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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t48: Gaṇeśa Daivajñya

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t48

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English

Gaṇeśa Daivajñya

v2.c12.s2.t48.1

He was a very famous astronomer. The astronomical works of no other astronomer are in use all over India at present as those of Gaṇeśa Daivajñya.

v2.c12.s2.t48.2

His father's name was Keśava, mother's name Lakṣmi, Kauśika his gotra and Nāndgāon, on the western sea-coast, his place of residence. These facts havlready been stated above.

v2.c12.s2.t48.3

Viśvanātha, in his commentary “Viśvanāthī” on Graha Lāghava, observes, “the works which Gaṇeśa Daivajñya, my preceptor compiled, have been enumerated by his nephew, the astronomer Nṛsiṃha, in two verses in his commentary on Grahalāghava. They are :—

v2.c12.s2.t48.4

कृतवादौ ग्रहलाघवं लघुबृहत्तिथ्यादिचिंतामणी ॥
सत्सिद्धान्तशिरोमणौ च विवृतिं लीलावतीव्याकृतिं ॥
श्रीवुं दावनटीकां च विवृतिं मौहूर्ततत्वस्य वै ।
सत्श्राद्धादिविनिर्णयं सुविवृतिं चंद्रोर्णवाक्यस्य वै ॥ १ ॥
सुधीरंजनं तर्जनीयंत्रकं च सुकृष्णष्टमीनिर्णयं होलिकाया
लघुपायपातस्तथान्याः..........”

v2.c12.s2.t48.5

*Translation :*—Gaṇeśa Daivajñya appears to have compiled the following works :—The Grahalāghava, the Laghutithi Cintāmaṇi, the Bṛhattithi-cintāmaṇi, the Siddhāntaśiromaṇīṭīkā, the Līlāvatīṭīkā, the Vivāhavṛndāvanatikā, the Muhūrtatatvaṭīkā, the Śrāddhanirṇaya, the Candorṇavaṭīkā, the Tarjaniyantra, the Kṛṣṇāṣṭamīnirṇaya, the Holikānirṇaya, the Laghupāyapāta (i.e. a table for calculating Mahāpāta), etc.

v2.c12.s2.t48.6

Even Gaṇeśa has himself mentioned the names of some of his works in his work, *Vivāhavṛndāvanatikā*. They are,

v2.c12.s2.t48.7

कृतवादौ ग्रहलायवकरणं तिथ्यादिसिद्धद्वयं
श्लोकैः श्राद्धविधिं सवासनतया लीलावतीव्याकृतिं ॥
सप्रेक्षमुहूर्ततत्वविवृतिं पर्वादिसन्निर्णयं ॥
तस्मान्मंगलनिर्णयाद्यथ कृता वैवाहसदीपिका ॥

v2.c12.s2.t48.8

*Translation :*—(Not necessary)

v2.c12.s2.t48.9

This list mentions the additional work, Parvanirṇaya. It is not that these works have been mentioned in their chronological order. Still, the Grahalāghava appears to have been compiled first. In this work, Śaka 1442 has been adopted as the epochal year for planetary calculation. At this time he must have been at least 20/22 years of age. In other words his date of birth may have been about Śaka 1420. The work *Laghucintāmaṇi* was written in Śaka 1447 and the Līlāvatīṭīkā in Śaka 1467. The *Pātasāraṇi* shows that it was compiled some time after Śaka 1460. The author has seen a printed Edition of Vṛndāvanatikā and it has mentioned its date of compilation in a curious way. It is given thus :—

v2.c12.s2.t48.10

The Dates

v2.c12.s2.t48.11

हायनार्क १२ लवंतुल्यमायनं तद्युतीरस ६ युता युतिर्भवेत् ॥
सापि सागर ४ युतोऽपोद्धृतं तत्त्रिनेत्र २३ लव एव पक्षकः ॥ १ ॥
पक्षः सपक्ष २ यदि वासरः स्यात् तदीयरामां ३ शसमस्तिथिः स्यात् ॥
यच्चाखिलैक्यं * कुयमा २१ हतं तत् नंदा ९ धिकं मत्सवत्सराः स्युः ॥
तद्यनतिथिपक्षस्तुल्यतां यांति यस्मिन्.........॥

v2.c12.s2.t48.12

∗ (Samvatsara 12th + Ayana 1st + Yoga 19th + Naksatra 23rd + Paksa 1st + Week day 3rd + Tithi 1st + Month 11th) × 21 + 9 = 1500.

