrapada Uttarabhādrapada Revati
3015
18263
5265-21960
Aquarius upto 4575 & Pisces 0 upto 2565 Pisces upto 4575 and Aries 0
2010
18263
5265 21960

Page #56

The above table proves the originality of the Jaina system. There were unequal divisions and unequal velocities of certain groups of constallations showing that their distances of the earth were taken to be different. The angular and linear velocities signify the complete manipulation of the motion.
NOTE
Yoga : The sum of the longitudes of the sun and the moon, expressed in
minutes of arc, as divided by 800, gives a quotient; next greater integer to which determines the serial number of yoga. In the pāeñcārga, ending time of a yoga is given. In Jaina astronomy, however, the word yoga carries the meaning of kinematric appearance of the moon or the sum against the background of a nakşatra.70
This is also not mentioned in the
Karana : Half of a tithi is a karaña.
above texts.
Lagna
: It is the point of intersection of the ecliptic with eastern horizon
at an instant. It is meant usually for astrology.
70.
Cf. G. A., pp. 293 et seq. For various other types of yogas in Jaina astrology, vid. Jyotişasāra, trans. B. D. Jain, Calcutta, 1923, pp. 40 et seq.
37

Page #57

6. KINEMATICS OF ASTRAL BODIES
Candraprajñapti's commentaries71 give for greater details of a Jaina calendar based on calculation of motion of various types of heavenly bodies, especially that of the sun, the moon, and the nakşatras. Tiloyapanṇatt172 as well as Trilokasara,73 Lokavibhāga and Jambudvipa prajñapti also relate the concise knowledge of the above.
NAKSATRA SYSTEM ABROAD
In Prakrit, Jyotişka is written as Jodisiya or Joisiya or Joisia, reminding one, of the word Zodiac74. Controversy regarding the relation between the Indian nakşatra, Arabic al-manazil, "moon-stations", and the Chinese hsiu systems. The earliest reference outside Asia is in a Greek papyrus of the +4th century. The origin is common, but the question is which is the oldest ? Both in China and India, the new year was reckoned from the mansion corresponding to Virginis, and in both cultures Pleiades was one of the four quadrantal asterisms. Two important statements are, "The nakshatra do not show so clearly the 'coupling' arrangement discovered by Biot (4), whereby hsiu of greater or lesser equatorial breadth stand opposite each otherf." "The Chinese has possessed', from fairly early times, a twelvefold division of the year and the equator, which being based upon hsiu and palaces, consisted of unequal parts.9 "75
One more statement by Needham and Ling is, "Now in these texts there is never any mention of any zodiac or of constellations lying along the ecliptic; the earliest documentary evidence of this conception occurse just after 420. On the other hand, the Seleucid cuneiform texts of the -3rd and -2nd centuries give great prominence to the Zodiac, and use ecliptic
71. Cf. C. P., comms. by Malayagiri and Amolaka Rşi. Cf. also, S. P. 2. Cf. T.P,, II, ch. VII.
73.
Cf. T. S., ch. IV.
74. Compare the lunar Zodiac of China with that of Jaina School. Cf. Needham & Ling, op. cit., pp. 252 et. seq.
Cf. ibid, pp. 253, 258.
75.

38

Page #58

coordinates exclusively. Finally, the thirty-six Old Babylonian asterisms were confused with the Egyptian decans and twelve of them ousted to make room for the Zodiacal constellations. One might fairly surmise, therefore, that the equatorial moon-stations of East Asia originated from Old Babylonian astronomy before the middle of the -Ist millennium and probably a long time before."76
MATHEMATICAL ASTRONOMY
The authors, it appears, have not gone through the details of the nakşatra system of Zodiac in the Jaina School. The tables above speak of a great similarity between the Jaina School and the Chinese School and the transmission could be thought possible, both east and west ways, even before the Budhists entered into the lands. The Zodiac of the Jaina School was so predominant that every nakşatra of the Zodiac had its own sign and Yogatārās.77
According to Neugebauer, “ Thus magic, number mysticism, astrology are ordinarily considered to be the guiding forces in Babylonian science. As far as mathematics is concerned, these ideas have had to be most drastically revised since the decipherment of mathematical texts in 1929 ................ Early Mesopotamian astronomy appeared to be crude and merely qualitative, quite similar to contemporary Egyptian astronomy. At best since
76. Cf. ibid., p. 256. 77. The C, P, mentions, "Gosisāvali, Kāhāra, Sauņi, pupfovayāra, vāviya,
ņāvā, āsakkhandhaga, bhaga, churagharae, ya Sagaduddhi ||1|| miga sisāvali, ruhira bindu, tula, vaddhamāņa, padāgā, pāgāra, pallanke, hatthe, muhuphullae ceva |12|| Khilaga, dāmiņi, egtāvali ya gayadenta, vicchuyaņangūle, ya gayavikkame, ya tatto, sihanisīyā, ya santhāņā. 11311 p. 312, (10.9 1). The T. P, II mentions variants : Viyasaya sayalauddhi kuranga siradivatoraņāņam ca || Adavavāraua vamniya go muttam sarajugāņam ca 1| 465 || Hatthuppaladivāņam adhiyaranam hāraviņa singā ya 11 Vicchuva dukkaya vāvi kesarigayasisa āyārā || 466 11 Murayam pata ntapakkhi seņā gayapuvva avara gattā ya Il pāvā hayasira sarisā ņam culli kitti yādiņam 11 467 11
It appears that C. F. belonged to the observations taken in the north and the T. P. observations might have been taken in the south of India, resulting in the difference of signs of the Zodiac.
Cf. T. P. II, vv. 463-464 & C. P, 10.9. 1, p. 313 for stars of the nakşatras.
39

Page #59

the Assyrian period, a turn towards mathematical description becomes visible and only the last three centuries B. C. furnished us with texts based on a consistent mathematical theory of lunar and planetary motion,"78
In the above context, it may be remarked that the Jaina School by the early centuries B. C. had already developed a mathematical theory of the motion of heavenly bodies, but, as Yativrşabha79 mentions, by his time, the description of the motion of planets had become extinct. Yet, what remains, in C. P., S. P. or T. P., is enough to prove that they were in possession of a complete calendar based on mathematical theory, which was ingenious and original. The astro-universe of this school is rather a symmetrical mathematical structure, with a set-theoretic base, depicting the details of a non-summable stretch, yet finite in measure. For example, the total number of astral images is the quotient set obtained by dividing the square of the Jagaśreņi (set of points) by the product of the set of the squared finger width (pratatăngula), and the square of 256. The distribution of the astral objects is symmetrical and based on the five kinds of Joigana (astralgroups). The moon, the sun, the planet, the constellation (nakşatra), and scattered stars (prkirņaka tārās).80 The moon is the head of the family of eighty-eight planets, twenty-eight nakşatras, and 66975 (10)14 stars.81
SYMMETRIC SETTING
Picture of the Celestial Phenomena in Jaina School is unusual.
The phenomena of the heavenly events in all the islands could be represented by those in relation to the Jambūdvipa wherein, a strange theory of real and counter bodies, exists.82 Upto certain number of islands, the astral bodies are in motion with mathematical symmetry of exact bodies placed on fictitious orbits, as if images at diametrically opposite ends. Beyond these islands and oceans the astral bodies have been assumed at rest.
The Jambů island is one lac yojana in diameter, all the subsequent alternately placed oceans and islands being double the preceding in diameter, forming a geometrical progression with one as the initial term and two as the common ratio. It is quite clear that such a symmetry denotes the manipulation of the causality theory through an abstract, mathematical model, principle theoretic in nature, surviving through consistency. 78. op. cit., p. 97. 79. Cf. T. P., II, 7.457, 7.458.
Cf. T. P. II, 7.29, 7.30. Cf. also T. S., 4.361, 4.303. 81. Cf. T. S., 4.362. Cf. also G, A., pp. 257 and 274 et seq. 82. Cf. T. S., 4.308. Cf, also T. P. G., pp. 86–95. Cf. also G. A., p. 253.
40

