गणितसारसंग्रह (महावीराचार्य - प्रो. लक्ष्मीचन्द्र जैन सविस्तार हिन्दी अनुवाद सटीक)

६८ गणितसारसंग्रह
and comprehensive, and who on the occasion when he met me in
person at Madras showed great interest in the contemplated
publication of the Gaṇita-sāra-saṅgraha and thereafter read a paper
on that work at the Fourth International Congress of Mathe-
maticians held at Rome in April 1908. Accordingly I requested him
to write an introduction to this edition of the Gaṇita-sāra-saṅgraha,
given in brief outline what he considers to be its value in building
up the history of Hindu mathematics. My thanks as well as the
thanks of all those who may as scholars become interested in this
publication are therefore due to him for his kindness in having
readily complied with my request; and I feel no doubt that his
introduction will be read with great appreciation.
Since the origin of the decimal system of notation and of the
conception and symbolic representation of zero are considered to
be important questions connected with the history of
Hindu mathematics, it is well to point out here that in the
Gaṇita-sārasaṅgraha twenty four notational places are mentioned,
commencing with the units place and ending with the place called
mahākṣōbha, and that the value of each succeeding place is taken
to be ten times the value of the immediately preceding place.
Although certain words forming the names of certain things are
utilized in this work to represent various numerical figures, still in
the numeration of of numbers with the aid of such words
the decimal system of notation is almost invariably followed.
If we took the words moon, eye, fire and sky to represent respectively
1, 2, 3 and 0, as their Sanskrit equivalents are understood in this
work, then, for instance, fire-sky-moon-eye would denote the number
2103, and moon-eye-sky-fire would denote 3021, since these nominal
numerals denoting numbers are generally repeated in order from
the units place upwards. This combination of nominal numerals
and the decimal system of notation has been adopted obviously for
the sake of securing metrical convenience and avoiding at the same
time cumbrous ways of mentioning numerical expressions; and it
may well be taken for granted that for the use of such nominal
numerals as well as the decimal system of notation Mahāvīrācārya
was indebted to his predecessors. The decimal system of notation is

गणितसारसंग्रह ६९
distinctly described by Āryabhaṭa, and there is evidence in his
writings to show that he was familiar with nominal numerals. Even
in his brief mnemonic method of representing numbers by certain
combinations of the consonants and vowels found in the Sanskrit
language, the decimal system of notation is taken for granted; and
ordinarily 19 notational places are provided for therein. Similarly
in Brahmagupta's writings also there is evidence to show that he
was acquainted with the use of nominal numerals and the decimal
system of notation. Both Āryabhaṭa and Brahmagupta claim that
their astronomical works are related to the Brahma-siddhānta; and
in a work of this name, which is said to form a part of what is
called Śākalya-saṁhitā and of which a manuscript copy is to be
found in the Government Oriental Manuscripts Library here,
numbers are expressed mainly by nominal numerals used in accordance
with the decimal system of notation. It is not of course meant to
convey that this work is necessarily the same as what was known
to Ārayabhaṭa and Brahmagupta; and the fact of its using nominal
numerals and the decimal system of notation is mentioned here for
nothing more than what it may be worth.
It is generally recognized that the origin of the conception of
zero is primarily due to the invention and practical utilization of a
system of notation wherein the several numerical figures used have
place-values apart from what is called their intrinsic value. In
writing out a number according to such a sytem of notation, any
notational place may be left empty when no figure with an intrinsic
value is wanted there. It is probable that owing to this very reason
the Sanskrit word śūnya, meaning 'empty', came to denote the zero;
and when it is borne in mind that the English word 'cipher' is derived
from an Arabic word having the same meaning as the Sanskrit śūnya,
we may safely arrive at the conclusion that in this country the
conception of the zero came naturally in the wake of the decimal
system of notation : and so early as in the fifth century of the
Christian era, Āryabhaṭa is known to have been fully aware of this
valuable mathematical conception. And in regard to the question
of a symbol to represent this conception, it is well worth
bearing in mind that operations with the zero cannot be

