[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [A History of the Kerala School of Hindu Astronomy (in Perspective)](https://indike.org/pramana/ins.science.sarma-1972) › c7 # A History of the Kerala School of Hindu Astronomy (in Perspective) c7: Chapter I. Some Salient Features of Kerala Astronomy A History of the Kerala School of Hindu Astronomy (in Perspective) c7 - **Language:** English ## Contents - [c7.s1 1. Introduction](https://indike.org/pramana/ins.science.sarma-1972.c7.s1) — 1 part - [c7.s2 2. Spirit of enquiry](https://indike.org/pramana/ins.science.sarma-1972.c7.s2) — 7 parts - [c7.s3 3. Stress on observation and experimentation](https://indike.org/pramana/ins.science.sarma-1972.c7.s3) — 6 parts - [c7.s4 4. Concern for accuracy](https://indike.org/pramana/ins.science.sarma-1972.c7.s4) — 4 parts - [c7.s5 5. Researcher's outlook](https://indike.org/pramana/ins.science.sarma-1972.c7.s5) — 2 parts - [c7.s6 6. Continuity of tradition](https://indike.org/pramana/ins.science.sarma-1972.c7.s6) — 4 parts - [c7.s7 7. Basic features of Kerala astronomy](https://indike.org/pramana/ins.science.sarma-1972.c7.s7) — 23 parts - [c7.s8 9. Dṛk system of astronomy](https://indike.org/pramana/ins.science.sarma-1972.c7.s8) — 6 parts ### Chapter I. Some Salient Features of Kerala Astronomy ### 1. Introduction ### [c7.s1.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s1.1) Mathematics and astronomy are two of the scientific disciplines to which significant contributions have been made, down the centuries, by Kerala scholars. The land of Kerala, a narrow strip of territory tucked away between the Western Ghats and the Arabian sea, produced superb mathematicians from very early times. The fervour with which the sister science of astrology, in its different branches, was cultivated, had had the beneficial effect of promoting the study of mathematics and astronomy, for the latter provided the basic framework for the practice of the former. The social structure which confined mainly, to certain sections of the community, the study of these disciplines and the freedom from political or religious upheavals which Kerala enjoyed helped the uninterrupted development, here, of these sciences. As a result of all this, significant strides were made and a very large number of treatises came to be written, down to the 19th century, in these disciplines. However, only a fraction of these works have come down to us, the bulk having been lost on account of the ravages of time and the inclement climate of the land which had a highly detrimental effect on the palmleaf manuscripts on which these works had been inscribed. The highly conservative outlook of the custodians of extant manuscripts of these technical texts, the local Malayalam language in which many of these works have been composed or commented upon and the rather obscure Malayalam script used for writing the manuscripts have all stood in the way of a proper study and interpretation of these works in terms of modern mathematics and thereby institute a proper evaluation thereof. In fact, modern scientific studies on Kerala astronomy have been based mainly on just a handful of texts as have, so far, been made available in print, out of the few hundreds of texts still available in the form of manuscripts. ### 2. Spirit of enquiry ### [c7.s2.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s2.1) At the outset, a reference might be made to the mental outlook and spirit of enquiry that characterised Kerala astronomers and mathematicians in their investigations. Parameśvara of Vaṭaśreṇi (c. 1360-1455), who revised the then prevailing Parahita system of computation and evolved new methods in his work entitled Dṛggaṇita,¹ makes a revealing statement in this regard, in the beginning of that work. He says : ### [c7.s2.2](https://indike.org/pramana/ins.science.sarma-1972.c7.s2.2) dṛśyante vihaga dṛṣṭyā bhinnāḥ parahitoditāḥ | pratyakṣadṛṣṭāḥ spaṣṭāḥ syur grahāḥ śāstreṣv itīrtam || I.