Page #60

In the centre of the Jambū island has been supposed a type of celestial axis, Meru83 mountain, perfectly symmetrical, having a height of one lac yojana, in the forms of various frustrums of cones, joined at different heights, and having a lowermost base with a diameter of 10090 14
11 yojanas, where as the uppermost base has a diameter of 1000 yojanas. That is how, the motion of all astral bodies around it, or placed at rest in far off islands, suggest the idea of a celestial diagram of a complex nature.
SHADOW PLANETS
Due to the postulation of two suns and two moons along with the families in both parts of their celestial sphere, one in each half, placed at diametrically opposite ends, the mystery resembles that in China, Greece and Babylon.84 which has not been explained so far, whether its purpose was some mathematical convenience for calculations of the motion and positions of the invisible bodies in the other half.85
In astrological Jaina texts, like the Jñanapradipikā, there has been use of invisible planets, with different types of orbits, say in Jinendramālā,86
83. Cr. T. P. G., vv. 7.1780 et seq. Compare this description with that given
by Aryabhata -I. Cf. Jain, L. C., Āryabhata -I and Yativīşabha -a Study in Kalpa and Meru, I. J. H. S., vol. 12. no. 2., nov. 1977, pp.
135–146. 84. Needham and Ling remark, “But as we shall seel, the Chinese had
themselves imagined, from ancient times, the existence of a counterJupiter' which moved round diametrically opposite the planet itself. There was a Greek parallel to this in the strange Pythagorean theory of the counter-earth', apparently due to Philolaus of Tarentum (late -5th century), which was devised either to bring the number of planets up to a perfect number, 10, or to explain lunar eclipses, m Perhaps both originated from a more ancient Babylonian Theory."
Op. cit., p. 228, vol. III. 85. Cf. Jõānapradipikā, trans. ed. by R. V. Pandeya, Arrah, 1934, vv.
8, 9, pp. 3,4 for invisible planets, named as dhūma, vyatipāta, pariveşa,
indradhanu and dhvaja. 86. Ed. S. Singh, Bombay, 1958. pp., 2, 3, 4, for setting of opposite rāzis and
planets, cf. pp. 14, 15, 18, 19. The English translation of this text was published at Madras by N. C. Aiyar, as stated by Singh. In both, Jinendramātā and Jñānapradipikā, astrological consideration has been given to invisible planets, or shadow planets.
41

Page #61

Needham and Ling have further opined as follows, 87 “Here Thai Yin is not, as might be supposed, the moon, but an invisible 'counter Jupiter' which moved round in the opposite direction to the planet itself. Jupiter (Sui hsing?), with the other planets, appears to move eastwards or anticlockwise through the stars, so a 'shadow-planet' (Thai sui3 or Sui Yin4 ) was invented to move with them, accompanying the sun. Wang Chhung, in The Lun Heng, devotes a whole chapter d to this peculiar theory. The twelve Jupiter-stations were named tzhub and the whole cycle of years a chi,6 The names for the years have survived in two forms, one set astronomical another astrological;9 and it was natural therefore that they should sometimes also have been used for the months of a single year and " for the double hours of a single day, as well as for the years of the Jupiter cycle, a The astronomical terms were used to designate the positions of Jupiter, the astrological or calendrical terms applied to the positions of counterJupiter. 6" 88 If it is possible to trace out the details of planetary motion in some text of Jaina School, it may throw some light as to the source of the above theory. However, from the available data about the planets and Yuga theory, the motion of the Jupiter, alongwith astrological theory in Jinendramālā or Jñānapradipikā, the secrets could be unravelled to a great extent.
MOTION OF ASTRAL BODIES
The whole of the celestial path has been divided into 109800 celestial parts (Gagana Khanda). But half of the path is covered by one sun, one moon, and its family, without any correlation, in twenty-four hours or thirty muhūrtas. The other half path is covered simultaneously, in the opposite sense, in so far as their journeys start from opposite ends. Thus only 54900 parts are needed for practical purposes of a calendar, and now from the above knowledge it appears that the other half might have some other use
The motion of the astral bodies every muhūrta is given as follows :89
The naksatras The sun
1835 celestial parts 1830 , ,
87. Cf, op. cit., vol. III., pp. 402, 404. 88, Compare this with the nakşatra samvatsara where the Jupiter's twelve
year motion is correlated with that of the nakşatras : Jam vā bahassa i mahaggahe duvālasahim samvaccharehim savvem nakkhatta mandalam
samāņei Il 10.20, C. P., sūtra 2. 89. Cf. T. S., 4.402 and 4.405. The T. P. has not mentioned about rāhu.
42

Page #62

The moon
The rahu
or 12
The kinematic motion of the nakşatras is actually due to the rotation of the earth, Keeping or regarding them as fixed, the relative motion of remaining bodies with respect to the nakşatras can be found to be 5, 67, and 5 celestial parts per muhurta. 12
1
2
61
Now the rahu, as it appears from the Trilokasara (11th century), is a fictitious body meant for a seasonal or sayana tu or karma year (samvatsara), By this rahu, celestial parts are traversed in
61 12
of a solar
1768 celestial parts
11
1829
12
day, hence the stretch of a zodiacal sign of 300 or 4575 celestial parts is travelled in a month of 30 solar days. Thus 54900 celestial parts are traversed in 360 days or twelve months. This rahu, thus defines the mean annual
1
motion of the sun, which describes 1830 celestial parts in
30
of a day or 3600 in a day which defines the basic unit, solar day, used in astronomy. The Tattvarthasūtra also describes, "The astral bodies the sun, the moon, the planets, the constellations and the scattered stars, in the human region (nploka), are characterized by incessant motion around Meru, and they cause the divisions of time.90
RELATIVE MOTION OF NAKSATRAS
such revolutions make 359
""
The daily motion of the nakşatras is defined as 1835 celestial parts muhurta or 48 minutes. Thus 54900 celestial parts or
degrees per
35 1835

د.
1830
1060
3600 are covered in 1835 part of a day, or 23 hours 56 minutes and 4 1835
seconds. Modern value of such a sidereal day is 23 hours 56 minutes 4.1 1685
seconds. Thirty such revolutions make 29 1835 days. Three hundred sixty
days. Three hundred sixty-six such revolu
5 days. Relatively this will be regarded as rotation of 1835 respect to a fixed nakşatra or a star therein, without any as the first point of Aries has at the rate of 50."2 per
tions make 365 the earth with proper motion annum).
90. Cf. Reality, op. cit., ch. 4, vv. 12-14,
43
1
30