७० गणितसारसंग्रह
carried on–not to say cannot be even thought of easily–without a
symbol of some sort to represent it. Mahāvīrācārya gives, in the
very first chapter of his Gaṇita-sāra-saṅgraha, the results of the
operations of addition, subtraction, multiplication and division
carried on in relation to the zero quantity; and although he is wrong
in saying that a quantity, when divided by zero, remains unaltered,
and should have said, like Bhāskarācārya, that the quotient in such
a case is infinity, still the very mention of operations in relation to
zero is enough to show that Mahāvīrācārya must have been aware
of some symbolic representation of the zero quantity. Since
Brahmagupta, who must have lived at least 150 years before
Mahāvīrācārya, mentions in his work the results of operations in
relation to the zero quantity, it is not unreasonable to suppose that
before his time the zero must have had a symbol to represent it in
written calculations. That even Āryabhaṭa knew such a symbol is
not at all improbable. It is worthy of note in this connection that in
enumerating the nominal numerals in the first chapter of his work,
Mahāvīrācārya mentions the names denoting the nine figures from 1 to
9, and then gives in the end the names denoting zero, calling all the
ten by the name of saṅkhyā : and from this fact also, the inference
may well be drawn that the zero had a symbol, and that it was well
known that with the aid of the ten digits and the decimal system of
notation numerical quantites of all values may be definitely and
accurately expressed. What this known zero-symbol was, is, however,
a different question.
The labour and attention bestowed upon the study and trans-
lation and annotation of the Gaṇita-sāra-saṅgraha have made it
clear to me that I was justified in thinking that its publication might
prove useful in elucidating the condition of mathematical studies as
they flourished in South India among the Jainas in the ninth century
of the Christian era; and it has been to me a source of no small
satisfaction to feel that in bringing out this work in this form,
I have not wasted my time and thought on an, unprofitable
undertaking. The value of the work is undoubtedly more historical
than mathematical. But it cannot be denied that the step by step
construction of the history of Hindu culture is a worthy endeavour,

गणितसारसंग्रह ७१
and that even the most insignificant labourer in the field of such
an endeavour deserves to be looked upon as a useful worker.
Although the editing of the Gaṇita-sāra-saṅgraha has been to me a
labour of love and duty, it has often been felt to be heavy and taxing;
and I, therefore, consider that I am specially bound to acknowledge
with gratitude the help which I have received in relation to it. In
the early stage, when conning and collating and interpreting the
manuscripts was the chief work to be done, Mr. M. B. Varadaraja
Aiyangar, B. A., B. L., who is an Advocate of the Chief Court at
Bangalore, co-operated with me and gave me an amount of aid for
which I now offer him my thanks. Mr. K. Krishnaswami Aiyangar,
B. A.; of the Madras Christian College, has also rendered consider-
able assistance in this manner; and to him also I offer my thanks.
Latterly I have had to consult on a few occasions Mr. P. V. Seshu
Aiyar, B. A., L. T., Professor of Mathematical Physics in the Presidency
College here, in trying to explain the rationale of some of the rules
given in the work; and I am much obliged to him for his ready
willingness in allowing me thus to take advantage of his expert
knowledge of mathematics. My thanks are, I have to say in
conclusion, very particularly due to Mr. P. Varadacharya, B. A.,
Librarian of the Government Oriental Manuscripts Library at Madras,
but for whose zealous and steady co-operation with me throughout
and careful and continued attention to details, it would indeed
have been much harder for me to bring out this edition of the
Gaṇit-sāra-saṅgraha.
$\left. {l} February 1912,
Madras. \right}$ M. RANGACHARYA.

INTRODUCTION
BY
DAVID EUGENE SMITH
PROFESSOR OF MATHEMATICS IN TEACHERS' COLLEGE,
COLUMBIA UNIVERSITY, NEW YORK.
We have so long been accustomed to think of Pāṭaliputra on
the Ganges and of Ujjain over towards the Western Coast of India
as the ancient habitats of Hindu mathematics, that we experience
a kind of surprise at the idea that other centres equally important
existed among the multitude of cities of that great empire. In the
same way we have known for a century, chiefly through the labours
of such scholars as Colebrooke and Taylor, the works of Āryabhaṭa,
Brahmagupta, and Bhāskara, and have come to feel that to these
men alone are due the noteworthy contributions to be found in
native Hindu mathematics. Of course a little reflection shows this
conclusion to be an incorrect one. Other great schools, particularly of
astronomy, did exist, and other scholars taught and wrote and added
their quota, small or large, to make up the sum total. It has, however,
been a little discouraging that native scholars under the English
supremacy have done so little to bring to light the ancient mathe-
matical material known to exist and to make it known to the Western
world. This neglect has not certainly been owing to the absence of
material, for Sanskrit mathematical manuscripts are known, as are
also Persian, Arabic, Chinese, and Japanese; and many of these are
well worth translating from the historical standpoint. It has rather
been owing to the fact that it is hard to find a man with the requisite
scholarship, who can afford to give his time to what is necessarily
a labour of love.
It is a pleasure to know that such a man has at last appeared
and that, thanks to his profound scholarship and great perseverance,

