Pramāṇa · Search · About · API

Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t37: Bhāskarācārya

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t37

Language
English

Bhāskarācārya

v2.c12.s2.t37.1

He was a very famous astronomar. Not only is his fame resounding throughout our country for the last 700 years, but it has reached even the foreign countries. A brief account of his work will now be given.

v2.c12.s2.t37.2

He has the Siddhānta Śiromaṇi and the Karaṇa Kutūhala, two astronomical works, to his credit. He writes in the Śiromaṇi.

v2.c12.s2.t37.3

HIS DATE

v2.c12.s2.t37.4

रसगुणपूर्णमही १०३६ समशकनृपसमयेऽभवन्ममोत्पत्तिः रसगुण ३६ वर्षे मया सिद्धांतशिरोमणी रचितः ।। ५८ ।। गोले प्रश्नाध्याये

v2.c12.s2.t37.5

Translation :—

v2.c12.s2.t37.6

“I was born in the Śaka year 1036 and I compiled the Siddhānta Śiromaṇi when I was 36 (58th verse).”

v2.c12.s2.t37.7

This shows that the year of his birth was Śaka 1036 and that he compiled Siddhānta Śiromaṇi when he was in his 36th year. The epoch adopted for the Karaṇakutūhala is Śaka 1105. From this, he appears to have compiled it in that year. He has himself written a commentary named Vāsanābhāṣya on two chapters of the Siddhānta Śiromaṇi, Grahagaṇita and Golādhyāya. At one place (in the chapter on the soli-lunār parallels of declination) in it he observes “I have similarly quoted the ‘Sarakhaṇḍakas’ in the karaṇa work” ; and he has, at some places in the commentary adopted 11° as the ayanāṃśa. This ayanāṃśa value of 11°, according to his view, was true in Śaka 1105. So he seems to have written the commentary about the Śaka year 1105. However, a part of the commentary may have been written before this and some portion may possibly have been written along with the original Siddhānta. He compiled the Karaṇa work in the 69th year of his age and a portion of the commentary also was written then. This speaks of his energy and intelligence at such a ripe age. Such people are very rare in our country at present. His works and other works also contain so much evidence about his date that there is absolutely no doubt about it.

v2.c12.s2.t37.8

ANCESTRY

v2.c12.s2.t37.9

Bhāskarācārya has recorded a brief history of his ancestors and has mentioned the place of his residence in the following verses :—

v2.c12.s2.t37.10

आसीत् सह्यकुलाचलाश्रितपुरे त्रैविद्यविद्वज्जने नानासज्जनवात्रि विज्जडविडे शाण्डिल्यगोत्रो
द्विजः ।
श्रीतस्मार्तविचारसारचतुरो निःशेषविद्यानिधिः साधूनामवधिर्महेश्वरकृती
दैवज्ञचूडामणिः ॥ ६१ ॥
तज्जस्तच्चरणारविन्दयुगलप्राप्तप्रसादः सुधीर्मुग्धोद्धीधकरं विदग्धगणकप्रीतिप्रदं स्फुटम् ।
एतत् व्यवतसद्धुक्तियुक्तिबहुलं हेलावगम्यं विदां सिद्धांतग्रथन कुबुद्धिमथनं चके
कवि भास्करः ॥ ६२ ॥
गोले प्रश्नाध्यायः

v2.c12.s2.t37.11

*Translation :*

v2.c12.s2.t37.12

(61) There was a Brāhmaṇa, Maheśvara by name, and belonging to Śāṇḍilya ‘Gotra’, who lived in the village of Vijjadavida, which was sheltered by the ranges of Sahyadri mountains, and which was inhabited by learned men well versed in the three Vedas. He was the foremost among astrologers and best of virtuous persons, a treasure of all knowledge and skilled in the study of the Śruti and Smṛti works.

v2.c12.s2.t37.13

(62) The poet Bhāskara, who was his son and worshiped his feet was very intelligent and he compiled a Siddhānta work which was aimed at being the enlightener of the ignorant and very much liked by the scholars, which was full of true and clear statements, accompanied by reasoning, which was easily intelligible to learned men and antidote to wrong thinking.

v2.c12.s2.t37.14

It is clear from this that his gotra was Śāṇḍilya ; his father’s name was Maheśvara from whom he got his learning. His place of residence was Bijjadavida, near the Sahyadri mountains.