Page #63

Now with respect to the nakşatras, the sun moves 5 celestial parts less per muhūrta. Thus it traverses 150 celestial parts in a day and 54900 parts or 3600 in 366 days, which is in relation to fixed stars. The average solar month is thus of 30 days.
Similarly the moon covers 67 celestial parts less with respect to the nakgatras, per muhūrta, covering the strip of 54900 celestrial parts in 27 31 solar days or 27.313 days, where as the modern value for a lunar side real month is 27:32166 days.
61
The stu rāhu moves 1829 16 celestial parts per 48 minutes, and
describes the strip of 54900 celestial parts in a 1990 solar day. Relative to nakşatras the stu rāhu moves celestial parts in a muhūrta. Hence it covers the strip of 54900 celestial parts or 3600 in 360 solar days. This is
22259 a stu year. The mean solar day is thus equal to solar day is thus equal to 210601
- The modern value of this is 24 hours, 3 minutes, 56-5 seconds. It appears that this rāhu was perhaps responsible for division of year and the strip into twelve equal parts, for it gives 12 stations as well, and consequently led to the invention of 12 rāśis, or 12 zodiacal signs. No where in the history of astronomy, one comes across with such a rāhu as in the Trilokasāra, described above. Here one degree has been set in equivalence with one day, 91 as in China.
The motion of the stars has been mentioned to be greater than that of the nakşatras, showing that the school was aware of the proper motion
91. For such a description of the sun, Needham and Ling quote, “The
uniform and apparently circular rotation of the heavenly bodies is mentioned many times in texts which are probably much older than Chang Hệng or even Lohsia Hung, for example the Chi Ni Tzut book e and the Wên Tzu5 book. The former (perhaps of —3rd or -4th century) speaks of the sun's path as a turning ring (hsün huan) with limits but no starting-point (wei shih yu chi7) ever rotating (chou huis) and never still, the sun moving 10 each day.' (The extremely early appearence of this graduation system, which led to 36570 instead of 3600 in the Chinese circle, should be noted.] Cf. pp. 218, 219.
44

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of stars, although details are not available.92 The sun, the moon and the moving planets have their solstices (ayanas), but the nakgatras and the stars have no laws for solstice:s.93
RELATIVE MOTION OF THE SUN
The motion of the sun is 1830 celestial parts per muhūrta. Thus the full stretch of 54900 parts are described in 30 muhūrtas or 24 hours. This is the mean motion. The ketu, an invisible planet moves along with the sun under it at a depth of four standard fingers below, causing the eclipse at periodic intervals. All the astral bodies are described to move leaving a distance of 1121 yojanas from the celestial axis ( Meru ) so far as the Jambūdvipa is concerned.94
The solar and lunar zodiac ( Cāra kşetra) has an extension of
yojanas.95 Out of this, 180 yojanas are covered in the Jambūdvipa
by the sun and the moon, whereas the remaining stretch lies in the Lavaņa ocean,96 In the Tiloyapannatti, the description of 15 roads of the moon,
92. Cf. T.P., II, 7.896. The miscellaneous stars are of two kinds; moveable
and immoveable. Cf. ibid. 7.494. Cf. also ibid., 7.497. 93. Cf. ibid., 7.498 and 7.499. 94. Cf. T. P., II, 7.201, & T. S., 4.345. 95. Needham and Ling remarks regarding Chinese and Babylonian zodiacs
are important, "Now in these texts there is never mention of any zodiac or of constellations lying along the ecliptic; the earliest documentary evidence of this conception occurs e just after-420. On the other hand, the Seleucid Babylonian cuneiform texts of the —3rd and -2nd centuries give great prominence to the zodiac, and use ecliptic. coordinates exclusively. Finally, the thirty-six Old Babylonian asterisms were confused with the Egyptian decans and twelve of them ousted to make room for the zodiacal constellations. One might fairly surmise, therefore, that the equatorial moon-stations of East Asia originated from Old Babylonian astronomy before the middle of the -- 1st millennium and probably a long time before.” Cf, op. cit., III,
p. 256. 96. Cf. T. S., 4.374.
45

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and one hundred and eighty-four paths of the sun are described in details of their velocities in Yojanas through the asterisms zodiac (cara mahi).97
The orbits of the sun being 184, there are 183 solar days in a single solstice, implying that its continuous motion is in a winding and unwinding spiral, each of which is at an interval of about 2 yojanas. Every day the -yojanas. The first internal orbit of the sun
170
61
last orbit is about 315106 yojanas in
total shift in the path is
is 315089 yojanas, and the
circumference. 98
It is strange, how the measure of length of day is 18 muhurtas when the sun is in first internal orbit, and that of night is 12 muhurtas, if India had its centre of learning at Ujjain or Patliputra99. Reverse is the case when the sun is in the last external orbit, Dixit finds that this increase and decrease mentioned in Vedanga Jyotişa, applies to regions in 340 North latitude of the earth. This place may be near about Kashmir, or Gandhāra. Mathematically he calculates this to lie between 34046' and 34055' of North latitude 100.
97.
by
In the Trilokasara, one finds the mention of Karkaţa (cancer) and makara (capricornus). The motion of the sun in the next spiral orbit is
98.
99.
100.
38
61
Cf. T. P,, II, 7.117 to 7-271. The description of the length of day and night as well as that of bright and dark areas for different roads is given from vv. 7.276 to 7.455.
Cf. T. P., II, vv. 7-254 to 7.263. Cf. also T. S., 4.378.
Cf. T. S., 4.379 and T. P. II, 7.277. In the Babylonian and Egyptian scheme, Neugebauer describes the length & its variation on pp. 116, 159 and 86, 94. However, for India he opines, "This was fully in line with a discovery which had been made by Kugler in 1900, namely, that the ratio 3:2 of longest to shortest day used by both systems in columms C and D of the Babylonian lunar ephemerides also appears in Hindu astronomy, though this ratio is totally incorrect for the main parts of India." Cf. op. cit., p. 162. Cf. also D. Pingree, (1974) Mesopotamian Origin of Ancient Indian Mathematical Astronomy, I. H. A., IV, pp. 1-12.

Cf. op. cit., pp. 125, 126, 131. Cf. also Sharma, S. D., and Lishk, S S., "Length of the Day in Jaina Astronomy," Centaurus 22.3, Andelsbogtrykheriet.
46

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either accelerated or retarded, rather the sun is in retarded motion every instant while moving out, and is in accelerated motion every instant while moving towards inner side. 101 This also signifies the Kinematic motion for covering of unequal distances in equal time for a mean solar day. The ranges of vision and the rise stations also find place in these texts. The calendrical details of the ayanas, parvas, tithis, vişupas have been given in great details, along with charts in the Candraprajñapti in dialogue style. 102
RELATIVE MOTION OF THE MOON
Kinematically, all the astral bodies have been regarded hemispherical, with spherical side towards the earth, the diameter of the moon being yojanas and that of the sun being 23yojanas. 103
56
21
Two types of rāhus are described for the moon, dina rāhu and parva rāhu. The former causes the phases of the moon, the latter causes lunar eclipses. 104
Regarding the relative motion of the moon with respect to the nakşatras, the moon travels 67 celestial parts, kinematically less, than those traversed by the nakşatras, covering the strip of 54900 celestial parts in 27 solar days or 27.313 days, the modern value for the lunar sidereal month being 27.32166 days. The relative motion of the moon with respect 101. Cf. T. S., 4.380. Cf. Needham and Ling, p. 292 for Chinese discovery of
tropic of cancer in +349. Cf, also T. S., 4.381 to 4.386. Cf. T. P., II, 7.291 to 7.420 for bright and dark areas. For acceleration etc., cf. ibid., 7 265, and T. S., 4.388. According to Chou Pei, the sun could illuminate an area only 167000 li in diameter; people outside this would be said to be in dark. Cf. Needham and Ling, p. 211. The Jaina
School, due to its discoidal maps, gave these areas projected on a plane. 102. Cf. C. P., T. P. and T. S. at proper places. 103. Cf. T. P. 7.37, 7.218, 7.39, 7.68, 7.91, 7.95, 7.98, 7.100 and 7:108 for
planets and consellations as well. In China only the sun's diameter is described. Cf. Needham & Ling, pp. 300, 332, 573 (c). Similarly no
record is available in Babylon, Egypt and Greece. 104. Cf. C, P., pp. 693–702; T. S., 4.340, 4.342, T. P., 7.202, and 7.205 to
7.216. Cf, also G. A., pp. 279-288. For Chinese conception, cf. Needham and Ling, pp. 175, 228, 252 (c), 416, where the idea of monster and colours appears to be imported from India, or a work from the west, "Kieou-tche."
47