गणितसारसंग्रह ७३
we are now receiving new light upon the subject of Oriental
mathematics, as known in another part of India and at a time
about midway between that of Āryabhaṭa and Bhāskara, and two
centuries later than Brahmagupta. The learned scholar, Professor
M. Raṅgācārya of Madras, some years ago became interested in
the work of Mahāvīrācārya, and has now completed its translation,
thus making the mathematical world his perpetual debtor; and I
esteem it a high honour to be requested to write an introduction
to so noteworthy a work.
Mahāvīrācārya appears to have lived in the court of an old
Rāṣṭrakūṭa monarch, who ruled probably over much of what is now
the kingdom of Mysore and other Kanarese tracts, and whose name
is given as Amōghavarṣa Nṛpatuṅga. He is known to have ascended
the throne in the first half of the ninth century A. D., so that we
may roughly fix the date of the treatise in question as about 850.
The work itself consists, as will be seen, of nine chapters like
the Bīja-gaṇita of Bhāskara; it has one more chapter than the
Kuṭṭaka of Brahmagupta. There is, however, no significance in
this number, for the chapters are not at all parallel, although certain
of the topics of Brahmagupta's Gaṇita and Bhāskara's Līlāvatī are
included in the Gaṇita-Sāra-Saṅgraha.
In considering the work, the reader naturally repeats to
himself the great questions that are so often raised:—How much of
this Hindu treatment is original? What evidences are there here
of Greek influence? What relation was there between the great
mathematical centres of India? What is the distinctive feature, if
any, of the Hindu algebraic theory?
Such questions are not new. Davis and Strachey, Colebrooke
and Taylor, all raised similar ones a century ago, and they are by
no means satisfactorily answered even yet. Nevertheless, we are
making good progress towards their satisfactory solution in
the not too distant future. The past century has seen several
Chinese and Japanese mathematical works made more or less
familiar to the West; and the more important Arab treatises are now
quite satisfactorily known. Various editions of Bhāskara have
appeared in India; and in general the great treatises of the Orient

७४ गणितसारसंग्रह
have begun to be subjected to critical study. It would be strange,
therefore, if we were not in a position to weigh up, with more
certainty than before, the claims of the Hindu algebra. Certainly
the persevering work of Professor Raṅgācārya has made this more
possible than ever before.
As to the relation between the East and the West, we should
now be in a position to say rather definitely that there is no evidence
of any considerable influence of Greek algebra upon that of India.
The two subjects were radically different. It is true that Diophantus
lived about two centuries before the first Āryabhaṭa, that the paths
of trade were open from the West to the East, and that the itinerant
scholar undoubtedly carried learning from place to place. But the
spirit of Diophantus, showing itself in a dawning symbolism and in
a peculiar type of equation, is not seen at all in the works of the
East. None of his problems, not a trace of his symbolism, and not
a bit of his phraseology appear in the works of any Indian
writer on algebra. On the contrary, the Hindu works have a style
and a range of topics peculiarly their own. Their problems lack the
cold, clear, geometric precision of the West ; they are clothed in that
poetic language which distinguishes the East, and they relate to
subjects that find no place in the scientific books of the Greeks. With
perhaps the single exception of Metrodorus, it is only when we come
to the puzzle problems doubtfully attributed to Alcuin that we find
anything in the West which resembles, even in a slight degree, the
work of Alcuin's Indian contemporary, the author of this treatise.
It therefore seems only fair to say that, although some know-
ledge of the scientific work of any one nation would, even in those
remote times, naturally have been carried to other peoples by some
wandering savant, we have nothing in the writings of the Hindu
algebraists to show any direct influence of the West upon their
problems or their theories.
When we come to the question of the relation between the different
sections of the East, however, we meet with more difficulty. What
were the relations, for example, between the school of Pāṭaliputra,
where Āryabhaṭa wrote, and that of Ujjain, where both Brahmagupta
and Bhāskara lived and taught ? And what was the relation of each