¹.2 || satkarmoditakalasya grahā hi jñānasādhanam | aspaṣṭavihagaiḥ siddhaḥ kalaḥ śuddho na karmaṇi || 3 || ye tu śastravidas tadvad golayuktividas ca taḥ | sphuṭakhecaravijñāne yatnaḥ kāryo dvijair ataḥ || 4 || sañcintyeti samālocya pūrvatantrāṇi yatnataḥ | sphuṭayuktim khecarāṇām goladṛṣṭyā samīkṣya ca || 5 || sphuṭakhecaravijñānam śiṣyair yaiḥ prarthitam dvijaiḥ | tebhyo Dṛggaṇitam nāma gaṇitam kriyate mayā || 6 || ### [c7.s2.3](https://indike.org/pramana/ins.science.sarma-1972.c7.s2.3) ¹ K. V. Sarma, The Dṛggaṇita of Parameśvara, Cr. ed. with Introduction, Hoshiarpur, 1963. Parameśvara is reputed to have made continuous astronomical observations for 55 years with the help of instruments : Cf. what Nilakaṇṭha Somayājin, who received instruction from Parameśvara, says in his Āryabhaṭīya-bhāṣya (Gola, 43) : \*Parameśvarācāryeṇa punaḥ grahaṇagrahayogādikam yantraḥ pañcapañcaśad-varṣakālam samyak parīkṣitam. Aha caivam...“grahendraḥ pañcapañcaśad-varṣakālasaḍaniare”\* etc. (Trivandrum Skt. Ser., No. 185, p. 154). ### [c7.s2.4](https://indike.org/pramana/ins.science.sarma-1972.c7.s2.4) '(The positions of) the planets derived according to the Parahita (system of computation) are found to be different (from their actual positions) as seen by the eye. And, in authoritative texts (śāstra) it is said that (only) positions as observed (should be taken) as the true ones. (I. i. 2). ### [c7.s2.5](https://indike.org/pramana/ins.science.sarma-1972.c7.s2.5) '(The positions of ) the planets are the means of knowing the times specified for (the performance of ) meritorious acts. (Here), times calculated from incorrect (positions of ) planets will not be auspicious for those) acts. (3) ### [c7.s2.6](https://indike.org/pramana/ins.science.sarma-1972.c7.s2.6) ‘Hence, efforts should be made for knowing the true (positions of) planets by those who are learned in the sciences and by those who are experts in spherics. (4) ### [c7.s2.7](https://indike.org/pramana/ins.science.sarma-1972.c7.s2.7) ‘Cogitating thus, and painstakingly studying the ancient texts and observing well the true positions of the planets according to the spherics, I am composing a manual on astronomy for the twice-born disciples who requested for a knowledge of the true (positions of the) planets’. (6). ### 3. Stress on observation and experimentation ### [c7.s3.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s3.1) An insight into the mediaeval astronomer’s methodology, which consisted of prolonged and repeated observation, experimentation, recording of readings, checking of the values obtained from observation with those obtained by computation and the postulation of corrections (\*saṃskāra\*), in order to make computation correspond with observation, might be illustrated by certain statements which Parameśvara makes elsewhere. In his sub-commentary \*Siddhāntadīpikā\* on the \*Mahabhāskarīya-bhāṣya\* of Govindasvāmin,¹ he has a long excursus on a number of eclipses which he had observed carefully and about which he had recorded the details, with a view to effecting necessary corrections to prevailing rules of computation or for formulating new rules therefor (\*op. cit.