v2.c12.s2.t37.15

There is a village named Pātan 10 miles S. W. of Calisgaon, in Khaṇḍeś ; at present it is a deserted place. In that village there is a stone inscription* in the Bhavānī’s temple. Cangadeo, a grandson of Bhāskarācārya was an astronomer at the court of king Siṅghana of the Yādava dynasty. This Siṅghana (Siṃha) ruled at Devagiri from Śaka 1132 to 1159. Cangadeo built a math (monastery) at Pātan for the teaching works of Bhāskarācārya and those of his descendants. King Saideva of Nikhumbha dynasty, a feudal king of siṅghana made an endowment for the maintenance of this monastery in Śaka 1129 and his brother, Hemadi, also made a grant. This information can be obtained from the above inscription. Cangdeva has drafted the contents of the inscription, a few years after Śaka 1128. The monastery does not exist now; but one finds traces of its existence. This inscription gives an account of the forefathers and successors of Bhāskarācārya as follows :—

v2.c12.s2.t37.16

∗ The Late Bhau Daji discovered the inscription and published it in the journal of the R. A. So, N. S. Vol. I p. 414 ff. It was again printed well on p. 340 ff, Vol I, of Epigraphia Indica, and Pātan, the name of the village occurs in it.

v2.c12.s2.t37.17

शाण्डिल्यवंशे कविचक्रवर्ती त्रिविक्रमोभूत् तनयोस्य जातः ।
यो भोजराजेन कृताभिधानो विद्यापतिर्भास्करभट्टनामा ॥ १७ ॥
तस्माद्गोविन्दसर्वज्ञो जातो गोविन्दसन्निभः । प्रभाकरः सुतस्तमात् प्रभाकर इवापरः ॥ १८ ॥
तस्मान्मनोरथो जातः सतां पूर्णमनोरथः । श्रीमानमहेश्वराचार्यस्ततोऽजनि कवीश्वरः ॥ १९ ॥
तत्सूनुः कविवृन्दवन्दितपदः सवेदविद्यालता-
कंदः कंसरिपुप्रसादितपदः सर्वज्ञविद्यासदः ।
यच्छिष्यैः सह कोऽपि नो विवदितुं दक्षो विवादी क्वचि—
च्छीमान भास्करकोविदः समभवत्सत्कीर्तिपुण्यान्वितः ॥ २० ॥
लक्ष्मीधराख्योऽखिलसूरिमुख्यो वेदार्थवित् तार्किकचक्रवर्ती ।
ऋतुक्रियाकाण्डविचारसारविशारदो भास्करनन्दोऽभूत् ॥ २१ ॥
सर्वशास्त्रार्थदक्षोऽयमिति मत्वा पुरादतः । जैत्रपालेन यो नतिः कृतश्च विबुधाग्रणीः ॥ २२ ॥
तस्मात् सुतः सिधणचक्रवर्तिदैवज्ञयोऽजनि चङ्गदेवः ।
श्रीभास्कराचार्यनिबद्धशास्त्रविस्तारहेतोः कुरुते मठं यः ॥ २३ ॥
भास्करचितग्रन्थाः सिद्धान्तशिरोमणिप्रमुखाः ।
तद्वंशकृताश्चान्ये व्याख्यया मन्महे नियमात् ॥ २४ ॥

v2.c12.s2.t37.18

*Translation :—*

v2.c12.s2.t37.19

(17) Trivikrama, the best of poets, was born in the Śāṇḍilya family. A son was born to him; he was named Bhāskarabhaṭṭa and was made the ‘Master of learning’ by king Bhoja.

v2.c12.s2.t37.20

(18) From him was born a son Govinda, who resembled Govinda (Lord Kṛṣṇa), from whom was born a son, named Pravākara, who was another Prabhākara (Sun).

v2.c12.s2.t37.21

(19) From him was born Manoratha who was the fulfiller of “manorath’s” (i.e. aspirations) of good men, and the great poet Maheśvara was born from him.

v2.c12.s2.t37.22

(20) His son, a scholar was so great and famous that his feet were worshipped by groups of scholars, he was the fruit borne by the creeper in the form of learning. he was the store of all knowledge, and he attained so much fame and was so great that there could rarely be found any one on earth to debate even with his disciples.

v2.c12.s2.t37.23

(21) Lakṣmīdhara was the son of Bhāskara. He was at the helm of all learned men, who interpreted the Vedas and was the leader of logicians and an expert in the science of ‘mīmānsā’.