v2.c12.s2.t48.13

Translation :—"Take 12 as the number for the saṃvatsara (hāyan). Add one (lava) for ‘ayana’ to it. Add 6 to the sum of these two numbers (i.e. 12+1), so as to obtain (19) as the number of Yoga. Add 4 to the sum which would give 23 as the number of nakṣatras and one (lava) for the pakṣa. If, a pakṣa is added to one more pakṣa (i.e. 1+2) it would give 3 as the number denoting the week day. Take 1 as the tithi number and 11 as the month number. Multiply the sum of all these numbers by 21 and increase the product by 9 (nanda). The result is the Śaka number".

v2.c12.s2.t48.14

From this we learn that the commentary was completed on Māgha Śukla Pratipada of Śaka 1500, Bahudhānya Saṃvatsara, during Uttarayaṇa, Dhaniṣṭhā, being the nakṣatra and Parigha, the yoga. The calculation for the first lunar day of the bright half of Māgha, in Śaka 1500, shows that it agrees with the given day of the week, nakṣatra and yoga. If this was nearly the time of the compilation of the Vivāhavṛndāvanaṭīkā, the author, must have been about 80 years old. Even it be supposed that he compiled the Grahalāghava at the age of 16, his age still comes to be 75 years. This is not an impossibility. The author however, found a manusript copy of the Vivāhavṛndavanatikā with Raghunātha Jośī at the authors’ birth place, the village of Murud in Dapoli tāluka in Konkan, which mentions the date of compilation in the simple line, “Rasanagamanatulye śaka Ānanda varṣe” “meaning”, in the śaka 1476, named, “Ānanda Saṃvatsara”. This appears to be reliable. The verse “hāyanārka etc……” must have been written by some one else.

v2.c12.s2.t48.15

GRAHALĀGHAVA

v2.c12.s2.t48.16

The Grahalāghava has adopted Śaka 1442 as the epochal year. The positions have been given true for the moment of sunrise of Monday, the New Moon day of the Phālguna of Śaka 1441 (i.e. the 19th March, 1520 A.D.): They are as follows :—

v2.c12.s2.t48.17

| Planet | s | ° | ' |
| Sun | 11 | 19 | 41 |
| Moon | 11 | 19 | 6 |
| Moon’s Apogee | 5 | 17 | 33 |
| Moon’s node | 0 | 27 | 38 |
| Mars | 10 | 7 | 8 |
| Mercury (mean commutation)* | 8 | 29 | 33 |
| Jupiter | 7 | 2 | 16 |
| Venus (mean commutation) | 7 | 20 | 9 |
| Saturn | 9 | 15 | 21 |

v2.c12.s2.t48.18

∗ The “mean commutation” means the distance of the mean planet from the mean Sun.

v2.c12.s2.t48.19

Gaṇeśa Daivajña states how the planets would agree with the positions calculated from ancient works :—

v2.c12.s2.t48.20

सौरौकौपिविधूच्चमंकलिकोनाब्जो गुरुत्वायजो- ।।

ऽसूग्राह च कुजज्ञक्रेकमथार्यः सेषुभागः शनिः ।।

शौक्रचं केंद्रमजायंमध्यगमितीमे यांति दृक्तुल्यतां ।।

v2.c12.s2.t48.21

मध्यमाधिकार.