\*, pp. 321-32). He commences the said excursus with the statement that he had been observing eclipses from Śaka 1315 (A.D. 1393), that he had found the observed times to have always preceded the computed times and, so, the computations needed corrections: ### [c7.s3.2](https://indike.org/pramana/ins.science.sarma-1972.c7.s3.2) ¹ T. S. Kuppanna Sastri, Cr. ed. of \*Mahabhāskarīya\* of Bhāskarācārya with the \*Bhāṣya\* of Govindasvāmin and the super-commentary \*Siddhāntadīpikā\* of Parameśvara, Madras, 1957. ### [c7.s3.3](https://indike.org/pramana/ins.science.sarma-1972.c7.s3.3) \*tithiviśva’-(1315)-same śāke prārabhya grahaṇam mayā |\* \*anekam īkṣitam, teṣu bhinnaḥ kālo dṛśa sadā || 2 ||\* \*pratyakṣakalas teṣu prāg gaṇitānītakālataḥ |\* \*ataḥ kāryo ’tra saṃskāro yaḥ kaścid gaṇakottamaiḥ || 3 ||\* (p. 321) ### [c7.s3.4](https://indike.org/pramana/ins.science.sarma-1972.c7.s3.4) He then enunciates the True positions of the Sun, Moon, Moon’s higher apsis and node at sunrise for a particular contemporary date as calculated by the application of the corrections proposed by him, so as to form the zero-readings for calculations beginning from that date. He also suggests that verifications should be made in course of time and further corrections postulated and applied as and when needed : ### [c7.s3.5](https://indike.org/pramana/ins.science.sarma-1972.c7.s3.5) \*asmin kāle tu ravīnduccapātānam sthitir īdṛśī |\* \*etatsiddhyartham asmābhiḥ saṃskārāntaram adṛtam || 91 ||\* . . . . . \*kalāntare tu saṃskāraś cintyatām gaṇakottamaiḥ ||93|| (p.332)¹\* ### [c7.s3.6](https://indike.org/pramana/ins.science.sarma-1972.c7.s3.6) ¹ On Parameśvara's astronomical observations, see K. V. Sarma, 'An-pattiyañcu kollatte tapassu' ('Fifty-five years' penance'), \*Mathrubhumi\* (Malayalam Weekly, Kozhikode), 7.10.1956, pp. 29-30. ### 4. Concern for accuracy ### [c7.s4.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s4.1) The concern of these astronomers for accuracy in the results of computations is reflected in a statement, again by the same author, in another work of his. Towards the close of an extensive work on the computation of eclipses, entitled \*Grahaṇamaṇḍana\*,² Parameśvara observes, in all humility, that the times of contact etc. as obtained through the calculations enunciated in that work may, at times, differ slightly from observed positions.³ He hastens to add that these small differences must be due to factors which he could not take into account or which had not been identified thus far. But, as a practical scientist, he is confident that it would be possible to postulate, as a result of further observations and experimentations, the necessary corrections by the application of which even these small differences could be eliminated : ### [c7.s4.2](https://indike.org/pramana/ins.science.sarma-1972.c7.s4.2) ² K.V. Sarma, \*Grahaṇamaṇḍana\* of Parameśvara, Cr. ed. with Introduction, Translation and Appendix, Hoshiarpur, 1965. ### [c7.s4.3](https://indike.org/pramana/ins.science.sarma-1972.c7.s4.3) ³ Cf., Ibid. : \*kālo 'nena ca siddhaḥ kadācid api bhidyate svalpam ||66||\* ### [c7.s4.4](https://indike.org/pramana/ins.science.sarma-1972.c7.s4.4) \*śastrad alabdha ekaḥ saṃskāro grahaṇakarmaṇi ravīndvoḥ |\* \*asty eveti ca kalpyaḥ gaṇakavarair yuktividbhir ataḥ || 98 ||\* \*dṛṣṭvā bahuparagān sañcintya ca golayuktim iha gaṇakaiḥ |\* \*kalpyaḥ sa tu saṃskāras tasmad, athava gurūpadeśena || 99 ||\* ### 5. Researcher's outlook ### [c7.s5.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s5.1) The endeavour among Kerala astronomers for continuous efforts at improving their results is reflected in the enunciation by Parameśvara in a later work of his, viz. Dṛggaṇita, a correction to one of his earlier works, the Grahaṇamaṇḍana. This correction which is to be applied to the Mean positions of the Sun, Moon, Higher apsis and Node as calculated according to the Grahaṇamaṇḍana is given at the close of his Dṛggaṇita, II. 47-50, with the introductory statement : ### [c7.s5.2](https://indike.org/pramana/ins.science.sarma-1972.c7.s5.2) kāryo graheṣu Grahaṇamaṇḍanokteṣv ataḥ param | saṃskāras tam ca vakṣyāmi tatra noktam yato mayā || II. 47 || ### 6. Continuity of tradition ### [c7.s6.