v2.c12.s2.t37.24

(22) He being known to be well versed in all sciences was invited by king Jaitrapāla to his court, and was made the leader of all scholars.

v2.c12.s2.t37.25

(23) From him was born a son named Cangadeo, who was the senior most astrologer at the court of Emperor Singhana. He constructed a monastery with the intention of propagating Bhāskarācārya’s works.

v2.c12.s2.t37.26

(24) All the works compiled by Bhāskara, the chief of which was the Siddhāntaśiromaṇi, and also the works compiled by his descendants, are to be regularly studied in my monsatery.

v2.c12.s2.t37.27

Bhāskarācārya’s genealogical table, prepared on the basis of the above verses is given in the margin :—

v2.c12.s2.t37.28

Trivikrama 1 Bhāskara Bhaṭṭa 1 Govinda 1 Prabhākara 1 Manoratha 1 Maheśvara 1 Bhāskara 1 Lakṣmīdhara 1 Canga Deo

v2.c12.s2.t37.29

The gotra and the name of Bhāskara’s father in this agree with those given by Bhāskarācārya himself. According to the inscription, the sixth person upwards from Bhāskarācārya in the table, was the tutor to king Bhoja Bhāskara, the author of Śiromaṇi, was born in Śaka 1036. Reckoning 20 years as the average for a generation, Bhāskara, the tutor of Bhoja, may be taken to have been born in Śaka 936. Hence it was not impossible for him to be the tutor of king Bhoja, the author of Rājamṛgāṅka, who lived in Śaka 964. The inscriptions further says that Lakṣmīdhara, the son of Bhāskara, the author of Śiromaṇi, was invited by king Jaitrapāla to his court and that his grandson, Cangadeo, was astronomer at the Court of Emperor Singhana. Jaitrapāla of Yādava dynasty ruled* at Devagiri from Śaka 1113 to 1132 and his son Singhana ruled from Śaka 1132 to 1169.

v2.c12.s2.t37.30

There is a village named Bahāl, 10 miles north of Calisgaon, in Khaṇḍeś, near the river Girana. There is an inscription in this villge in the temple of goddes Sārajā. According to this inscription, Maheśvara was the son of Manoratha, of Śāṇḍilya gotra; his son was Śrīpati who had a son, named Gaṇapati. His son Anantadeo was the Head Astrologer at the Court of King Sinha (Singhana) of Yādava dynasty. In Śaka 1144, he built the above mentioned temple** of the goddess. It was he who got the inscription carved. This description of ancestry agrees quite well with that given in the Cangadeo’s inscription. The first ancestor named in Cangadeo’s inscription, is the author of the work, ‘Damayantī Kathā’.

v2.c12.s2.t37.31

*See Prof. Bhandarkar’s History of the Deccan, (English) p. 82. **This inscription is reproduced on p. 112, Vol. III, Epigraphia Indica. The inscription states Dwārajā to be the name of the goddess.

v2.c12.s2.t37.32

THE PLACE OF RESIDENCE

v2.c12.s2.t37.33

Bhāskarācārya has not stated that he was patronised by any king, nor do we get such information in either of the two inscriptions. According to his statement, Vijjalaviḍa, was the place of his residence. The last two letters of this word suggest that Biḍ might have been the place. But Biḍ is a place in the Nizam state, 80 miles to the east of Ahmedanager. It is not situated near the Sahyadri ranges, and it is learnt from enquiry that there are no descendants of Bhāskarācārya living there at present. The Līlāvatī of Bhāskara was translated in Persian, by Akbar's orders in 1587 A.D. (Śaka 1509). The translator has stated in it that the birth place of the author was Bidar in the Deccan. Bidar is a place about 100 miles to the east of Sholapur* in the Nizam State, but it is not near the Sahyadris. It is a place 30 miles to the east of the well known city of Kalyan. The kings of the cālukya dynasty were ruling at Kalyan at the time of Bhāskarācārya. Even though such a great kindgom existed so near, nothing is mentioned anywhere about the association of Bhāskarācārya with it. From this, we may conclude that Bidar was not Bhāskarācārya's place of residence.