v2.c12.s2.t48.22

Translation :—(not necessary, since the sense is given in the following para). The places calculated for Sunrise on Monday, the New Moon day of Phālguna of Śaka 1441, according to the instructions given above agree completely. That is, calculated from the modern Sūrya Siddhānta, the places of the Sun, and the Moon’s apogee and that of the moon diminished by 9 minutes would agree with the positions given above. Calculated from the Karaṇaprakāśa of the Āryapakṣa, the places of Jupiter, Mars, the Moons' node and that of Saturn increased by 5°, would agree with the positions mentioned above. The anomaly of Mercury agrees with that calculated from the Karaṇakutūhala of Brahmapakṣa; and the anomalies of Venus, as calculated from Karaṇaprakāśa and Karaṇakutūhala agree with the above position when added up and halved. Gaṇeśa has, however, left out seconds of arc in all the position and increased or decreased the minutes in some cases ; hence, in certain cases, there is some discrepancy as far as minutes of arc are concerned. While calculating the places mentioned above, the ahargaṇa for Karaṇaprakāśa comes to 156334 and that for Karaṇakutūhala to 123113*. It is obvious how very laborious it would be to make calculations with these figures of ahargaṇa. Gaṇeśa has advocated the method of calculating planets' places from the ahargaṇa itself ; but he has employed a device by which the ahargaṇa figure is not allowed to increase too much. He has assumed a cycle of the ahargaṇa of 4016 days, since this happens to be the approximate number of days in the period of 11 years; and the planet's mean motion during this period is termed the "dhruva'. The application of this motion** gives the mean place. The ahargaṇa never exceeds the number 4016 because of this device.

v2.c12.s2.t48.23

HIS SPECIALITY

v2.c12.s2.t48.24

Another speciality of the Grahalāghava is that it has done away with the use of sines and arcs. Inspite of this there is absolutely no harm in saying that this work gives results by no means less accurate than those obtained from any of the earlier Karaṇa works. Modern English works give tables of sines not only for each degree, but even for each minute of arc ; and some works are so compiled that they give the sines of even seconds of arc. Our works give sines of angles of 3¾ degrees and their multiples. Thus, the number of tabular sines is 24 ; but the karaṇa works generally give only 9 (at an interval of 10°) or even less. Even though the Grahalāghava has not used the sines, the method of finding the sun's true places, as adopted by Grahalāghava, gives a value even more accurate than that obtained from other Karaṇa works making use of sines ; not only this, but in some cases it gives more accurate values than those Siddhānta works which contain the values for 24 tabular sines. Gaṇeśa has been on the whole, very keen on seeing that the calculations at all stages would be easily done.

v2.c12.s2.t48.25

∗ No commentator has pointed out just as the author has done, the particular works from which the different planetary places have been derived by Gaṇeśa Daivajña.

v2.c12.s2.t48.26

∗∗ The period of 11 years gives a variable number of days ; and the author has so adopted the device that the error corresponding to this variation would not escape.. The explement of the planet's motion in the cycle is given; if this explement subtracted from the epochal position and the motion for the ahargaṇa added to the remainder, the mean position of the planet for the given moment.

v2.c12.s2.t48.27

It is true that because of this, certain results turn out to be somewhat approximate, but the other karaṇa works also do not fare any better in this respect. In the conclusion Gaṇeśa remarks.

v2.c12.s2.t48.28

पूर्वं प्रौढतराः क्वचित् किमपि यत् चतुर्थुज्ये विना
ते तेनवै महातिगर्वंकुमुद्गगेऽधिरोहंति हि ॥
सिद्धांतोक्त मिहाखिलं लघुकृतं हित्वा धनुज्यै मया
तदगर्वो मयि मास्तु किं न यदहं तच्छास्त्रतौ वृद्धधीः ॥

v2.c12.s2.t48.29

*Translation* :—(not necessary, since the sense is given in the next para).