गणितसारसंग्रह ७५
of these to the school down in South India, which produced this
notable treatise of Mahāvīrācārya ? And, a still more interesting
question is, what can we say of the influence exerted on China by
Hindu scholars, or vice versa? When we find one set of early inscrip-
tions, those at Nānā Ghāt, using the first three Chinese numerals,
and another of about the same period using the later forms of Mesopo-
tamia, we feel that both China and the West may have influenced
Hindu science. When, on the other hand, we consider the problems
of the great trio of Chinese algebraists of the thirteenth century,
Ch'in Chiushang, Li Yeh, and Chu Shih-chieh, we feel that
Hindu algebra must have had no small influence upon the North
of Asia, although it must be said that in point of theory the Chinese
of that period naturally surpassed the earlier writers of India.
The answer to the questions as to the relation between the
schools of India cannot yet be easily given. At first it would seem
a simple matter to compare the treatises of the three or four great
algebraists and to note the similarities and differences. When this
is done, however, the result seems to be that the works of Brahma-
gupta, Mahāvīrācārya, and Bhāskara may be described as similar
in spirit but entirely different in detail. For example, all of these
writers treat of the areas of polygones, but Mahāvīrācārya is the
only one to make any point of those that are re-entrant. All of them
touch upon the area of a segment of a circle, but all give different
rules. The so-called janya operation (page 209) is akin to work
found in Brahmagupta, and yet none of the problems is the same.
The shadow problems, primitive cases of trigonometry and gnomo-
nics, suggest a similarity among these three great writers, and yet
those of Mahāvīrācārya are much better than the one to be found in
either Brahmagupta or Bhāskara, and no questions are duplicated.
In the way of similarity, both Brahmagupta and Mahāvīrācārya
give the formula for the area of a quadrilateral,
√((s - a)(s - b)(s - c)(s - d))
—but neither one observes that it holds only for a cyclic
figure. A few problems also show some similarity such as that
of the broken tree, the one about the anchorites, and the

७६ गणितसारसंग्रह
common one relating to the lotus in the pond, but these prove
only that all writers recognized certain stock problems in
the East, as we generally do to-day in the West. But as already
stated, the similarity is in general that of spirit rather than of
detail, and there is no evidence of any close following of one writer
by another.
When it comes to geometry there is naturally more evidence
of Western influence. India seems never to have independently
developed anything that was specially worthy in this science.
Brahmagupta and Mahāvīrācārya both use the same incorrect rules
for the area of a triangle and quadrilateral† that is found in the
Egyptian treatise of Ahmes. So while they seem to have been
influenced by Western learning, this learning as it reached India
could have been only the simplest. These rules had long since been
shown by Greek scholars to be incorrect, and it seems not unlikely
that a primitive geometry of Mesopotamia reached out both to
Egypt and to India with the result of perpetuating these errors. It
has to be borne in mind, however, that Mahāvīrācārya gives correct
rules also for the area of a triangle as well as of a quadrilateral
without indicating that the quadrilateral has to be cyclic. As to the
ratio of the circumference to the diameter, both Brahmagupta and
Mahāvīrācārya used the old Semitic value 3, both giving also √10
as a closer approximation, and neither one was aware of the works
of Archimedes or of Heron. That Āryabhaṭa gave 3·1416 as the
value of this ratio is well known, although it seems doubtful how
far he used it himself. On the whole the geometry of India seems
rather Babylonian than Greek. This, at any rate, is the inference
that one would draw from the works of the writers thus far known.
As to the relations between the Indian and the Chinese algebra,
it is too early to speak with much certainty. In the matter of
problems there is a similarity in spirit, but we have not yet enough
translations from the Chinese to trace any close resemblance. In
each case the questions proposed are radically different from those
found commonly in the West, and we must conclude that the
algebraic taste, the purpose, and the method were all distinct in the

गणितसारसंग्रह ७७
two great divisions of the world as then known. Rather than
assert that the Oriental algebra was influenced by the Occidental
we should say that the reverse was the case. Bagdad, subjected
to the influence of both the East and the West, transmitted
more to Europe than it did to India. Leonardo Fibonacci, for
example, shows much more of the Oriental influence than Bhāskara,
who was practically his contemporary, shows of the Occidental.
Professor Raṅgācārya has, therefore, by his great contribution
to the history of mathematics confirmed the view already taking
rather concrete form, that India developed an algebra of her own;
that this algebra was set forth by several writers all imbued with
the same spirit, but all reasonably independent of one another; that
India influenced Europe in the matter of algebra, more than it was
influenced in return; that there was no native geometry really
worthy of the name; that trigonometry was practically non-existent
save as imported from the Greek astronomers; and that whatever of
geometry was developed came probably from Mesopotamia rather
than from Greece. His labours have revealed to the world a writer
almost unknown to European scholars, and a work that is in many
respects the most scholarly of any to be found in Indian mathematical
literature. They have given us further evidence of the fact that
Oriental mathematics lacks the cold logic, the consecutive
arrangement, and the abstract character of Greek mathematics, but
that it possesses a richness of imagination, an interest in
problem-setting, and poetry, all of which are lacking in the treatises of
the West, although abounding in the works of China and Japan. If,
now, his labours shall lead others to bring to light and set forth mor
and more of the classics of the East, and in particular those of early
and mediaeval China, the world will be to a still larger extent his
debtor.