v2.c12.s2.t37.34

It is stated in the 22nd verse of the Canga Deo's inscription that “king Jaitrapāla called Lakṣmidhara, son of Bhāskarācārya from the town, ‘Pātan’. The village of Pātan is very near to Devagiri (Daulatabad), the capital of the Yādava Kings and it is near the Candwad hills which are off shoots of the Sahyadris; that is, it is “sheltered by the Sahyadri range”, in the words of Bhāskarācārya. The village of Bahāl where Anant-Deo, a descendant of Bhāskara built the temple, is only about 20 miles from Pātan. This shows that Bhāskarācārya's original place of residence was, beyond doubt, the village Pātan itself or some village near it bearing some such name as Vijjalaviḍa. It is not known at present.

v2.c12.s2.t37.35

Subject matter of Siddhānta Śiromaṇi

v2.c12.s2.t37.36

The Siddhānta Śiromaṇi is divided into four main parts which are also called Chapters. Each part has a number of chapters in it. The first part is termed as the ‘Pāṭīgaṇita’ or Līlāvatī, by the author. This can be said to be an independent work on arithmetic and mensuration.. It consists of about 278 verses. In between are also given explanations of examples in prose. In the beginning are given in it some tables of various measures; next follow the terms for the places of digits in a number up to ‘parārdha’ which is the 18th place. Next come the eight fundamental operations, addition, subtraction, multiplication, division, square and square root, and cube and cube root. They are termed ‘parikarmāṣṭaka’. Then come subjects like, fundamental operations for fractions and those for zero, ‘iṣṭakarma’ (unitary method), rule of three, rule of five, progressions etc. Similarly, these are followed by areas and volumes of different figures and solids. Next come subjects like ‘kuṭṭakagaṇit, pākṣika viparyaya and sarvāṃśika viparyaya”, amongst which is given an example of special importance. “A peacock was sitting on a pole, 9 cubits in height. It saw a serpent at a distance of 27 cubits, approaching a hole at the foot of the pole. It jumped to catch the serpent. Both moved at the same speed. How far away from the pole will they meet?” The answer given is ‘12 cubits away from the pole’. This answer is correct if the peacock is supposed to have flown along the hypotenuse of the right angled triangle i.e. 15 cubits in a straight line. But it is worthnoting that the important mathematical idea that the path of a flying peacock would be a curve much different from the circumference of a circle which is not found in other Sanskrit works, had occurred to Bhāskarācārya. It is needless to say that such popular beliefs as that one can count the leaves of a tree by studying Līlāvatī, are baseless ; but they indicate people's reverence for the work. The second part of the work is known as ‘ bījagaṇita ’ (Algebra). It contains the following subjects :— the addition etc. of positive and negative numbers, of unknown quantities and of surds. Then come the chapters on subjects like ‘ kuṭṭaka ’ and ‘ varga-prakṛiti ’, simple equations of one unknown quantity, simultaneous equations of more than one unknown and equations involving squares and higher powers of one or more unknown quantities. This consists of about 213 verses in all, with some prose portions in between.

v2.c12.s2.t37.37

¹ *See Pott's Algebra (1886) Sec. II.

v2.c12.s2.t37.38

The parts known as ‘ golādhyāya ’ and ‘ gaṇitādhyāya ’ are devoted to astronomy. The first part treats of all subjects related to planetary calculations which have been mentioned in the list of Adhikāra given in the Introduction. The number of verses in it, including those in the commentary, is stated to be 4346. The part known as ‘ golādhyāya ’ deals with the theory of all questions discussed in the ‘ gaṇitādhyāya ’, a description of the three worlds, a chapter on instruments of observation etc. The number of verses mentioned is 2100. In the end is given a very short but important chapter named “ jyotpatti ”. In the middle is given a short chapter entitled ‘ description of seasons ’ ; it has been compiled by Bhāskarācārya only to exhibit his poetic gift.