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to the sun being 62 celestial parts in oth day, it covers the stretch of 54900 celestial parts in 29 or 29.516 days, where as the modern value for lunar synodic month is 29-5305 days. This is the data for a mean motion of the moon. 105
743 The motion of the stu rähu with respect to the moon is -18 celestial parts less in a muhūrta, hence the moon covers 54900 celestial parts ahead of it in 29 13 or 29.555 days, which represents lunar fictitious synodic month. The mean of true and fictitious being 29.535, it differs from modern value by .005 only. 106
The motion of the moon is also in spiral orbits, its zodiac being the stretch of $1158 yojanas. The roads or the orbits of the moon are defined
to be 15, with an interval of 35 497 yojanas cach, in the Jambūdvipa and Lavaṇasamudra. 107 The motion of the moon in yojanas per muhūrta for different paths is detailed. 108 This is a very important record in linear
105. Cf. T. P., 7.508. Cf. Neugebauer, pp. 118, 121, 162 and Needham and
Ling, pp. 392-401, vol. III. 106. Cf. T. S., 4.402 and 4.405. For comparison with Babylonian lunar
velocity, cf. Neugebauer, pp. 118, 119, 121, the mean velocity being 13; 10.350 per day. The mean synodic month was close to 29, 31, 54
days. Cf. ibid., p. 122. 107. Cf. T. P., II, 7:125, 7.120 & T. S., 4.396, 4.377. The eccentric circle
theory of sun's motion was recognized in China after about +570. Akin to three types of nakşatres in Jaina School, in China, the planispheres consisted of 'three roads' each marked with twelve stars, one for each of the months corresponding to their heliacal risings. The central road was called Anu, the outer road as Ea, and inner road as
Enlil. Cf. Needham and Ling, vol. III, p. 256. 108. Cf. T. P. 7.186 to 7.200. These details are not available in T. S., nor
in C. P.
48

Page #68

measure. Its path is also given through various nakgatras, along eight paths, 109
The motion of planets is not available in the records of practically all the ancient Jaina texts. Only Thāņāńga ( g. 699) mentions ninc orbits of the venus. Samvāyāiga (19.3) states that the venus, rising in the west, moving through nineteen nakşatras, sets in the west alone.
109. Cf. T. P., 7.460-462. For Chinese system, cf. Needham and Ling,
p. 225. Cf. also Neugebauer, pp. 5, 81, 82, 89, 116 (India), 102, 140, 170, 180, 207. In thc Tiloypannatti, details of stars & symbols for their collection are given in 7-463-467. The names of eighty-eight planets are available. Cf. T, P., II, 7.363-370, and so on.
49

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7. RATIONALIZATION OF YOJANA
1. CHINESE LI
The word yojana appears in every earlier Jaina text. It has been used either for denoting areual distances as velocities of heavenly bodies, or as distances as straight lines on a plane surface. It has also been used to denote heights. It seems to have been derived from the word Yojanā, meaning something like a pattern or some principle of organization. In China a parallel word, though not exactly Yojana, carrying a similar meaning got evolved in Neo-Confucian 110 thought, “] he induction of a specific principle from many observations ( b', the second part of resolutio) was represented in Neo-Confucian thought by the search for the underlying or intrinsic patterns (lil). Some one said to Hsü Hêng 2 (+1209 to +1281):
If we fully apprehend (lit. exhaust) the patterns of the things of the world, will it not be found that every thing must have a reason why it is as it is ( so i jan chih ku3) ? And also a rule (of co-existence with all other things) C to which it cannot but conform ( so i tang jan chih tsê 4 ) ? Is not this just what is meant by Pattern (lil)?d
Hsü Héng agreed, saying that this brought out very well the meanings of the technical terms employed. All the spatio-temporal relations of all organisms and events in the universe were determined by the ubiquitous manifestations of li. "Wherever there is li', said Chheng 1-Chhuan 5 (+1033 to + 1108 ), 'east is east and west is west.'e”
For calculation of cosmic distances, extended pattern-principle (thui li 4 ) appears to have been applied.111 Patterns had the aspects from within and outside.
110. Cf. Needham and Ling, vol. III, p. 163. 111. Cf. ibid. p. 164, 165. This word 'thui 'goes back to Mohists, cons--
tantly found in scientific contexts. If the pattern was fully apprehended in one matter only, inferences could be drawn about other matters of the same class.
50

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2. TYPES OF ANGULAS
In the Jaina School, or even elsewhere, a yojana is equivalent to 768000 angulas. 112 But, it is only in this school that yojana depends on three patterns of angula which are used for measuring different types of objects. The three different kinds of the angulas113; ātmāngula, utsedhāngula, and pramāņāngula. The Śvetāmbara School takes 1000 utsedha angulas equal to one pramāņa angula whereas the Digambara School mentions 500 utsedha angula as equivalent to one pramāņāngula. The Buddhist 1 angnli-parva is equal to 2 angulas of the Jainas. According to this correspondence a yojana is equal to 8 miles, and the corresponding Svetambara pramāņa yojana is equal to 8000 miles, but the Digambara pramāņa yojana is equal to 4000 miles.
The utsedhangula is accomplished by definition and called a sūcyangula (linear finger width). This is used to measure the heights of subhuman, and hellish bodies, as well as the residence and cities etc. of four types of gods. Pramānāngula is used to measure the regions, the islands, oceans, mountains, altars, rivers, ponds and tanks etc. The atmängula depends upon the region and time and the human beings corresponding to them, and is used to enumerate ornamental objects (jhāri, kalaśa, darpaņa, etc.) as well as gardens, cities and residence ch. of human beings.114
3. EVOLUTION OF YOJANA
Yojana appears in Suryasiddhanta, and is used for class-measures of the planets etc. 115 Dixit opines that according to vacaspati and Šabdārņava kosas, a yojana may be taken to be 16000 hands or 5 miles. The Chinese traveller Hiven-Thsang found out that a yojana, equivalent to 30 li could be equal to 6-12 miles. He also mentioned a yojana equal to 40
112. A very illustrative article on "The Evolution of Measures in Jaina Astronomy" by Lishk and Sharma in, Tirthankara vol 1 nos. 7-12, 1975, 73-92, may be seen.
113. Cf. G. A., T. P. II, T. S. A comperative study has been given by Muni Mahendra Kumar, II, pp. 233, et. seq.
114. Cf. T. P., II, 7-107-113. For details of the Svetambara school, cf. G. A., pp. 448, 449, 450.
115. Cf. Dixit, p. 420. According to him, in many texts, a yojana is equal to 32000 hands. Taking a hand equal to 19-8 inches, a yojana is 10 miles which comes in contradiction to diameter of the earth. According to Megasthenes (-302 to -293) a yojana was equal to 96000 angulas.