v2.c12.s2.t48.30

The purport of these verses is "Earlier and more advanced astronomers did their calculation work without chords and sines only in very rare cases, and still they boasted *on that account, why then should not the writer (Gaṇeśa) feel proud like them, since he effected the whole calculation of the Siddhānta work without sines and arcs ? But he ought not to boast because he obtained this knowledge only from their works. Gaṇeśa is right in claiming that he incorporated in the Grahalāghava every subject dealt within the Siddhāntas, and that is why, the Grahalāghava came to be known as "Siddhāntarahasya". A number of Karaṇa-works have been found and many of them treat the method of finding the true places of planets only. There are only three or four works like the Karaṇa-Kutūhala which help in calculating most of the items metnioned in the Siddhānta’s but none of them is as complete and exhaustive as the Grahalāghava. A commentary on this work was compiled by Gaṅgādhara in Śaka 1508 by Mallāri in Śaka, 1524 and by Viśvanātha about Śaka 1534. There are also some more commentaries on it. The author got at Bārśī a copy of the Grahalāghava written in Śaka 1605. It shows that the Grahalāghava very soon came into extensive use, in the country. At present, they make calculations from the Grahalāghava alone in Mahārāṣṭra, Gujerat and many parts of Karnatak. This very work** is used by the Deccanis at Vārānasi, Gwalior and Indore. This work appears to be in use in other provinces also. As the methods of calculation in this work are very simple and satisfy the needs of Siddhānta work, they very soon came into extensive use everywhere and it was also natural that they eclipsed the earlier Karaṇa works.

v2.c12.s2.t48.31

PLANETARY CORRECTIONS

v2.c12.s2.t48.32

The following table will show how the places of planets, true for the beginning of Śaka 1442, and calculated from the Grahalāghava, are compared with those calculated from the European works, the basis of comparison being their elation to the Sun.

v2.c12.s2.t48.33

∗ In the Adhikāra (Section) on Three Problems in his Karaṇa Kutūhala, Bhāskarācārya observes. "इति कृतं लघुकार्मुकशिनिजनीग्रहणकर्म विना वृतिसाधनं ॥ १२ ॥", "this calculation of shaddow (chāyā udynti) has been effected without the help of sines and arcs"

v2.c12.s2.t48.34

∗∗ The Government Almanacs published at Indore and Gwalior are calculated with the helf of the Grahalāghava and the Tithi Cintāmaṇi, and are used practically every where in the two States. The Grahalāghava almanac is used in the major part of Hyderabad Deccan State.

v2.c12.s2.t48.35

| Planet | ° | ' |
| Sun | 0 | 0 |
| Moon | -0 | 2 |
| Moon's apogee | +1 | 55 |
| Moon's node | -0 | 17 |
| Mars | +0 | 44 |
| Mercury's Śīghrocca | +8 | 21 |
| Jupiter | +0 | 58 |
| Venus's Śīghrocca | +1 | 22 |
| Saturn | +1 | 29 |

v2.c12.s2.t48.36

It appears from this that Mercury's place is very erroneous. The places of Venus, Saturn and Moon's apogee show a discrepancy of 1° to 2°. Others show a difference within 1°. The Moon's place is remarkably correct. The place of the Moon's node is not very erroneous. Gaṇeśa's father, Keśava, has already mentioned in the account of his work, about his claims that he ascertained the place of the Moon and Rāhu from the Solar eclipse. It appears that there is such a serious discrepancy in Mercury's place, because, Mercury is not easily observable as it is visible only for a few days in the year. Another fact that must be remembered is that the above errors occur in the mean places of planets. But only the true places of planets are found by actual observation. While considering Bentley's method, it has already been shown on page 30, that the discrepancy in the actual places of planets at the time of the Grahalāghava might have been much less. It has been shown later on in almanacs what is the extent of error seen at present while calculating figures from the Grahalāghava.

v2.c12.s2.t48.37

Gaṇeśa observes that the places of planets calculated from certain works tally with their observed places on application of certain corrections; accordingly he has suggested a correction of 5° for Saturn's place, which is very excessive. Similarly he has proposed a correction of some minutes of arc in the case of other planets also. It is quite obvious, therefore, put forwarded the names of ancient works only by way of nominal support while recording the actual positions of planets in his own time.