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s6.1) Still another significant characteristic of Kerala astronomy and mathematics relates to the regular continuity of traditional knowledge that was handed down from father to son or from teacher to disciple, in succession. Some of the known lines of tradition extend through several centuries. An old palmleaf document discovered and published by the present writer¹ records a line of tradition which extends from the 13th to the 17th centuries : Govinda Bhaṭṭatiri of Talakkuḷam (1237-95)→pupil : grandfather of Parameśvara (13th-14th cent.) → grandson-pupil : Parameśvara (c. 1360-1455) → son : Dāmodara (15th cent.) → pupil : Nīlakaṇṭha Somayājī (1444-1545) → pupil : Jyeṣṭhadeva (c. 1500-1600) → pupil : Acyuta Piṣāraṭi (1550-1621). Another similar astronomical chronology recorded in the Aranmula-vilāsam Haṃsappāṭṭu by Kṛṣṇan Āśān, author of Bhāṣā-Jātakapaddhati, carries the above-noted tradition to the beginning of the 19th century ;² Acyuta Piṣāraṭi (1550-1621) → pupil : Tṛppāṇikkara Potuvāḷ → pupil : Nāvāyikkuḷattu Āzhāti → pupil : Pulimukhattu Poṭṭi (1686-1758) →pupil : Rāman Āśān (18th cent.) → son : Kṛṣṇan Āśān (1756-1812) This line continues as follows : Kṛṣṇadāsa (1756-1812) → pupil : Dakṣiṇāmūrti Mūssatu of Maṅgalaśśeri, in Aranmuḷa (18th-19th cent.) → pupil : Bālarāman Piḷḷa of Nāḷekāṭṭil family of Mānnār (19th cent.) → pupil : Prince Rājarāja Varma (Vidvān Karindran Ceruṇṇi Koyittampurān of Kilimānūr) (1812-46).¹ The importance of the continuity of tradition in a practical, demonstrative discipline like astronomy, at a time when there was not a proliferation of printed books and public schools, is self-evident. And, the part played by these traditions in keeping alive the torch of astronomical enquiry in Kerala cannot be underestimated. ### [c7.s6.2](https://indike.org/pramana/ins.science.sarma-1972.c7.s6.2) ¹ K.V. Sarma, ‘Direct lines of astronomical tradition in Kerala’, Pt. Charudeva Shastri Felicitation Volume, Delhi, 1972; ‘Oru Jyotiṣa-granthavari’ (An astronomical document), (in Malayalam), Mathrubhumi (Kozhikode, Kerala), 19.5.1957. ### [c7.s6.3](https://indike.org/pramana/ins.science.sarma-1972.c7.s6.3) ² See Ulloor S. Parameswara Aiyar, Kerala Sāhitya Charitram, (History of Kerala literature), Vol. II, (Trivandrum, 1954), pp. 321-22. ### [c7.s6.4](https://indike.org/pramana/ins.science.sarma-1972.c7.s6.4) ¹ Ibid. ### 7. Basic features of Kerala astronomy ### [c7.s7.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.1) (a) \*Adherence to the Āryabhaṭan system.\* From at least the 7th century, if not earlier, Kerala had been the bastion of the Āryabhaṭan school of astronomy. While the view expressed in certain quarters that Āryabhaṭa hailed from Kerala² has yet to be substantiated, there is no doubt about the extensive popularity of this system in the land. The later Kerala schools are all based on the Āryabhaṭan system. Most of the known commentaries on the \*Āryabhaṭīya\* have been written by Kerala mathematicians. Well-nigh, every one of the scores of astronomical works produced in Kerala follow the \*Āryabhaṭīya\* basically. And, the efforts of Kerala mathematicians have generally been directed towards the revision, supplementation and correction of Āryabhaṭan astronomy and mathematics with a view to deriving more accurate results. ### [c7.s7.2](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.2) ² For the latest essay in this direction, see K Damodaran Nambiar, ‘Āryabhaṭan’, \*Mathrubhumi\* (Malayalam Weekly, Kozhikode, Kerala), Oct. 18, 1970, pp. 15-16, 41. ### [c7.s7.3](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.3) (b) \*Kaṭapayādi notation.