v2.c12.s2.t37.39

His Capability

v2.c12.s2.t37.40

Bhāskarācārya has adopted from the Brahmasiddhānta the numbers of revolutions and other elements of all planets given in the chapter on mean places and the degrees of epicycles in the chapter on true places. The corrections to be applied to mean positions of planets have been taken in toto from the work ‘ Rājamṛgāṅka ’. Even the precessional motion has been taken from earlier works. In short, there is nothing new in Bhāskarācārya's works which is obtainable by observation ; but his work is full of knowledge obtainable only after deep study. This sort of knowledge is the origin of the theory of the Science of astronomy. The work Siddhāntaśiromaṇi has reached such a high degree of excellence on account of various simplified methods and the explanation of their underlying theory, covering all subjects from the trifling calculation of planets' places from ‘ ahargaṇa ’ to ‘abstruse questions like that of parallax and the sine theory, that we can really understand the essence of Indian astronomy by reading even this single work ; and it appears that it is on account of this Bhāskarācārya became so very famous. Several works of varying quality might have been thrown into the background because of this work. In view of the fact that even the Brahma Siddhānta which was revered by Bhāskarācārya like a preceptor, was surpassed by Bhāskara Siddhānta, one can easily guess how many other authors might have been consigned to oblivion because of Bhāskara's works. The period from Āryabhaṭa I to Bhāskarācārya is regarded as the most brilliant period so far as the development of Indian Astronomy is concerned. It is during this period that the Khaliphs of Baghdad in their days of prosperity invited astronomers from India, got the Hindu works translated into Arabic and Latin, and the Arabs and Greeks became disciples of Hindus. It was in this very period that the problem of ‘ Ayana ’ motion was fully studied. Several authors of works might have flourished in this flourishing period of astronomy ; but some of them are now known only in name, while some others are not even so lucky. It is no doubt due to the march of time ; but it is felt at the same time that Bhāskarācārya was responsible for this to a great degree. No other author of equal calibre was born after him. Bhāskarācārya’s works are well known in every nook and corner of the sub-continent of India. Not only this, but they have been, translated also even in foreign languages. But it is the misfortune of our country that such a genius failed to make any of the important discoveries made in Europe in modern times or even lay the foundation of at least one of them. Bhāskarācārya did not make any efforts in respect of observation. The author inclined to believe even from his meagre experience that if he had done it, his intelligence which was devoted to the task of merely explaining theories like a commentator would have definitely been diverted to new discoveries.

v2.c12.s2.t37.41

His works contain nothing new ; still, because he has devoted all his intellectual power to theory, his works do contain some new discoveries which are obtainable by study and not by observation. To him the knowledge of the sphere was at his fingure’s ends. He has suggested a number of new methods in the chapter on three problems and has shown his ingenuity in dealing with several questions in them. Earlier astronomers had not described, in their study of the gnomon, the method of calculating the length of the shadow in any whatever direction but he alone has described it. He has remarked, “ Earlier astronomers had been labouring under a delusion in respect of the calculation of the Mahāpāl (Soli-lunar parallel of declination); 1described the correct method”. Earlier astronomers appear to be regarding the arc of the latitude to be lying along the declination circle, that is perpendicular to the equator but he has clearly shown that latitude is perpendicular to the ecliptic. The correction known as ‘ udayantar ’ is one of his discoveries. It is briefly described here :—

v2.c12.s2.t37.42

“ When finding planets’ places from the ahargaṇa, the days are all supposed to be of equal length ; but actually they are not so. Even at the equator, the days are somewhat longer or shorter than 60 ghaṭis (i.e. 24 hours) and this causes the difference between the moments of mean and true sunrise. The places of planets calculated from the ahargaṇa are true for mean sun rise. To deduce their places true for the true sunrise, earlier writers have prescribed the corrections known as ‘ bhujantar ’ and ‘ cara ’. Bhāskarācārya has prescribed one more correction known as ‘ udayantara ’. The sun’s motion in the ecliptic is not always uniform. The time of true sunrise differs from the time of mean sunrise according to the equation of centre, that is, the difference between the true and mean longitude of the sun. The correction due to this is called ‘ Bhujantar ’. The earth rotates round its axis : it rotates in the plane of the equator and not in that of the ecliptic. It is on account of this fact, that the 30° arc of the ecliptic does not always require the same time to come above the horizon as an equal arc of the equator. The correction necessary to cover this irregularity has been called ‘Udayantara’ by Bhāskarācārya and this correction is evidently necessary to be applied. The corrections of ‘ bhujantara ’ and ‘ udayantara ’ together are included into one term called “ the equation of time ” by the European astronomers. Thus Udayantara was one of the discoveries of Bhāskarācārya. Ranganātha, the commentator of the Sūrya Siddhānta has attempted to show in his commentary on the 59th chapter that this correction was desired by the author of the Sūrya Siddhānta and has remarked that the author had not mentioned it as it was very small. The author of the Siddhāntatatvaviveka has attempted to refute Bhāskarācārya’s argument about the need of the adoption of this correction of ‘ udayantara ’, but this attempt has proved futile as it shows sheer obstinacy. The Siddhānta-śiromaṇi discusses new trivial questions other than that of ‘ udayantara ’ and has in the discussion pointed out at two or three places, Brahmagupta’s error’.