51

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and 16 li amounting to 8 or 3 miles. 116
Fleet estimated the value of yojana to be 9 yojanas. Cunningham, after collating several variations, concludes that a yojana is equivalent to 6-7 miles, and Lishk and Sharma have also accepted this value from various considerations that follow. 117
4. RATIONALIZATION
Rationalization of the various data given in Jaina texts has been attempted by the above authors. For example the heights of various planetary bodies and the sun etc, from an unknown region, 118 uparima tala (upper surface of the Citra earth, are as follows : 119 The stars
790 Yojanas to 900 Yojanas The sun
800 Yojanas The moon 880 The nakşatras 884 The Mercury 888 The Venus 891 The Jupiter The Mars
897 The Saturn 900
894
56
Now the measures given about for the sun, the moon etc. immediately appear to contradict the modern view, as well as the date of diameter
48 of them given in Jaina texts, (Sum * and moon 20 yojanas }. Similarly, the distance between the innermost orbit and outermost orbit of the sun is 510 yojanas. Lishk and Sharma propose to regard this as arcual distance or roughly 480 of arc, 10 being equivalent to 69.9 miles on the earth's sphare. 116. Cf. ibid., pp. 423, 424. D. A. Somayaji derives a yojana as approxi
mating to 5 miles. L. C. Jain has derived in TPG, a value equivalent
to that of Fleet. Cf. Lishk and Sharma op. cit. 117. Cf, Lishk and Sharma, op. cit., “The Evolution........., 118. Svetāmbara School, S. P. and C. P., regard this region as the extremely
plane-beautiful earth-part of ratna-prabhā earth. 119. Cf. T. P., II, vv. 7.36, 7:65, 7•82, 7.83, 7-89, 7.93, 7.99, 7.104, 7.108
7.112, Cf. also G. A., pp. 257, 259.
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510 yojanas = 48 X 69.9 miles, thus
1 yojana = 6,6 miles roughly. HEIGHT AS LATITUDE
Accordingly the height 800 yojanas of the sun, converted into degrees by the same scale becomes sa
nec 800 X 6.7 = 77.50. Sharma and Lishk
69.9 regard this as the region of the projected ecliptic round the north pole (Meru directed point), also called the plane earth Citrā. 120 If this is the north polar distance of the sun, naturally, the moon at 880 yojanas shall mean, 80 yojanas towards the south of the sun, or below it in celestial diagram. According to the same scale, as suggested above, the maximum north polar distance of the moon from the sun or ecliptic is proposed to be 80 x 6.7 69. 90
= 7.70, the modern value being 50 8' 40", to which may approximate the former if a yojana is taken to be 5 miles.121
In the same way, the belt from 790 yojanas to 900 yojanas, or 110 yojanas becomes 10X6. = 10.60, a modern value of the lunar zodiac. 122
69.9
Thus the recognition of the heights of the heavenly bodies above the Citra, by Sharma and Lishk, though at present controversial, is praiseworthy and creditable. They proceed on to recognize a correspondence between two patterns of yojanas :
800 Y=50000 y, where Y is in the Tiloyapaņņatti units, and radius of the Jambūdvipa is 50000 y. On this basis they have derived the obliquity of the ecliptic (230.5), in structure of the mathematical model of Meru,123 120 Cf. “Latitude of the moon as determined in Jaina Astronomy",
Sramaņa, vol. 27, no. 2, pp. 28–35. Cf. also Lishk, S. S., and Sharma, S. D., Notion of circular flat earth in Jai
ar flat earth in Jaina Cosmography, The Jaina Antiquary, vol. xxviii, no. 1-2, July 1976. pp. 1-5. 121 This easily leads to the concept of celestial latitude which are measured
north or south of the ecliptic, from 00 to 900. 122 Cf. Neugebauer, pp. 102, 103; 82, 89 and 166, 186, for various
civilizations. Cf also Needham and Ling, p. 173. 123 Cf. Lishk, S. S. and Sharma, s. D., Notion of obliquity of ecliptic
implied in concept of Mount Meru in Jambūdvipaprajñapti, Jain Journal, Calcutta, Jan. 1978, 79-92.
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“A peculiarity of the school of Aryabhata is their assertion of measure of the great circle on the celestial sphere as 12,474,720,576,000 yojanas, which is the distance moved by the sun, the moon, or star and planets in a yuga (acon). According to Lishk and Sharma, the origin of this tradition may be traced back to the Jaina's practice of measuring celestial distances in terms of corresponding distances as projected over the earth.124
124 “Role of Pre-Aryabhata Jaina School of Astronomy in the Development
of Siddhāntic Astronomy,” I. J. H. S., vol. 12, no. 2, Nov. 1977, pp. 106-113.
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8. CALENDRICAL YUGA SYSTEM
The quinquennial yuga or cycle was prevalent in various schools of India, as it was in Jaina school. But, it began with Abhijit. In a cycle of five years there are 60 solar months, 61 stu months, 62 lunar months, 67 nakşatra months and 57 intercalary months. Now one solar year is of
3
13
366 days, one piu year is of 360 days, one lunar year is of 354
days,
one nakşatra year is of 327 2
days and one intercalary lunar year is of
383 days 210 muhūrtas. Thus all these years will simultaneously begin and close once in a cycle of 156 cycles of 5 years each, because 156 x 5 years will make 780 solar years, 793 ștu years, 806 lunar years, 871 nakşatra years and 744 intercalary lunar years, 125
Thus the yuga of 285480 days corresponds with the cycles of the following years :
366 x 780 = 285480 solar 360 x 793 = 285480 stu
the following products
125 The equivalence is clear from
x 60 = 21960 x 61 = 21960
156
=
780 solar years
12 156
N
=
793 ftu years
12
1.56
X
= 806 lunar years
12
12 x 62 = 21960 32754 x 67 = 21960 ( 383 days 21 19 muhūrtas ? =21960
156
-= 871 naksatra years
X
12
57 tầx 156 = 744 intercalary
lunar years
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354
12
62
X 806 = 285480 lunar
51
327 × 871 = 77
285480 nakşatra
18
383 days 21 muhurtas × 744 62
285480 intercalary lunar.
In a yuga, half the stretch of the full circle, 54900 celestial parts s covered 1768 times by the moon, 1830 times by the sun, and 1835 times by the nakşatras.126