\* An extremely convenient method of expressing numbers through letters, known as the \*Ka-ṭa-pa-yādi\* notation, has been extensively used in Kerala from very early times. A legendary author named Vararuci is credited with this innovation and the authorship of the popular collection of \*Candra-vākyas\* or \*Vararuci-vākyas\* (‘Moon computation sentences’), composed in this notation. The \*Grahcāranibandhana\* of Haridatta (A.D. 683) also uses this notation extensively. In this notation, each of the four series of consonants beginning with \*k, ṭ, p,\* and \*y\* in the Sanskrit alphabet stands for the digits 1 to 9. In conjunct letters, the value only of the final consonants is to be taken into account. Vowels following the consonants have no value. \*n\* and \*ñ\* and the pure vowels stand for zero. ### [c7.s7.4](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.4) The letter \*l\*, which is peculiar to Dravidian denotes 9.¹ The versatility of the notation rests in the fact that even long and intricate numbers can be expressed through apparently meaningful expressions and verse-bits, facilitating their easy verification and memorisation.² The numerous sine and other mnemonic tables which form a characteristic feature of the Kerala School of astronomy are couched in this notation. ### [c7.s7.5](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.5) ¹ The simple rule for this notation is given by the verse : ### [c7.s7.6](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.6) ² See \*e.g.\*, the chronogram 'ācāryavag abhedya' which is kali day 1434160, on which Śaṅkarācārya introduced certain reforms; and the Moon-sentence, 'gir naḥ śreyaḥ' denoting 0°-12'-3". ### [c7.s7.7](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.7) (c) \*Basic principles.\* In their mathematical work, Kerala authors and, for that matter, Indian authors in general, based themselves on the fundamentals of arithmetic, algebra, geometry and trigonometry. They were aware also of properties of numbers, to some extent. Calculus and higher mathematics, as developed in the West during the last three hundred years, were not known, but strict application of geometry, trigonometry and algebra, coupled with clear analytical thought and intuition, have enabled Kerala astronomers to arrive at important results and enunciate theorems which were later rediscovered in the West, some after several centuries.³ ### [c7.s7.8](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.8) ³ For a resume of the more important of these anticipations, see below, Ch. II. ### [c7.s7.9](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.9) 8. Parahita system of astronomy ### [c7.s7.10](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.10) A significant event in the annals of Kerala astronomy was the promulgation, in A. D. 683, of the \*Parahita\* system by Haridatta (\*c.\* 650-700) through his \*Grahacāranibandhana\*⁴ and \*Mahāmārga-\* ### [c7.s7.11](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.11) ⁴ Cr. ed with Intro. by K.V Sarma, K.S. Research Inst., Madras, 1954. On the discovery and identification of this thitherto unknown basic text of the \*Parahita\* system see K. V. Sarma, 'Parahita-gaṇitattinte mūlagrantham', \*Mathrubhumi\* (Mal. Weekly, Kozhikode), Oct. 10. 1954. ### [c7.s7.12](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.12) \*na-ñāv acaś ca śūnyāni, saṅkhyāḥ ka-ṭa-pa-yādayaḥ |\* \*miśre tūpāntahalsaṅkhyā, na ca cintyo halaḥ svaraḥ ||\* ### [c7.s7.13](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.13) \*Sadratnamālā\* of Śaṅkara Varman nibandhana.