v2.c12.s2.t48.38

Keśava, Gaṇeśa's father had almost prepared the ground for applying corrections to old works by taking observations, as he had noticed discrepancies in the planets' places obtained from the earlier works, and he compiled the Graha Kautuka accordingly; Gaṇeśa observes in Laghu Cintāmaṇi that he finally corrected the planets after observing the loopholes still left in that work. A comparison of Graha Kautuka and Grahalāghava would confirm this statement. In the Chapter on the risings and settings, in Grahalāghava, he remarks :—

v2.c12.s2.t48.39

पूर्वोक्ता भृगुचंद्रयोः क्षणलवाः स्पष्टा भृगोश्चोनिता ।।
द्राम्यां तैरुदयास्तदृष्टिसमता स्याल्लक्षितैपा मया ।। २० ।।

v2.c12.s2.t48.40

Translation :—(not necessary)

v2.c12.s2.t48.41

In this he says that it was his experience that the moments of risings and settings of Venus are found to be true when the kālāmśas mentioned by earlier astronomers are diminished by two. All these things go to prove that he was himself an observer. One of the legends that has become quite current about him, says that it was not necessary for him to look to the ground, while walking, because his feet had got eyes. This is of course, an impossibility. Still it goes to show that his attention was always directed to the sky while walking. Another legend says that he was always found to be gazing at the sky while sitting on huge slabs of stone on the seashore. This was quite possible. Many such slabs are found on the sea coast in Kankan and it is very convenient to take observations while sitting in such quiet places.

v2.c12.s2.t48.42

Calibre

v2.c12.s2.t48.43

Gaṇeśa was perhaps able to produce a work like the Grahalāghava which proved more accurate in the light of observation than Graha Kautuka, because his own experience was coupled with that of his father; and although the methods described in Graha Kautuka are, in some cases, more convenient than those of Grahalāghava, still, in certain other matters, the Grahalāghava is found to be more convenient. Hence, Graha Kautuka may have gone out of use giving place to Grahalāghava. Considering all things I am inclined to think that his father was more competent than Gaṇeśa himself. However, looking only to the utility of the works the Grahalāghava is certainly superior because the experience of both father and son have been combined in that work.

v2.c12.s2.t48.44

The Grahalāghava contains chapters on the following 14 subjects:—(1) Mean places (2) True places (3) Places of five planets (4) Three problems (5) Lunar Eclipse (6) Solar Eclipse (7) “Māsagaṇagrahana” (8) Approximate places of planets (9) Risings and settings (10) Shadow (11) Shadow of stars (12) Elevation of Moon’s Cusps (13) Conjunctions of planets (14) Mahāpāta. They contain respectively 16, 10, 17, 26, 13, 13, 19, 8, 25, 6, 12, 4, 4 and 14 verses in different metres and 187 verses in all. At present only these 14 chapters are widely known. But the commentaries of Mallāri and Viśwanātha contain a 15th Chapter of 15 verses entitled ‘Pañcāngagrahana’. Since the 14 chapters already include 4 chapters devoted to eclipses, this must have been considered superfluous and allowed to be lost. Gaṇeśa appears to have purposely sacrificed accuracy in certain cases because of his tendency to simplify calculations and hence, he has added two more chapters on eclipses (7th and 8th) even when 2 chapters out of 14 had been devoted to the eclipses of the sun and the moon. The addition was altogether redundant. Grahalāghava appears to also have undergone certain changes in its different versions. In the copy of the Grahalāghava written in Śaka 1605, which the author got at Bārśi the 15th Chapter had been omitted while the chapter on ‘Pañcatārā contained 3 more verses which discuss some points about planets’ risings and settings. These verses are not found in Viśwanātha’s commentary. Some verses show variations in readings. Again the Viśwanāthī commentary contains some verses which are not found in the copy of the Grahalāghava printed by Kṛṣṇaśāstrī Godbole. A verse describing the method of calculating the moon’s latitude accurately is given in the Viśwanāthī commentary and also in Kṛṣṇa Śāstrī’s edition, but it was not found in the copy obtained by author at Bārśi. Different copies of the work give the sequence of certain verses in different ways. It is found at present in the chapter on ‘nakṣatrachāyā’ a verse, attributed by Viśvanātha to Nṛsiṃha, nephew of Gaṇeśa, but it is not to be found in the Bārśi-copy. Anyway, even though there are some variations here and there, they have not given rise to any perversion so far as the author's original methods are concerned.