प्रस्तावना की अनुक्रमणिका
अंकगणित—3, 4, 6, 7 , 10, 15.
अंक-ज्योतिष—4.
अनन्त राशियों का गणित—9.
अनुकल कलन—( Integral Calculus ) 4, 5.
अनुयोग सूत्र—7.
अपरिमेय—( Irrational ) 4.
अमोघवर्ष—1, 10.
अर्थमितिकी—( Arithmetica ) 4, 18.
अर्थसंदृष्टि—9, 20.
अलौकिक गणित—9.
अल्पबहुत्व—( Comparability ) 26, 34.
अविभाज्यों की रीति—( Method of indivisibles ) 4.
असद्भास —( Paradoxes ) 4, 26.
अहिंसा—12, 13, 14, 17, 30.
आमिस—( Ahmes ) 3.
आर्किमिडीज़—4, 5.
आर्यभट—7.
इटली—2, 4.
उद्स्थैतिकी—( Hydrostatics ) 5, ( स्थैतिकी )—5.
कर्म सिद्धान्त—16, 17.
कापरनिकस—5.
काल्पनिक राशि—( Imaginary quantity ) 11.
कुन्तल—( Spiral ) 5.
कुफू—( Khufu ) 13, 14, 16, 17.
केंटर, जार्ज—9, 15, 16.
कूट स्थिति रीति—( Rule of false position ) 3.
गणितसारसंग्रह—1, 9, 16.
गणितीय विश्लेषण—( Mathematical Analysis ) 2, 3, 4, 10.
ग्रीक—4, 5, 7, ( यूनानी )—7, 14, 15.
गोम्मटसार टीका—34.
चतुर्गति ( चदुचंकमण )—16, 23.
चतुर्भुज—11, 15, 20.

गणितसारसंग्रह ७९
चलन कलन—( Differential calculus ) 5.
चीन—21, 30, 31, 32, 33, 34.
ज़ीनो ( Zeno ) 4, 26, 27, 28, 29. ( तर्क )—27, 28.
ज्योतिर्विज्ञान—3, 6.
ज्योतिष—8, 14, 15, 16, 18, 22, 25, ( पटल ) 12, ( वेदांग )—6, 7.
टॉलेमी—18, 30.
टोडरमल—20, 26, 34.
डाओफेंटस—5, 11, 18.
डेडीकेन्ड—4.
तीर्थंकर—12, ( वर्द्धमान महावीर ) 13, 14, 18, 19, 20, 23, 29, 30, 32, 34.
तिलोयपण्णत्ती—17, 19, 21, 26, 30, 34, ( त्रिलोकप्रज्ञप्ति )—7, 15.
त्रिभुज—2, 3, 4, 5, 11, 20, 22.
त्रिकोणमिति—( Trigonometry )—7, 8.
थेलीज्—4, 13, 18, 21, 22.
दशमलवपद्धति—( Decimal system ) 2, 3, 7, ( दाशमिक ) 18, 19, 20.
निःशेषण विधि—( Method of exhaustion ) 4.
नेब्युकडनेज़र—20.
नेमिचन्द्रार्य—15.
परमाणु—( Indivisible ultimate particle ) 26, 27, 28, 29, 32.
परिधि व्यास अनुपात ( π )—2, 3, 15.
पेप्स— 5
पिथेगोरस—3, 4, 5, 12, 13, 16, 18, 19, 20, 21, 23, 24, 25, 26, 34.
पिरेमिड—( स्तूप )—3, 4, 16, 17.
पेपायरस ( मास्को )—4, 15, ( रिन्ड )—3.
प्रदेश ( Point )—26, 28, 29.
फलनीयता—( Functionality ) 2.
बीजगणित—( Algebra ) 3, 6, 7, 10, 11, 12, 18, 20.
बेबिलन—2, 3, 12, 15, 17, 20, 21, 22, 30.
ब्रह्मगुप्त—8, 10, 11, 12.
ब्राह्मण साहित्य—6.
ब्राह्मी—6.
भारत—5, 12, 13, 15, 19, 20, 26, 30, 32, 33.
भास्कर—9.
महावीराचार्य—1, 9, 10, 11, 12, 16.
माया गणना—7.
मिस्र—3, 4, 12, 13, 14, 15, 16, 17, 22, 23.