¹ The event is recorded in several later works. For instance, the \*Sadratnamālā\* of Śaṅkaravarman says : ### [c7.s7.14](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.14) ācaryāryabhaṭapraṇītagaṇitam prāyaḥ sphuṭam tat kalau ‘gotrottuṅga’-(3623)-mitābdake vyabhicaran brahmādisiddhāntake | ... ... ... dṛgvaiṣamyavaśāt ‘mahāsthala’-(3785)-mite kalyabdake niścitaḥ saṃskāro vibudhair yataḥ parahitatvam teṣu vīneṣv ayam || (6.¹, 3) ### [c7.s7.15](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.15) ¹ This seems to be the full-fledged theoretical treatise of the \*Parahita\* system while the \*Grahacāranibandhana\* is only its working manual. Manuscripts of this work have not yet come to light; the work is known through its reference by Haridatta himself in the \*Grahacāranibandhana\*, 3. 44. ### [c7.s7.16](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.16) ‘The astronomical treatise composed in Kali 3623 (A.D. 522) by Āryabhaṭa gave well-nigh accurate results, whereas the \*siddhāntas\* ascribed to Brahmā etc. had (by that time) tended to be inaccurate. (When its results too tended to be inaccurate, as exemplified by their) not tallying with observation, the correction called \*Parahita\* was adopted by the wise in Kali 3785 (A.D. 683) for the planets other than the Sun’.² ### [c7.s7.17](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.17) ² For other references to this event and the identity of Haridatta and his works, see K.V. Sarma, \*Grahacāranibandhana\*, op. cit., Intro., pp. v-ix. ### [c7.s7.18](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.18) Tradition says that the inauguration of the system took place on the occasion of the twelve-yearly \*Māmāṅkam\* (\*Mahā-magha\*) festival held at Tirunāvāy on the Malabar coast.³ ### [c7.s7.19](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.19) ³ See ibid., pp. vi-vii; Ulloor S. Parameswara Aiyar, \*Kerala Sahitya Charitram\*, vol. I, (Trivandrum, 1953), p. 165. ### [c7.s7.20](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.20) Haridatta based his system on the \*Āryabhaṭīya\*, but improved upon it in several ways. He made computation easier by specifying simple multipliers and divisors for the various calculations, including the derivation of the positions of the planets. His use of the \*Kaṭapayādi\* notation made his composition elegant. He introduced the unique system of enunciating graded tables of the Sines of the arcs of Anamoly and of Commutation of the different planets (\*Manda-jyā\* and \*Śīghra-jyā\*) at intervals of 3° 45’, to facilitate the computation of the true positions of the planets. His \*Grahacāra-nibandhana\* being only the computation manual of the system, deals, mainly, with the calculation of the Kali days elapsed, \*tithi\* and \*nakṣatra\* of any day, the mean and retrograde motion of the planets and their Mean and True positions. One of the corrections introduced by Haridatta to make Āryabhaṭan results more accurate, is called \*Bhaṭa-saṃskāra\* or \*Śakābda-saṃskāra\* (on account of its being calculated for the years beginning from the ‘\*śakābda\*’ of Āryabhaṭa, viz., 444), and is particularly significant. This correction specifies that for every completed year after Śaka 444, a correction in minutes (\*kalā\*) of −9/85, −65/134, −13/32, +45/235, +420/235, −47/235, −153/235 and +20/235 should be made to the Mean positions of the Moon, Moon’s apsis, Moon’s node, Mars, Mercury, Jupiter, Venus and Saturn, respectively, no correction being necessary in the case of the Sun.