Similarly many problems regarding seasons, parvas, tithis, motion, solstices, equinoxes, avam rātris, and so on, have been solved in full details in the Candraprajñapti, for the whole yuga of five years which are of various types.
=
126 Rationale: 1 yuga=1830 days=54900 muhurtas. Now in one muhurta, the moon moves 1768 c. p., therefore in 54900 muhurtas, it moves 54900 × 1768 = 97063200 celestial parts.
These divided by half the stretch, i. e. 54900 celestial parts, give set of 1768 half-stretches.
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9. ASTRONOMICAL THEORY
1. Introduction
Albert Einstein, in an article, distinguished between various types of theories in physics127. Some of these theories could be specified as principle theories and other could be recognized as constructive theories. The physical theories of astronomy also fall under this demarcation.
PRINCIPLE THEORIES
The principle theories employ the analytic method. Their basic elements are not constructed hypothetically ab initio. They are rather empirically discovered. The basic concepts and principles form general characteristic of natural processes. They give rise to mathematically formulated criteria which is required to be satisfied by the separate processes or their theoretical representations. These theories are logically perfect and have a secured foundation. However, if a single principle fails or if a single inconistency arises, the whole structure has to be remodelled because, then it is next to impossible to retain its originality. Thus the principles herein are required to be powerfully supported by experience and should be reconciliable logically.
CONSTRUCTIVE THEORIES
The constructive theories, on the other hand, follow the synthetic method. One has to try to find out a simple and formal scheme to construct a representation of more complex phenomena. If it is possible to understand a group of natural phenomena, through this, it may be regarded as the success of the constructive theory. These theories could be made complete, clear and adaptable, and could be subjected to remodelling without shattering the complete edifice.
127 Vid. “What is the Theory of Relativity ?, from
London, 1956, 227-232.
Ideas and Opinions,
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2. WHAT IS JAINA THEORY ?
One has thus to see to what class the Jaina astronomical theory belongs ? In what way the analytical method adopted in developing the principles of the theory, and to what extent they are mathematically formulated ? The abstraction method takes us on one side to the Samaya and Pradeśa, which are both regarded indivisible as the ultimate particle Paramāņu is indivisible. On the other side, there is the Rajju and the periods like the Pudgala or Bhāva parāvartana. Then they reach the infinities in time and space, through unending periodic phenomena.
We find several instances, when the actual figures are projected, deformed, stretched and yet hold on the invariance for their measure, Then one has to see how much perfect these theories had been made through the application of logic like the Syādvāda, and Anekānta. There is no doubt that whenever a path is needed, and is necessitated, the intellect and intuition find their own way of abstracting out strange and unusual methods like the method of exhaustion, real and counter replacements, setting up of a new system of observation through a new frame, and assimilating all the past known procedures.
It appears that when the Jaina principle theory began to disappoint the scholars in getting consistent results of the natural processes, it was replaced by the constructive theories evolved all the world over. 128 One has to mark out where the differences in measures of observation and calendar arose, in time reckoning at specified places. This naturally led to wrong prediction of the time of eclipses which had been a part of religious observation,
3. ECLIPSE THEORY
In the history of astronomy, Thales (C.-585), known for his maxim, “Know thyself,” was the first to predict a solar eclipse. It is presumed that he made use of the Babylonian saros period of 223 lunations. Vedic cycle was noted to be of 675 lunations based on recurrence of eclipses in three different colours (black, red and white ). Lishk has however observed from Sūryaprajñapti (v. 105) that the five colours of Rāhu (black, blue, red, yellow and white) yield a cycle of 336 eclipse years. But it is seriously felt that as the Jaina school had framed an astronomical theory, even the phenomena of eclipses could not have escaped their calculations, through the strange and mysterious setting of real and counter bodies. Although they could make correction in the precessional data, yet their 128 Cf. T. S. Kupanna Shastri, op. cit. (19).
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neglect in the precision of the motion of the sun against the background of stars led them to inconsistant and incompatible results, in course of time. They took 1830 days in their yuga of five years whereas it ought to have been 1826.2819 civil days, leading to a deficit of about a tithi in course of five years, 129 From Ganitānuyoga, pp. 303-305, the hours passed after 365 th day of the year is 5.81 hours, when the next year starts.
4. EVOLUTION OF EPICYCLES
The motion of the moon or the sun as described in Parkrit texts comprises of two motions : the rotation of the earth, which in turn, relatively gives a kinematic view of them; the other is their motion along the fixed stars. Both these, unified as one, were manipulated by the ancient school, through motion in circles for each day, with a constant radius, varying from day to day. Actually, due to the continuity of the motion, the geometrical figure of the path comes out to be an spiro-elliptic one, winding and
ft go unwinding. Its equation may be written in the form r=;
h+k Cos A, where
r is the radial distance of the sun from the earth, 0 is the angle through which it turns and f, g, h are constants. The dynamical laws found from the above are those of Newton, Einstein and one more, of attraction. 130
It is not known exactly, how this system further contributed or did not contribute to the development of the theory of eccentric and epicycles in Greece. If the Greek came to know about independent rotation of the earth, they must have tried to analyse the motion in two parts or through two types of circles. Or, if they wanted to trace the spiro-elliptic path through two circles, they must have planned to trace the path which had approximated simply as a circle for the specific day. As their geometry had become perfect by that time, it was not difficult for them to analyse the unified motion into two parts. Such attempts could also not be denied for India, but the records appear to start from the period of Āryabhaţa-I. Yet the yuga system was given, perhaps a priority, in which again, there were cycles, of periodic character, based on the following siddhāntas; as found by A. N Singh, 131
129 Cf. Dixit, op. cit., pp. 129-131. Cf. also, Petri, W., op. cit., for colours
of lunar eclipses. 130 Cf. Jain, L. C., [17], op. cit. 131 Cf. Radhakrishan, S., op. cit., article by Singh on Mathematics and
Astronomy, pp. 444 et seq., in History of Philosophy, Eastern and Western, London, 1957.
59

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(a) Everyastronomical phenomena recurs after a fixed period.
(b)
In the beginning of creation and each yuga, all the planets were in one line, i, e, at zero longitude.
(c) All heavenly bodies have equal linear motion.
(d) The rates of their angular motions are different.
(e) Motion of planets is irregular because they are attracted
towards moving points in the heavens.
(f) Earth is spherical like an iron ball surrounded by magnets.
It has to be seen whether this was a constructive theory.
60

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E
(A) BIBLIOGRAPHY OF SOURCE MATERIAL.
1] Ganitānuyoga, compiler Muni Kanhaiyalal, Kamal, trans. M. L.
Mehta, ed. S. Bharilla, Sanderao, 1970. 2 ) Reality, Eng. Trans. of Pūjyapāds Sarvārthasiddhi commentary
(of Tattvārthasūtra), S. A. Jain, Calcutta, 1960. 3 ] Pañcāstikāya of Kundakunda, trans. Prof. Chakraverty, Arrah, 1920. 4 ] Lokavibhāga, Simhasūri, Sholapur, 1962. 5 ] Tiloyapaņņatti of Yatiöşşabha, Parts I & II, Sholapur, 1943, 1952. 6 ] Jambūdvipa paņņatti of Padmanandi, Sholapur, 1958. 7 ] Jyotişakarandaka, (comm, by Malayagiri), Ratlam, 1928. 8 ] Lokaprakāśa, I, II, Surat, 1932, III, Bhavanagar, 1934. 9 ] Jambūdvipa paņņtti sūtra, Sikandarabad. 10 ] Thāņānga sūtra, Ahmedabad, 1937, 11 ] Trilokasāra of Nemi Chandra, Bombay, 1911. 12 ] Bphaddravyasamgraha of Nemicandra, Bombay, 1906. 13 ] Candraprajñapti sūtra, trans. Shri Amolaka Rşi, Sikandarabad. 14 ) Dhavalā commentary of Satkhandāgama, book 4, Amaraoti, 1942. 15 ] Gommaçasāra Jivakāņda, Nemicandra, J. L. Jaini, Bombay, 1927. 16 ] Sūryaprajñapti, Hindi trans. by Amolaka ķși, Sikandarabad (Virābda
2445); Comm, by Malayagiri, 1919, Sahesana. 17 ] Jivabhigama Sūtra. 18 ] Bhagavati Sūtra, trans. Amolaka Rşi, Sikandarabad also,
Bombay, 1918, also com. by Abhayadeva Sūri, Ratnapuri, 1937. 19 ] “Arşa Jyotişa,' Dvivedi, S., Benaras, 1906. ‘Atharva [ Vedānga
Jyotiga ] Jyotişa', Datta, Bhagvad, Lahore, 1924.
61

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20] Yantrarāja, Mahendra Sūri, Bombay, 1936.
21] Rana Sañcayaprakaraņa.
22] Jñanapradipika, trans. Pandeya, R. V., Arrah, 1934. 23] Jinendramālā, ed. & trans. Singh, S., Bombay 1958.
24] Jambudvipasamās of Umāsvāti, ed. Vijaya Simha Sūri, Ahmedabad,
1922.