v2.c12.s2.t48.45

Other works

v2.c12.s2.t48.46

Among other works of Gaṇeśa that are useful for the calculation of the almanac, Bṛhatcintāmaṇi and Laghucintāmaṇi are particularly noteworthy. They are helpful in quickly calculating figures for tithi, nakṣatra, and yoga. If tithi and other items of the almanac (pañcāṅga) were to be calculated by actually finding the true places of the sun and moon from the Grahalāghava, they would require unremitting labour for six months. If the tables prepared for calculating the mean and true positions of the sun and the moon are utilized, even then one would take according to the author's estimate, about 24 days, of ceaseless labour. But the work Laghucintāmaṇi expedites the calculations to such an extent that the tithis, nakṣatras and yogas could be calculated only in three days. The work can be finished still more quickly if the Bṛhatcintāmaṇi is used. And inspite of this economy of labour, it is found by comparison that the difference in ghaṭīpalas as obtained from Tithicintāmaṇi and those calculated direct with the help of Grahalāghava, never exceeds 30 palas. I do not propose to describe the nature and scope of Tithi Cintāmaṇi* for want of space. No such work was compiled by any one before Gaṇeśa Daivajña. The work entitled Makaranda which has already been described before (page 127), helps quick calculations; but its method is somewhat different, and its date is Śaka 1400, still, Gaṇeśa may not have even seen it at all. Hence, there is no harm in giving full credit for originality to the author of the Grahalāghava or having produced a work like the Tithi cintāmaṇi which is so very useful in calculation and which reduces one's labour to the barest minimum.

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Impeachment

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Kero Lakṣmaṇa Chatre has accused Gaṇeśa Daivajña in the following works :—"He simplified calculations by employing easy devices.....but, because of this, the results became approximate to that extent and this laid the foundation of future erroneous methods......Another result has been.........that the tradition of studying the Siddhānta works and of taking observations disappeared and the astronomers are deprived of the knowledge of the basic astronomical theory**." There are also some others who accuse the author of the Grahalāghava in the same way. But while considering Gaṇeśa Daivajña's work, it is no use accusing him for his approximate results by comparing his work with the modern European works. It should be considered what could be the best possible achievement with the means available in his time. Keropant Nānā and other critics do not seem to have considered this aspect of the question because there had been no means so far for judging the question whether earlier authors of Karaṇaworks could secure greater accuracy than Gaṇeśa or what original work was done by him with regard to the taking of observations. If the value of his work from this point of view be estimated there would be absolutely no room left for accusing Gaṇeśa Daivajña. Again, if less laborious methods yield the same results as the extremely laborious calculations gave from Siddhānta works, why should not such methods be accepted? There is no harm in saying that Gaṇeśa was not at all inferior to earlier astronomers in securing accuracy of results for any problem even while attempting to simplify the work of calculatior. Again it will be seen from the relation which the author has so far traced between all the siddhānta and karaṇa works, that Keropant was wrong in accussing Gaṇeśa of having laid the foundation of erroneous methods. If he means to say that the length of the year (adopted by Gaṇeśa) was inaccurate, the error had persisted from the very beginning. The author thinks that there were very few astronomers among the predecessors of Gaṇeśa in whom ingenuity and perseverance were so happily blended.

v2.c12.s2.t48.49

∗ Keropant has, in his tables of Planetary Calculations, described the method of calculating tithi which is exactly the same as that given in Gaṇeśa's Tithicintāmaṇi. The underlying theory has not been explained. But the author has explained, in an article in the issue of the Indian Antiquary for April 1887, the theory underlying every step of the method together with an illustrative example.

v2.c12.s2.t48.50

∗∗ Introduction to Keropant's Planetary Tables, P-2.