v2.c12.s2.t37.43

Karaṇa Kutūhala

v2.c12.s2.t37.44

The Karaṇa work, Karaṇa-Kutūhala, has adopted Śaka 1105 as the epoch year. The moment of sunrise on Thursday, the new moon day of Phālguna of Śaka 1104, is the epoch for which the positions are given. The mean places have been calculated from ahargaṇa. Bhāskarācārya regards his work as comparable to Brahma Siddhānta, as a matter of fact, it is so, only when the corrections recommended by Rājamṛgāṅka are applied. It is also called “ Grahīgamakutūhala ”. It was very well known. Some persons use this for calculation even now. It has already been pointed out that the figures claimed by the author of the Grahalāghava, as belonging to Brahmapakṣa, have been taken from this work. There is a voluminous work called “ Jagaccandrikāsāraṇī ” containing tables which are used to calculate planets’ places according to this work. The Karaṇa Kutūhala contains the following ten Adhikāras (chapters) (i) mean places (ii) true places (iii) three problems (iv) lunar eclipse (v) solar eclipse (vi) rising and setting (vii) elevation of moon’s cusps (viii) conjunction of planets (ix) Mahāpāta (x) pūrvasambhava (possibility of eclipses). These respectively contain 17,23,17,24,10,15,5,7, 16 and 5 verses, making 139 verses in all.

v2.c12.s2.t37.45

Commentaries

v2.c12.s2.t37.46

No other astronomical work can boast of having so many commentaries on them as the works of Bhāskarācārya. Some of them deal with all the four sections of the Siddhāntaśiromaṇi. Some others are written on only the first part called Līlāvatī, some on only the second part known as ‘ Bījagaṇita ’ and still others deal with the two parts ‘ grahagaṇitādhyāya ’ and ‘ golādhyāya’. The commentaries on Līlāvatī are mentioned below :—

v2.c12.s2.t37.47

Gaṅgādhara, the son of Govardhana and a resident of Jambusara, has written a commentary called ‘ Gaṇitāmṛtasāgarī ’; it probably belongs to Śaka 1342. This was also known as ‘ Aṅkamṛtasāgarī ’, and the Aufrecht catalogue states that Lakṣmīdhara was another name of Gaṅgādhara. Gaṇeśa Daivajñya, the author of Grahalāghava, wrote his commentary known as ‘ Buddhavilāsinī ’, in Śaka 1467. Dhaneśvara Daivajñya has written a commentary called ‘ Līlāvatibhūṣaṇa ’. Mahidāsa has written one in Śaka 1509. The commentary known as Līlāvativivṛtti has been written by Munīśvara in about the year 1557. The commentary by Mahidhara, as Līlāvativivaraṇa, refers to Munīśvara ; from this it appears to have been written after Śaka 1557. The Aufrecht Catalogue mentions the following additional commentaries :—

v2.c12.s2.t37.48

The ‘ Gaṇitāmṛta Lahari ’ by Rāmakṛṣṇa, son of Nṛsimha, (1339 A.D.); the Pāṭīgaṇita kaumudī, a commentary by Nārāyaṇa, son of Nṛsimha (1357 A.D.). Manoranjanā by Rāmkṛṣṇadeo, son of Sadādeva ; The Līlāvatī-bhūṣaṇa by Rāmacandra ; Nisṛṣṭadūtī by Viśvarūpa ; Gaṇitāmṛtakūpikā by Śuryadāsa ; the Udāharaṇa by Candraśekhara Patanāyak ; Udāharaṇa by Viśveśvara and commentaries by Dāmodara, Devisahāya, Paraśurāma Rāmadatta, Lakṣminatha, Vṛndāvana, Śridhara Maithila etc. Of these, the “ Nisṛṣṭadūtī ” commentary appears to belong to Munīśvara, because Viśvarūpa was another name of Munīśvara.

v2.c12.s2.t37.49

The commentaries on ‘Bījagaṇita’ :—The commentary known as Bījanavānkura by Kṛṣṇa, the famous astronomer at the court of Emperor Jāhāngīr was written in about Śaka 1524. It is also known as Bījapallava and Kalpalatāvatāra. It is very extensive. There is a commentary known as Bījaprabodha written by Rāmakṛṣṇa, son of Lakṣmaṇa, who was the son of Nṛsiṃha Deo of Amraoti. This Rāmakṛṣṇa calls himself a disciple of Munīśvara. From this it appears that it belongs to about Śaka 1570. The Aufrecht catalogue mentions “Bījavṛttikalpalatā” by Paramasukha, and ‘Udāharaṇa’ by Kṛpārāma, as additional commentaries.