८० गणितसारसंग्रह
मोहेनजोदड़ो—6.
यूक्लिड—4, 5.
यूडो—4.
यूनान—12, 13, 16, 17, 18, 19, 21, 22, 31, 34.
रज्जु—( Rope ) 3, 5, 15, 16.
रूपक संख्यायें—( Figurate numbers ) 4.
राशि सिद्धान्त—( Set theory ) 13, 20.
रेखागणित—( Geometry ) 4, 5.
बक्षाली ( भोजपत्र )—7, 11.
वीरसेनाचार्य—9, 15, 16, 21, 28.
शांकव गणित—( Conics ) 2, 4, 5.
शून्य—7, 10, 18, 34.
षट्खंडागम—9, 16, 19, 24, 26.
षाष्ठिका—( Sexagesimal ) 2, 18, 19, 20, 21.
समय—( Instant ) 26, 28, 29.
समीकरण—( Equation ) 2, 5, 6, 10, 11, 20.
सल्लागा ( गण )—9, ( अर्थ ) ( Logarithm )—19.
साक्राटीज—27.
सुमेर—2, 5, 18.
स्थान मान ( Place value )—3, 7, ( अर्हा )—10, 18, 19, 20.
स्फिंक्स—( Sphinx ) 13, 14.
हिपारकस—5.
हिरोडोटस—14, 16.

शुद्धि-पत्र
पृष्ठ पंक्ति अशुद्ध शुद्ध
प्रस्तावना १ ९ बेबीलोनिया बेबिलन
२ ११ बेबीलोन ”
२ १७ ” ”
३ ४ ” ”
३ ८ ” ”
३ १५ पैपीरियों पेपायरियों
३ २१ पेपिरस पेपायरस
४ ३ ” ”
४ ११ आर्किमिडीज़ आर्किमीडीज़
४ १६ पैथेगोरस पिथेगोरस
४ १७ ” ”
४ २२ ” ”
४ २३ ” ”
५ १ ” ”
५ ३ आर्किमिडीज़ आर्किमीडीज़
५ ८ अतिपरवलज अतिपरवलयज
५ १५ आर्किमिडीज़ आर्किमीडीज़
५ १६ हिपरकस हिपारकस
५ २५ डायोफेंटस डाओफेंटस
५ २८ मैरथान मैराथान
५ ३० बेबीलोन बेबिलन
८ १६ Peleian Pellian
९ २३ सम् सन्
११ १ बख्शाली बक्षाली
१५ ३३ Health Heath
२२ २२ Pythagorus Pythagoras
२४ ८ ” ”
२४ २९ ” ”
२५ ५ ” ”
२५ १३ ” ”
२५ २० ” ”
२६ ११ ” ”
२६ १५ ” ”

८२ गणितसारसंग्रह
पृष्ठ पंक्ति अशुद्ध शुद्ध
31 ३४ Civilization Civilisation
ग्रंथ ३ गाथा १४ बन्घेन्द्र° बन्धेन्द्र°
३ गाथा २३ गुणकै° गणकै°
४ गाथा २७ लीक्षा लिक्षा
५ गाथा ३३ संख्या तावलि° संख्यातावलि°
५ गाथा ३३ दल पल
६ गाथा ४४ फलशतद्वयम् पलशतद्वयम्
७ गाथा ५४ युगलयुग्मं युगलँयुग्मं
८ गाथा ७० संझा संज्ञाः
३७ २२ निम्रखित निम्नलिखित
११८ ६ भूलभूत मूलभूत
१८१ १४ विषय की छः प्रकार छठवें विषय
१९२ ९ आबाघा आबाधा
२०० १ अत्रोद्देशकः —
२०५ १ मिश्रक क्षेत्रगणित
२२१ ८ आदि से आदि लेकर गणनानीत
२६८ १६ इण्डुको इण्डुक
परिशिष्ट ११ ४ Ādhak Āḍhaka
११ ६ Adhvān Adhvāna
११ १५ Ādidhan Ādidhana
११ २७ Amōghvarsa Amōghavarṣa
१२ १२ Tirthnkar Tīrthaṅkara
१३ १८ Bhāgāpāvaha Bhāgāpavāha
१३ १९ भागसम्वर्ग भागसंवर्ग
१४ १० Crore crore
१५ २४ by be
१५ ३० Tiirthankara Tīrthaṅkara
१५ ३४ Tirthankara Tīrthaṅkara
२० २१ प्रपूर्णिका प्रपूरणिका
३८ १ परिशिष्ट-५ परिशिष्ट-२ अ
३९ ११ Ferminalia Terminalia
३९ ३० संचरित संरचित