62

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(B) BIBLIOGRAPHY OF SOME RESEARCH MATERIAL
Voo
"] Agrawal, M. B., Gañita evam Jyotişa ke Vikāsa meň Jainācāryon kā
Yogadāna, (Hindi), Thesis, Agra University, 1972. pp. 377. 2 ] Billard, R., Āryabhata and Indian Astronomy, 1. J. H. S., vol. 12,
no. 2, Nov. 1977, 207-224. 3] Billard, R., L'astronomic indienne, investigation des textes sanskrits
et des données numériques, Paris, Arien-Maisonneuve, 1971, 181 p. 4 ] Das, S. K., The Jaina School of Astronomy, I. H. Q., 8, 1934, 30-42. 5 ] Das, S. K., The Jaina Calendar, The Jaina Antiquary, 3.2, Sep.
1937, 31-36. 61 Gupta, R, C., Cirumference of the Jambūdvipa in Jaina
Cosmography, vol. 10, no. 1, 1975, 38-46. 71 Jaina, L, C., Tiloyapannatti kā Gasita, intr. to Jambūdvipa prajñapti
samgraha, Sholapur, 1958, 1-109. 8 ] Jain, L. C., Kinematics of the Sun and the Moon in Tiloyapaņpattı,
Tulsi Prajñā, J. V. B , Ladnun, Feb.-Mar. (1975), 60-67. 9] Jain, L. C., Jaina School of Mathematics (A study in Chinese
Influences and Transmissions), in “Contribution of Jainism to Indian Culture," ed. R. C. Dvivedi, Varansi, (1975), 206-220.
10 ] Jain, L. C., The Kinematic Motion of astral real and counter bodies
in Trilokasāra, Calcutta, I. J. H. S., vol. II, no. 1, 1976, 58-74. 11 ] Jain, L. C., Principle of Relativity in Jaina School of Mathematics,
Tulsi Prajna, J. V. B., Ladnun, 5, (1976), 20-28.
12 ] Jain, L. C., Ārybhata the Astronomer and Yativrşahha, the cosmo
grapher, Tirthankar, vol. 1, nos. 7–12, 1975, 102-10. 13] Jain, L. C., Certain Physical Theories in Hindu Astronomy, Prachya
Pratibha, vol. 5, no. 1, Jan, 1977, 75-86.
63

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14 ] Jain, L. C., Aryabhaţa-I and Yativșşabha - A Study in Kalpa and
Meru, I. J. H. S., vol. 12, no. 2, 1977, 135-149. 15 ] Jain, L. C., On the Contributions, Transmissions. and Influences of
the Jaina School of Mathematical Sciences. Tulsi Prajna, J. Y. B.,
Ladnun, vol. 3, no. 4, 1977, 121-134. 16 ] Jain, L. C., Distinct Features of Indian Astronomy upto Aryabhata-I,
Prachya Pratibha, vol. 4. no. 2, July 1975, 118-123. 17 ] Jain, L. C., On spiro-elliptic Motion of the Sun implicit in the
Tiloyapannatti, I.J. H. S., vol. 13, no. 1, 1978, 42-49. 18 ] Joshi, S. C., Nicolaus Copernicus and the Commentariolus I. J. H. S.,
vol. 9, no. 1, May 1974, 25–30. 19 ] Kupannashastri, T. S., The School of Aryabhata and the Peculiarities
thereof, I. J. H. S., vol. 4, nos, 1-2, 1969, 126-134. Cf. also “ A historical Development of certain Hindu astronomical Processes," in
the same volume. 20 ] Kuchment, M. M., (S. S. S. R. )-Cosmology of Newton, Proc.
of XIII Int. Cong. of Hist, of Sc., Moscow, 1971, 223-225. 21 ] Lishk, S. S. and Sharma, S. D., Post-Vedānga Pre Siddhāntic Indian
Astronomy, Paper read at I, N. S. A., New Delhi, 1974 (Summer
School), 233-1-16. 22] Lishk, S. S. and Sharma, S. D., The Evolution of Measures in Jaina
Astronomy, Tirthankar, 1 (7-12), 1975, 83-92. 231 Lishk, S. S. and Sharma, S. D., Occultations of the Moon in Jaina
Astronomy, Tulsi Prajna, 3, 1975, 64-69. 24 ] Lishk, S. S. and Sharma, S. D., Chatrātichatra Yoga in Sūrya
prajňapti, Tirtharkar, vol. 2, no. 1, Mar. 1976, 27-35 & 41. 25 ] Lishk, S. S. and Sharma, S. D., Notion of circular flat Earth in Jaina
Cosmography, The Jaina Antiquary, vol. XXVIII, Jul. 1976, No.
1, 2; 1-5. 26 | Lishk, S. S. and Sharma, S. D., Sources of Jaina Astronomy in Jaina
Canonical Literature, The Jaina Antiquary, vol. 29, no. 1-2, 1976,
19-32. 27 ] Lishk, S. S. and Sharma, S. D., Notion of Obliquity of Ecliptic
implied in the Concept of Mount Meru in Jambūdvīpaprajñapti, Jain Journal, Calcutta, Jan. 1978, 79-92.
64