v2.c12.s2.t37.50

Gaṇeśa Daivajñya, author of the Grahalāghava, has written a commentary on “Grahaṇitādhyāya and Golādhyāya”. Gaṇeśa, the great grandson of Gaṇeśa Daivajñya, the author of the Grahalāghava, wrote a commentary known as ‘Śiromaṇi Prakāśa, about Śaka 1500. The commentary known as Vāsanākalpalatā or Vāsanāvārtika by Nṛsiṃha, a resident of Golagrām, belongs to Śaka 1543. The Marīci commentary by Munīśvara or Viśvarupa is very extensive and the best one. It was written in Śaka 1557. Siddhāntasūryodaya, a commentary by Gopinātha, brother of Raghunātha and son of Bhairava, was written after Śaka 1450.

v2.c12.s2.t37.51

The following are the commentaries on the complete work of Siddhāntaśiromaṇi :—Sūryadāsa, son of Jñyānarāja, has written a commentary known as Sūryaprakāśa on all the four sections. The part of this commentary relating to Līlāvatī and Bīja was written in Śaka 1460. Paramādiśvara, the commentator of Āryabhaṭa I, is said to have written a commentary called Siddhāntadīpikā on the works of Bhāskarācārya. It appears to have been written on all the four sections. The commentary “Mitabhāṣiṇī”, by Ranganātha, son of Nṛsiṃha, a resident of Golagrām, was written soon after Śaka 1580.

v2.c12.s2.t37.52

The Aufrecht Catalogue mentions the following additional commentaries :—The ‘Gaṇitatatvacintāmaṇi by Lakṣmidāsa, son of Vācaspati (1501 A.D.) The Udāharaṇa, by Viśvanātha; and the commentaries by Rājagiripravāsī Cakracuḍāmaṇi, Jayalakṣmaṇa or Jaya Lakṣmi, Maheśvara, Mohandāsa, Lakṣminātha, Vācaspatimitra (?) and Harihara. Most of them might be confined to Grahaṇitādhyāya and Golādhyāya only.

v2.c12.s2.t37.53

The Karaṇa Kutūhala, has been commented upon by Soḍhala, by Padmanābha, son of Nārmada, and by Śaṅkar kavi. The last commentary has adopted Śaka 1541 as the year for its examples. There is a commentary dated Śaka 1482, which contains an example; the commentator was a resident of Unnata Durga. The place has 4-48 as the palabhā and 60 yojanas west, as deśāntar (longitude). The Aufrecht Catalogue mentions the following additional commentaries :—Gaṇitasār conforming to Brahmasiddhānta and written by Keśavārka; ‘Gaṇakakumudakaumudī’ by Harṣagaṇita; the Udāharaṇa by Viśvanātha, and the commentary by Ekanātha.

v2.c12.s2.t37.54

There may be* many more commentaries on Bhāskarācārya’s works. The Līlāvatī was translated in Persian in Śaka 1509 and the Bīja in Śaka 1597. Colebrooke has published the English translation of Līlāvatī and Bījagaṇita in 1817 A.D. Paṇḍit Bāpudeva Śāstri published an English translation of Golādhyāya in the Bibliotheca Indica in 1861 A.D. The translation contains a number of notes. All parts of Śiromaṇi and the Karaṇakutūhala have been printed at several places in our country.

v2.c12.s2.t37.55

∗ The author has taken the information about some of the commentaries enumerated above from other books. He has not seen all the commentaries personally.

v2.c12.s2.t37.56

Mādhava (Śaka 1185) the commentator of Ratnamālā, and other writers have mentioned, ‘Bhāskarvyawahāra,’ a work on Muhūrta. It may be a work by Bhāskarācārya. A verse of Bhāskara has been quoted in connection with marriages in the commentary on Vivāhapaṭala by Rāma (Śaka 1446). A reference to the work Vivāhapaṭala by Bhāskara was also found in the ‘Śārṅgiya’ Vivāhapaṭala and in other one or two works; and a small volume named Bhāskaravivāhapaṭala which is in the Deccan College collection, gives no information other than the author’s name. It appears however, that Bhāskarācārya might have written a work entitled “ Vivāhapaṭala ”.

Cites (19)