JĪVARĀJA JAINA GRANTHAMĀLĀ

1. Tiloyapaṇṇatti of Yativṛṣabha (Part I, Chapters 1-4) : An Ancient
   Prākrit Text dealing with Jaina Cosmography, Dogmatics etc.
   Prākrit Text authentically edited for the first time with various
   Readings, Preface & Hindi Paraphrase of Pt. Balachandra by
   Drs. A. N. Upadhye and H. L. Jain. Published by Jaina Saṁskṛti
   Saṁrakṣaka Saṁgha, Sholapur (India). Double Crown pp. 6-38-
2. Sholapur, 1943. Price Rs. 12·00. Second Edition, Sholapur,
3. Price Rs. 16·00.
4. Tiloyapaṇṇatti of Yativṛṣabha (Part II, Chapters 5-9). As above,
   with Introductions in English and Hindī, with an alphabetical
   Index of Gāthās, with other Indices (of Names of works mentioned,
   of Geographical Terms, of proper Names, of Technical Terms, of
   Differences in Tradition, of Karaṇasūtras and of Technical Terms
   compared) and Tables (of Nāraka-jīva, Bhavana-vāsī Deva,
   Kulakaras, Bhāvana Indras, Six Kulaparvatas, Seven Kṣetras,
   Twentyfour Tīrthaṅkaras, Age of the śalākāpurṣas, Twelve Cakra-
   vartins, Nine Nārāyaṇas, Nine Pratiśatrus, Nine Baladevas,
   Eleven Rudras, Twentyeight Nakṣatras, Eleven Kalpātīta, Twelve
   Indras, Twelve Kalpas and Twenty Prarūpaṇās). Double Crown
   pp. 6-14-108-529 to 1032, Sholapur, 1951. Price Rs. 16·00.
5. Yaśastilaka and Indian Culture, or Somadeva's Yaśastilaka and
   Aspects of Jainism and Indian Thought and Culture in the Tenth
   Century, by Professor K. K. Handiqui, Vice-Chancellor, Gauhati
   University, Assam, with Four Appendices, Index of Geographical
   Names and General Index. Published by J. S. S. Sangha, Sholapur.
   Double Crown pp. 8-540. Sholapur, 1949. Price Rs. 16·00.
6. Pāṇḍavapurāṇam of Śubhacandra : A Sanskrit Text dealing with
   the Pāṇḍava Tale. Authentically edited with various Readings,
   Hindi Paraphrase, Introduction in Hindi etc. by Pt. Jinadās.
   Published by J. S. S. Sangha, Sholapur. Double Crown pp.
   4-40-8-520. Sholapur, 1954. Price Rs. 12·00.

८४ गणितसारसंग्रह
4. Prākṛta-śabdānuśāsanam of Trivikrama with his own commentary :
Critically Edited with Various Readings, an Introduction and
Seven Appendices ( 1. Trivikrama's Sūtras; 2. Alphabetical Index
of the Sūtras; 3. Metrical Version of the Sūtrapāṭha; 4. Index of
Apabhraṁśa Stanzas; 5. Index of Deśya words; 6. Index of
Dhātvādeśas, Sanskrit to Prākrit and vice versa; 7. Bharata's
Verses on Prākrit ) by Dr. P. L. VAIDYA, Director, Mithilā
Institute, Darbhanga. Published by the J. S. S. Sangha, Sholapur.
Demy pp. 44-478. Sholapur, 1954. Price Rs. 10.00.
5. Siddhānta-sārasaṁgraha of Narendrasena : A Sanskrit Text dealing
with Seven Tattvas of Jainism. Authentically Edited for the first
time with various Readings and Hindi Translation by Pt. JINADAS
P. PHADKULE. Published by the J. S. S. Sangha, Sholapur. Double
Crown pp. about 300. Sholapur 1957. Price Rs. 10 00.
6. Jainism in South India and Some Jain Epigraphs : A learned
and well documented Dissertation on the career of Jainism in the
South, especially in the areas in which Kannada, Tamil and
Telugu Languages are spoken, by P. B. DESAI, M. A., Assistant
Superintendent for Epigraphy, Ootacamund. Some Kannaḍa
Inscriptions from the areas of the former Hyderabad State and
round about are edited here for the first time both in Roman and
Devanāgarī characters, along with their critical study in English
and Sārānuvāda in Hindī. Equipped with a List of Inscriptions
edited, a General Index and a number of illustrations. Published
by the J. S. S. Sangha, Sholapur. Sholapur 1957. Double Crown
pp. 16-456. Price Rs. 16.00.
7. Jambūdīvapaṇṇatti-Saṁgaho of Padmanandi : A Prākrit Text
dealing with Jaina Geography. Authentically edited for the first
time by Drs. A. N. UPADHYE and H. L. JAINA, with the Hindī
Anuvāda of Pt. BALACHANDRA. The Introduction institutes a careful
study of the Text and its allied works. There is an Essay in Hindi
on the Mathematics of the Tiloyapaṇṇatti by Prof. L. C. JAIN,
M. Sc., Jabalpur. Equipped with an Index of Gāthās, of Geogra-
phical Terms and of Technical Terms, and with additional
Variants of Amera Ms. Published by the J. S. S. Sangha, Sholapur.
Double Crown pp. about 500. Sholapur, 1957.