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28 ] Lishk, S. S. and Sharma, S. D., Role of pre-Aryabhata Jaina School
of Astronomy in the Development of Siddhāntic Astronomy, I. J. H. S., vol. 12, no. 2, Nov. 1977, 106-113.
29 ] Lishk, S. S., and Sharma, S. D., Season Determination through the
Science of Sciatherics in Jaina School of Astronomy, I. J. H. S., vol. 12, no. 1, May 1977, 33-44.
30 ] Nahata, A, C., Jaina Jyotişa aura Vaidyaka Grantha, Shri Jaina
Siddhānta Bhaskara, Arrah, vol. 4, no. 2, 1937, 110-118.
31 ] Neugebauer, O., The Equivalence of eccentric and epicyclic Motion
according to Apollonius, Scripta Mathematica, vol. 24, 1959, 5-21. 32 ] Pande, M. C., Pre-copernican Astronomy in Europe, I. J. H. S.,
vol. 9, no. 1, 1974, 123–137.
33 ] Petri, W., Colours of Lunar Eclipses according to Indian Tradition,
1. J. H. S., vol. 3, no. 2, 1968, 91-98. 34 ] Pingree, D., Mesopotamian Origin of ancient Indian Mathematical
Astronomy, J. H. A., IV, 1974, 1-12. 35 ) Saraswati, T. A., The Mathematics in the first four Mahādhikāras of
the Trilokaprajñapti, Jour. Gang. Res. Inst., 18 (1961–62), 27-51. 36 ] Sen, S. N., Epicyclic-eccentric planetary theories in ancient and
medieval Indian Astronomy, I. J. H. S., vol. 9, no. 1, 1974, 107–
37] Sharma, S. D. and Lishk, S. S., Latitude of the Moon as determined
in Jaina Astronomy, śramaņa, vol. 27, no. 2. Dec. 1975, 28-35
(Varansi ). 38 ] Sharma, S. D. and Lishk, S. S., Length of the Day in Jaina
Astronomy, Centaurus, 22 : 3, Andelsbogtrykheriet. 39 ] Shastri, N. C., Jaina Jyotişa Sāhitya, Acharya Bhikshu Smriti
Grantha, Calcutta, Sec. ii (1961), 210-221. 40 ] Shastri, N. C., Gțīka-pūrva Jaina-Jyotişa Vicārādhārā, Br. Chanda
bai Abhinandan Granth, Arrah, 1954, 462-466. 41 ] Shastri, N. C., Bhārtiya Jyotişa kā poșaka Jaina-Jyotiņa, Varni
Abhinandan Granth, Saugar, 1962, 478-484. 42 ] Shastri, N. C., Jaina Pañcānga, Shri Jaina Siddhanta Bhaskar, 8.2,
Dec, 1941, 74-80.
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43 ) Shea, W. R., Gorge Locher's “Disquisitiones mathematicae de contro
versiis et novitatibus astronomicis" and Galileo's “Dialogue on the two world systems,” Proc. of XIIIth Int. Cong. of Hist, of Sc. Moscow.
1971, 211-218. 44 ] Shukla, K. S., Astronomy in India before Aryabhaţa-I, paper read
at silver jub. cele. of B. G. P, Lucknow, 24-10-76, pp. 1-11. Cf, also Jha, P., Āryabhata I : His School, Jour. of the Bihar Research
Soc., vol. 4 : pts. i & iv, Jan. Dec. 1969, 102-114. 45 ] Sikdar, J. C., The Jaina Concept of Time, Res. Jour. of Phil,, Ranchi,
vol. 4,1 (1972), 75-88. 46 ] Sikdar, J. C,, Eclipses of the Sun and the Moon according to Jaina
Astronomy, I. J. H. S., vol. 12, no. 2, Nov. 1977, 127-136. 47 ] Singh, A. N., History of Mathematics in India from Jaina Sources.
The Jaina Antiquary, 16, no, ii (1950) 54–69, Arrah. 48 ] Thibaut, G., On the Sūryaprajñapti, Jour. of the Asiatic Society of
Bengal, 49 (1), 1880, 107–127, 181-206. 49 ] Thibout, G., Contributions to the Explanations of Jyotisha Vedānga,
Jour. A. S. of Bengal, 46 (1), 1877, 411-437. 50] Chakravarthy, G. N., Concept of the Structure of Space Time,
I. J. H. S., vol. 5, no. 2, Nov. 1970, 219-228.
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(C) BIBLIOGRAPHY OF BOOKS
1] "Nature of the Universe', trans. R. E. Latham, Penguin Books, 1951. 2] The Almagest', trans. R. C. Taliaferro, “Great Books of the Western
World”, series, vol. 16, Book I-Chicago, 1952. 3) “De Revolutionibus Orbium Celestium (1543)', Royal Astronomical
Society. 4] "Dialogue concerning the two chief world systems Ptolemic and
Copernican', trans. Stillm.en Drake, Univ. of California Press, 1933. 5) 'Philosophiae Naturalis Principia Mathematica', Drake, A. M., trans.
F. Cajori, Univ. of California Press, 1946. 6 ] "Mein Welt bild', Einstein, A., Amsterdam, 1934. 7] “The Expanding Universe,' Eddington, A. S., Cambridge, 1933. 8 ] 'The Nature of the Universe', Hoyle, F., New York, 1960. 9 ] A History of Geometrical Methods’, Coolidge, J. L., Oxford, 1940. 10 ] Ideas and Opinions', Einstein, A., London 1956. 11 ] Cosmology, Old and New’, Jain, G. R., Indore, 1942. 12 ] "Spherical Astronomy', Prasad, G., Allahabad, 1973. 13 ] Bhāratiya Jyotişa’ of Shankara Balkrishṇa Dixit, trans. Jharkhandi,
S. N., Lucknow, 1975. 14 ] 'Bhāratiya Jyotişa’, Shastri, N. C., New Delhi, 1976.
15 ] 'A Concise History of Science in India’, Bose, D. M., Sen, S. N.,
Subbarayappa, B. V., New Delhi, 1971. 16 ] 'L'Inde Classique, École Fran, caise- d 'Extrême-Orient, Renou, L.
and Filliozat, J., Hanoi, 1953. 17 ] “Bhārtiya Samskști meṁ Jaina Dharma kā Yogadāna, Bhopal, 1962.
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18 ] “The Jaina Sources of the History of Ancient India, (100 B. C. to A. D.
900), Jain, J. P., Delhi, 1964. 19 ] Der Jainismus”, Von Glassnapp, Berlin, 1925. . 20 ] Viśva Prahelikā', Muni Mahendra Kumar, II, Bombay, 1969. 21 ] "On Mathematics and Mathematicians', Moritz, R. E., Newyork,
1942 (Dover). 22 ) Reality-Sarvārtha Siddhi of Pūjyapāda', Jain, S. A., Calcutta, 1960. 23 ] Jyotişasāra’, trans. Jain, B. D., Calcutta, 1923. 24 ) Science and Civilization in China', Needham, J. and Ling, W.,
vol. 1 (1954), vol. 3 (1959), Cambridge. 25 ] Ancient Hindu Astronomy', Somayaji, D. A., Dharvar, 1971, 26 ] “The Exact Sciences in Antiquity', Neugebauer, O., Providence, 1957. 27 ] "Census of the Exact Sciences in Sanskrit, Series A, vol. I (1970),
vol. II (1971), Philadelphia,
History of Philosophy; Eastern and Western', Ed. Radhakrishnan, S, et al., London, 1957. [ This contains an article, Scientific Thought in Ancient India' by Singh, A. N., on Mathematics and Astronomy,
pp. 444 et seq. ] 29 ] "The Vedic Cycle of Eclipses', Sharma Shastry, R., Mysore, 1938. 30 ] "Geometry in Ancient and Medieval India', Saraswati, T. A.
Delhi, 1978. 31 ] "Treasures of Jaina Bhandaras', Shah, U. P., Ahmedabad, 1978. 32 ] Science Awakening', Waerden, B. L., Holland, 1945. 33 ] “Aryabhata’, Volodarski, A. E., (Russian), Moscow, 1977. 34 ] History of Mathematics' 1; Ribnikov, K. A., (Russian);
Moscow, 1960. 35 ] “Albirū ni's India', Albiruni, trans. (Hindi), Sharma, R. K., Allahabad,
1967. Cf, also, Sachau, New Delhi, 1964, 36 ] "The Positive Sciences of the Hindus’, Seal, B, N., Delhi, 1958. 37 ] "A History of the Kerala School of Hindu Astronomy,' Sarma, K. V.,
Hoshiarpur, 1972. 38 ) Hindu Achievement in Exact Sciences', Sarkar, B. K., London, 1918.
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39 ] ‘A History of Science', Sarton, G., vols. I, II, New York, 1965. 40 ] “Āryabhaţa-Indian Astronomer and Mathematician', Shukla, K. S.,
New-Delhi, 1976 (INSA). 41 ] Hindu Astronomy', Brennand, W., London, 1896, 42 ] “Man and the Cosmos' by Ritchie Calder, Britannica Perspectives,
vol. 1, 1768–1968, Chicago, 1968. 43 ) A History of Ancient Mathematical Astronomy', Neugebauer, O.,
Berlin, 1975. 44 ) Kevala Jñāna Praśna Cūdāmaņi' ed. Shastri, N. C., Kashi. 45 ] “Theories of the Universe', Munitz, M. K., Illinois, 1957. 46 ] "Die Kosmographie der Inder,' Kirfel, W., Bonn, 1920.
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1. C. P.
2.
U A G

D.
3.
4. G. J. K.
5. L. P.
6. L. V.
7.
P. A.
8. R. S. P.
9.
S. K.
10. S. P.
11.
T. P.
12. T. P. G.
13. T. S.
14. V. P.
G. A.
(D) ABBREVIATION
Candraprajñapti
Dhavala (commentary)
Gaņitānuyoga
Gommaţasāra Jivakāņḍa
Loka prakāśa
Loka vibhāga
Pañcastikāya
Ratna Sañcaya Prakarana
Şat khanḍāgama
Suryaprajñapti
Tiloyapanṇatti
Tiloyapanṇatti kā Gaņita
Trilokasara
Viśvaprahelikā.
70

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APPENDIX-A
REST 15 EMPTY SPACE
OR NON- UNIVERSE
THE UNIVERSE
TR - 1oca y
- Z RUKS
UPPER UNIVERSE
5R
100000 Yojanas [Moreoverse]
ANEK UNIVERSE
737
7 Rayus
-
ELE
THE UNIVERSE 15 CONSTITUTED OF SIX TYPES OF FLUENTS: BIOS, MATTER, SPACE, TIME, AETHER and ANTI-AE HER (JIVA, PUDGALA, A kis'A, KĀLA,
DHARMA and ADHARMA)

Page #91

APPENDIX - B
THE UNIVERSE
K1R
2R -+*+R
2R->
PLAN
TR
- 10000.Y
K
7 Rajusby
-*
ELEVATION
R.S. YIEW

Page #92
4 . TE ALGET 1 JUT JUTJUT PUT PUTI