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He was undoubtedly superior to Bhāskarācārya in the matter of observations. Now-a-days the tradition of studying the Siddhānta works is almost lost. Not to speak of the Siddhānta works, one comes across very few astronomers who have thoroughly studied at least the Grahalāghava in its entirety. But this is not the fault of Gaṇeśa's works. Later history will show that he was succeeded by many more astronomers who understood the secrets of the Siddhānta works, who themselves compiled the Siddhānta works and who were also observers. Gaṇeśa himself has written a commentary on Siddhānta Śiromaṇi and Līlāvatī. As regards compiling a work on theory, the work was already done by Bhāskarācārya. It is of course true that he was not attracted to make new discoveries of the kind made in Europe in his time, but it is not proper to blame Gaṇeśa Daivajña on that account, for the zest for knowledge was, wanirg among the people at large and, for several other reasons, the love of research had very nearly vanished.

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Commentaries

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There is a commentary on the Grahalāghava written in Śaka 1508 by Gaṅgādhara of the Tapar Village. Mallāri Daivajña wrote his commentary in the year Śaka 1524. It contains the astroromical theory. The Viśvanāthī commentary belongs to Śaka 1534. It contains illustrative examples. The commentary is also known as ‘Udāharaṇa’. The last two of these commentaries are printed. Calculations are seldom made from the Bṛhat Cintāmaṇi because it contains too many tables; for this purpose of calculation people prefer the Laghu Cintāmaṇi which is printed. It is full of figures and the errors in these figures which have been accumulating for generations have now grown to an enormous extent. Most of the tables have been corrected. There is a commentary, Subodhini by name, written on Bṛhat Cintāmaṇi by Viṣṇu Daivajña, which expands the theory. Cintāmaṇi Kānti, a commentary on the Laghucintāmaṇi, is written by Yajñeśvara, an astronomer. It contains the theory. The commentaries on the Muhūrtatatva and the Vivāhavṛndāvana have been printed. Tarjiyantra is a work meant to be used for ascertaining time. It is also called the Pratoda yantra; it is commented upon by Sakhārāma. There is another commentary by Gopinātha, a resident of Samgameśvar. The name of Gopinātha's father was Bhairava and that of his grandfather was Rāma. This work will be further dealt with in the chapter on instruments.

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There are two other Gaṇeśas, different from the author of the Grahalāghava; one of them is the author of the Tājak Bhūṣaṇa and the other of the Jātakālaṃkāra.

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A legend

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This account of the author of the Grahalāghava will be closed recounting a legend after about him. Keśava, his father, once predicted the moment of an eclipse. The king of the country, who was a yavana, somewhat ridiculed him, as the prediction did not come true. Keśava was very much grieved over this. He, therefore, started a penance in the temple of Gaṇapati at Nandigrāma. He had grown old at that time. Looking to his sad plight and firm devotion Gaṇapati told him in a dream that he (Keśava) would no longer be able to continue the work of observing and rectifying the positions of planets and that, Gaṇapati would therefore himself come to birth as his son to do the work for him. Accordingly, a son was born to him, who was named Gaṇeśa. People at present regard him as an incarnation of God. Two more stories about him have already been told. All such stories indicate the reverence for him on the part of the people. If once an intelligent person comes to be regarded as divine incarnation, the feeling grows strong that his achievement can never be equalled and this very feeling has been mainly responsible for the absence of discoveries in our country.

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His Descendants

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It appears that many of the descendants of Keśava and Gaṇeśa were also scholars. Ananta, Gaṇeśa's younger brother, wrote a commentary on Varāha Mihira's Laghujātaka, in ‘Jaya’ Saṃvatsara (Śaka 1456), and Ananta claims that it is shorter and easier than that of Utpala. Ananta had been guided in his studies by his brother Gaṇeśa. It appears from the Viśvanāthī commentary that there was a commentary on Grahalāghava by Nṛsiṃha, Gaṇeśa's nephew, but it could not be procured any where. Gaṇeśa had a son named Keśava, whose son Gaṇeśa wrote Śiromaṇiprakāśa, a commentary on the Siddhānta Śiromaṇi. It may have been written about Śaka 1520. A later descendant in his family, namely Keśava, son of Rudra, compiled a work entitled Lagna-kalā Pradīpa, in Śaka 1629, the name of the saṃvatsara being Sarvajit.

Cites (12)