गणितसारसंग्रह ८५
8. Bhaṭṭāraka-sampradāya : A History of the Bhaṭṭāraka Pīṭhas
especially of Western India, Gujarat, Rajasthan and Madhya
Pradesh, based on Epigraphical, Literary and Traditional sources,
extensively reproduced and suitably interpreted, by Prof. V.
JOHRAPURKAR, M. A., Nagpur. Demy pp. 14 + 24 + 326, Sholapur,
1958. Price Rs. 8/-.
9. Prābhṛtādisaṁgraha : This is a presentation of topic-wise
discussions compiled from the works of Kundakunda, the
Samayasāra being fully given. Edited with Introduction and
Translation in Hindi by: Pt. Kailashchandra Shastri, Varanasi.
Published by the J. S. S. Sangha, Sholapur, Demy pp.
10-106-10-288. Sholapur 1960. Price Rs. 6·0.
10. Pañcaviṁśati of Padmanandi : ( c. 1136 A. D. ). This is a collection
of 26 prakaraṇas ( 24 in Sanskrit and 2 in Prākrit ), small and
big, dealing with various religious topics : religious, spiritual,
ethical, didactic, hymnal and ritualistic. The text, along with
an anonymous commentary, critically edited by Dr. A. N. Upadhye
and Dr. H. L. Jain with the Hindi Anuvāda of Pt. Balachandra
Shastri. The edition is equipped with a detailed Introduction
shedding light on the various aspects of the work and
personality of the author both in English and Hindi. There
are useful Indices. Printed in the N. S. Press, Bombay. Double
crown pp. 8-64-284. Sholapur, 1962. Price Rs. 10/-.
11. Ātamānuśāsana of Guṇabhadra (middle of the 9th century A. D. ).
This is a religio-didactic anthology in elegant Sanskrit verses
composed by Guṇabhadra, the pupil of Jinasena, the teacher of
Rāṣṭrakūta Amoghavarṣa. The Text critically edited along with
the Sanskrit commentary of Prabhācandra and a new Hindi
Anuvāda by Dr. A. N. Upadhye, Dr. H. L. Jain and Pt.
Balachandra Shastri. The edition is equipped with Introductions
in English and Hindi and some useful Indices. Demy pp.
8-112-260, Sholapur, 1962. Price Rs. 5/-.
12. Gaṇitasāra Saṁgraha of Mahāvīrācārya ( c.9th century A. D.) :
This is an important treatise in Sanskrit on early Indian
mathematics composed in an elegant style with a practical

८६ गणितसारसंग्रह
approach. Edited with Hindi Translation by Prof. L. C. Jain,
M. Sc., Jabalpur. Double Crown pp. 17 + 34 + 282 + 82, Sholapur,
1963. Price Rs. 12/-.
13. Lokavibhāga of Simhasūri : A Sanskrit digest of a missing ancient
Prakrit text dealing with Jaina Cosmography. Edited for the
first time with Hindi Translation by Pt. Balachandra Shastri.
Double Crown pp. 8-52-256, Sholapur 1962. Price Rs. 10/-.
14. Puṇyāsrava-kathākośa of Rāmachandra : It is a collection of
religious stories in simple snd popular Sanskrit. The text
authentically edited by Dr. A. N. Upadhye and Dr. H. L. Jain with
the Hindi Anuvāda of Pt. Balachandra Shastri. (To be out soon).
15. Jainism in Rājasthān : This is a dissertation on Jainas and Jainism
in Rajasthan and round about area from early times to the
present day, based on epigraphical, literary and traditional
sources by Dr. Kailashchandra Jain, Ajmer. (To be out soon).
16. Viśvatattva-prakāśa of Bhāvasena ( 14th century A. D. ) : It is
a treatise on Nyāya. Edited with Hindi Summary and
Introduction in which is given an authentic Review of Jaina
Nyāya literature by Dr. V. P. Johrapurkar, Nagpur. (To be out
soon).
Works in preparation
Subhāṣita-saṁdoha, Dharma-parīkṣā, Jñānārṇava, Kathākośa
of Sricandra, Dharmaratnākara, etc.
For copies write to :
Jaina Samskrti Samrakshaka Sangha,
Santosh Bhavan, Phaltan Galli,
Sholapur ( C. Rly ) : India