¹ ### [c7.s7.21](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.21) ¹ 2. Ed. K. V. Sarma, as Appendix to the edn of \*Grahacāranibandhana\*, Madras, 1954. ### [c7.s7.22](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.22) A large number of astronomical manuals based on the \*Parahita\* system, including a \*Grahacāranibandhana-saṅgraha\*,² have come to be composed during later times, both in Sanskrit and in Malayalam, each taking off from a convenient contemporary epoch (\*khaṇḍa-dina\*) for which the True positions of the planets would have been fixed after elaborate calculations, these positions being used as zero-corrections for computation according to these manuals. Some of these incorporate also further corrections. ### [c7.s7.23](https://indike.org/pramana/ins.science.sarma-1972.c7.s7.23) ² 3. Cr. ed. by K V. Sarma, with Intro., V.V.R. Inst., Hoshiarpur, 1963. ### 9. Dṛk system of astronomy ### [c7.s8.1](https://indike.org/pramana/ins.science.sarma-1972.c7.s8.1) The \*Dṛk\* system promulgated by Parameśvara of Vaṭaśreṇi (c. 1360-1455), through his \*Dṛggaṇita\*,³ is, as pointed out above (§2), a revision of the \*Parahita\* system and was composed with a view to make the results of computation accord with observation. While no new methodology is enunciated here, new multipliers and divisors are given for the derivation of the Kali days and for the calculation of the Mean positions of planets. Minute corrections are given ### [c7.s8.2](https://indike.org/pramana/ins.science.sarma-1972.c7.s8.2) ³ Ker. Ast. 2 ### [c7.s8.3](https://indike.org/pramana/ins.science.sarma-1972.c7.s8.3) 1. The verse giving this correction reads as follows: ‘\*vagbhavo\*’ (444) \*nac chakābdāt dhana-śata-laya-hān manda-vailakṣya-rāgair\* \*āptābhir liptābhir virahitanavaś candra-tattuṅga-pātaḥ |\* \*śobhā-nirudha-saṃvid-gaṇaka-nara-hatan māgar-āptaḥ kujādyāḥ\* \*samyuktā jñāra-saurā virahitanukau jīvaśukrau, na bhānoḥ ||\* ### [c7.s8.4](https://indike.org/pramana/ins.science.sarma-1972.c7.s8.4) for these positions after long periods of time. Revised values are given for the positions of planets at zero Kali. Also, the values of the sines of arc of Anomaly (\*Manda-jyā\*) and of Commutation (\*Śīghra-jyā\*) are revised and given for intervals of 6 degrees.¹ ### [c7.s8.5](https://indike.org/pramana/ins.science.sarma-1972.c7.s8.5) ¹ On Parameśvara and the \*Dṛk\* system in general, see Intro. to \*Dṛggaṇita\*, \*op. cit.\*, pp. x-xiii. See also, K.V. Sarma, ‘Parameśvara’s \*Dṛggaṇita\*’, \*Mathrubhumi\* (Kozhikode), Aug. 28, 1960, pp. 19-21. ### [c7.s8.6](https://indike.org/pramana/ins.science.sarma-1972.c7.s8.6) As in the case of the \*Parahita\* system, a large number of manuals have come to be composed following the \*Dṛk\* system, both in Sanskrit and in Malayalam. The results obtained through this system being more accurate, this system was used for horoscopy (\*jātaka\*), astrological query (\*praśna\*) and the computation of eclipses (\*grahaṇa\*), while the \*Parahita\* continued to be used for fixing auspicious times for rituals and ceremonies (\*muhūrta\*). In order to cater to both the purposes, some of the later manuals have dealt with both the \*Dṛk\* and \*Parahita\* systems. ## Linked texts (4) - [Āryabhaṭīya](https://indike.org/pramana/in.astro.siddhanta.early.aryabhatiya) — Āryabhaṭa, Sanskrit - [Mahābhāskarīya](https://indike.org/pramana/in.astro.siddhanta.early.mahabhaskariya) — Bhāskara I, Sanskrit - [Dṛggaṇita](https://indike.org/pramana/in.astro.kerala.tantra.drgganita) — Parameśvara of Vaṭasseri, Sanskrit - [Grahaṇamaṇḍana](https://indike.org/pramana/in.astro.kerala.grahana.grahanamandana) — Parameśvara of Vaṭasseri, Sanskrit --- Source: [https://indike.org/pramana/ins.science.sarma-1972.c7](https://indike.org/pramana/ins.science.sarma-1972.c7) · Pramāṇa